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<title>Left Termination proof of ../tpdb/LP/talp/maria/fib.pl</title>
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<BR><B>Left Termination</B> of the query pattern
fib_in_2(g, a)
w.r.t. the given <I>Prolog program</I> could successfully be <font color=#00ff00>proven</font>:<BR><BR><BR><BR><pre>&#8627 <B>Prolog</B></pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><BR>Clauses:<BR><BR>fib(0, 0).<BR>fib(1, 1).<BR>fib(M, N)&#160;:-&#160;','(>(M, 1), ','(is(M1, -(M, 1)), ','(is(M2, -(M, 2)), ','(fib(M1, N1), ','(fib(M2, N2), is(N, +(N1, N2))))))).<BR>no_trace_main&#160;:-&#160;','(time(_), ','(fib(15, M), ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(write('Result '), ','(write(M), nl))))))))).<BR>trace_main(Eventfile)&#160;:-&#160;','(start_event_trace, ','(fib(15, M), ','(stop_event_trace, ','(save_trace(Eventfile), ','(write('Result '), ','(write(M), nl)))))).<BR>save_trace(X)&#160;:-&#160;','(write('Saving trace in file '), ','(write(X), ','(write('... '), ','(open(X, write, Y), ','(save_event_trace(Y), ','(close(X), ','(write('done.'), nl))))))).<BR>time(T)&#160;:-&#160;statistics(runtime, .(_, .(T, []))).<BR><BR>Queries:<BR><BR>fib(g,a).<BR><BR>Added definitions of predefined predicates.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 <B>Prolog</B></pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><BR>Clauses:<BR><BR>fib(zero, zero).<BR>fib(succ(zero), succ(zero)).<BR>fib(M, N)&#160;:-&#160;','(','(=(X, M), ','(=(X1, succ(zero)), isGreater(X, X1))), ','(','(isMinus(M, succ(zero), U), =(M1, U)), ','(','(isMinus(M, succ(succ(zero)), U), =(M2, U)), ','(fib(M1, N1), ','(fib(M2, N2), ','(isPlus(N1, N2, U), =(N, U))))))).<BR>no_trace_main&#160;:-&#160;','(time(_), ','(fib(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))), M), ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(write('Result '), ','(write(M), nl))))))))).<BR>trace_main(Eventfile)&#160;:-&#160;','(start_event_trace, ','(fib(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))), M), ','(stop_event_trace, ','(save_trace(Eventfile), ','(write('Result '), ','(write(M), nl)))))).<BR>save_trace(X)&#160;:-&#160;','(write('Saving trace in file '), ','(write(X), ','(write('... '), ','(open(X, write, Y), ','(save_event_trace(Y), ','(close(X), ','(write('done.'), nl))))))).<BR>time(T)&#160;:-&#160;statistics(runtime, .(_, .(T, []))).<BR>isPlus(zero, X, X).<BR>isPlus(succ(X), zero, succ(X)).<BR>isPlus(succ(X), succ(Y), succ(succ(Z)))&#160;:-&#160;isPlus(X, Y, Z).<BR>isPlus(succ(X), pred(Y), Z)&#160;:-&#160;isPlus(X, Y, Z).<BR>isPlus(pred(X), zero, pred(X)).<BR>isPlus(pred(X), succ(Y), Z)&#160;:-&#160;isPlus(X, Y, Z).<BR>isPlus(pred(X), pred(Y), pred(pred(Z)))&#160;:-&#160;isPlus(X, Y, Z).<BR>isMinus(X, zero, X).<BR>isMinus(zero, succ(Y), pred(Z))&#160;:-&#160;isMinus(zero, Y, Z).<BR>isMinus(zero, pred(Y), succ(Z))&#160;:-&#160;isMinus(zero, Y, Z).<BR>isMinus(succ(X), succ(Y), Z)&#160;:-&#160;isMinus(X, Y, Z).<BR>isMinus(succ(X), pred(Y), succ(succ(Z)))&#160;:-&#160;isMinus(X, Y, Z).<BR>isMinus(pred(X), succ(Y), pred(pred(Z)))&#160;:-&#160;isMinus(X, Y, Z).<BR>isMinus(pred(X), pred(Y), Z)&#160;:-&#160;isMinus(X, Y, Z).<BR>isTimes(X, zero, zero).<BR>isTimes(zero, succ(Y), zero).<BR>isTimes(zero, pred(Y), zero).<BR>isTimes(succ(X), succ(Y), Z)&#160;:-&#160;','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).<BR>isTimes(succ(X), pred(Y), Z)&#160;:-&#160;','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).<BR>isTimes(pred(X), succ(Y), Z)&#160;:-&#160;','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).<BR>isTimes(pred(X), pred(Y), Z)&#160;:-&#160;','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).<BR>isDiv(zero, succ(Y), zero).<BR>isDiv(zero, pred(Y), zero).<BR>isDiv(succ(X), succ(Y), zero)&#160;:-&#160;isMinus(succ(X), succ(Y), pred(Z)).<BR>isDiv(succ(X), succ(Y), succ(Z))&#160;:-&#160;','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).<BR>isDiv(succ(X), pred(Y), Z)&#160;:-&#160;','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).<BR>isDiv(pred(X), pred(Y), zero)&#160;:-&#160;isMinus(pred(X), pred(Y), succ(Z)).<BR>isDiv(pred(X), pred(Y), succ(Z))&#160;:-&#160;','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).<BR>isDiv(pred(X), succ(Y), Z)&#160;:-&#160;','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).<BR>isModulo(X, Y, Z)&#160;:-&#160;','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).<BR>=(X, X).<BR>isGreater(succ(X), zero).<BR>isGreater(succ(X), pred(Y)).<BR>isGreater(succ(X), succ(Y))&#160;:-&#160;isGreater(X, Y).<BR>isGreater(zero, pred(Y)).<BR>isGreater(pred(X), pred(Y))&#160;:-&#160;isGreater(X, Y).<BR><BR>Queries:<BR><BR>fib(g,a).<BR><BR>Added facts for all undefined predicates.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 <B>Prolog</B></pre><pre>          &#8627 PrologToPiTRSProof</pre><BR>Clauses:<BR><BR>fib(zero, zero).<BR>fib(succ(zero), succ(zero)).<BR>fib(M, N)&#160;:-&#160;','(=(X, M), ','(=(X1, succ(zero)), ','(isGreater(X, X1), ','(isMinus(M, succ(zero), U), ','(=(M1, U), ','(isMinus(M, succ(succ(zero)), U), ','(=(M2, U), ','(fib(M1, N1), ','(fib(M2, N2), ','(isPlus(N1, N2, U), =(N, U))))))))))).<BR>no_trace_main&#160;:-&#160;','(time(X), ','(fib(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))), M), ','(time(T), ','(write('Executed in '), ','(write(T), ','(write(' mS.'), ','(nl, ','(write('Result '), ','(write(M), nl))))))))).<BR>trace_main(Eventfile)&#160;:-&#160;','(start_event_trace, ','(fib(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(zero))))))))))))))), M), ','(stop_event_trace, ','(save_trace(Eventfile), ','(write('Result '), ','(write(M), nl)))))).<BR>save_trace(X)&#160;:-&#160;','(write('Saving trace in file '), ','(write(X), ','(write('... '), ','(open(X, write, Y), ','(save_event_trace(Y), ','(close(X), ','(write('done.'), nl))))))).<BR>time(T)&#160;:-&#160;statistics(runtime, .(X, .(T, []))).<BR>isPlus(zero, X, X).<BR>isPlus(succ(X), zero, succ(X)).<BR>isPlus(succ(X), succ(Y), succ(succ(Z)))&#160;:-&#160;isPlus(X, Y, Z).<BR>isPlus(succ(X), pred(Y), Z)&#160;:-&#160;isPlus(X, Y, Z).<BR>isPlus(pred(X), zero, pred(X)).<BR>isPlus(pred(X), succ(Y), Z)&#160;:-&#160;isPlus(X, Y, Z).<BR>isPlus(pred(X), pred(Y), pred(pred(Z)))&#160;:-&#160;isPlus(X, Y, Z).<BR>isMinus(X, zero, X).<BR>isMinus(zero, succ(Y), pred(Z))&#160;:-&#160;isMinus(zero, Y, Z).<BR>isMinus(zero, pred(Y), succ(Z))&#160;:-&#160;isMinus(zero, Y, Z).<BR>isMinus(succ(X), succ(Y), Z)&#160;:-&#160;isMinus(X, Y, Z).<BR>isMinus(succ(X), pred(Y), succ(succ(Z)))&#160;:-&#160;isMinus(X, Y, Z).<BR>isMinus(pred(X), succ(Y), pred(pred(Z)))&#160;:-&#160;isMinus(X, Y, Z).<BR>isMinus(pred(X), pred(Y), Z)&#160;:-&#160;isMinus(X, Y, Z).<BR>isTimes(X, zero, zero).<BR>isTimes(zero, succ(Y), zero).<BR>isTimes(zero, pred(Y), zero).<BR>isTimes(succ(X), succ(Y), Z)&#160;:-&#160;','(isTimes(succ(X), Y, A), isPlus(A, succ(X), Z)).<BR>isTimes(succ(X), pred(Y), Z)&#160;:-&#160;','(isTimes(succ(X), Y, A), isMinus(A, succ(X), Z)).<BR>isTimes(pred(X), succ(Y), Z)&#160;:-&#160;','(isTimes(pred(X), Y, A), isPlus(A, pred(X), Z)).<BR>isTimes(pred(X), pred(Y), Z)&#160;:-&#160;','(isTimes(pred(X), Y, A), isMinus(A, pred(X), Z)).<BR>isDiv(zero, succ(Y), zero).<BR>isDiv(zero, pred(Y), zero).<BR>isDiv(succ(X), succ(Y), zero)&#160;:-&#160;isMinus(succ(X), succ(Y), pred(Z)).<BR>isDiv(succ(X), succ(Y), succ(Z))&#160;:-&#160;','(isMinus(succ(X), succ(Y), A), isDiv(A, succ(Y), Z)).<BR>isDiv(succ(X), pred(Y), Z)&#160;:-&#160;','(isMinus(zero, pred(Y), A), ','(isDiv(succ(X), A, B), isMinus(zero, B, Z))).<BR>isDiv(pred(X), pred(Y), zero)&#160;:-&#160;isMinus(pred(X), pred(Y), succ(Z)).<BR>isDiv(pred(X), pred(Y), succ(Z))&#160;:-&#160;','(isMinus(pred(X), pred(Y), A), isDiv(A, pred(Y), Z)).<BR>isDiv(pred(X), succ(Y), Z)&#160;:-&#160;','(isMinus(zero, pred(X), A), ','(isDiv(A, succ(Y), B), isMinus(zero, B, Z))).<BR>isModulo(X, Y, Z)&#160;:-&#160;','(isDiv(X, Y, A), ','(isTimes(A, Y, B), isMinus(X, B, Z))).<BR>=(X, X).<BR>isGreater(succ(X), zero).<BR>isGreater(succ(X), pred(Y)).<BR>isGreater(succ(X), succ(Y))&#160;:-&#160;isGreater(X, Y).<BR>isGreater(zero, pred(Y)).<BR>isGreater(pred(X), pred(Y))&#160;:-&#160;isGreater(X, Y).<BR>write(X0).<BR>nl.<BR>start_event_trace.<BR>stop_event_trace.<BR>open(X0, X1, X2).<BR>save_event_trace(X0).<BR>close(X0).<BR>statistics(X0, X1).<BR><BR>Queries:<BR><BR>fib(g,a).<BR><BR>We use the technique of [30]. With regard to the inferred argument filtering the predicates were used in the following modes:
<BR><FONT COLOR=#0000cc>fib_in</font>: (b,f)
<BR><FONT COLOR=#0000cc>isGreater_in</font>: (b,b)
<BR><FONT COLOR=#0000cc>isMinus_in</font>: (b,b,f) (b,b,b)
<BR><FONT COLOR=#0000cc>isPlus_in</font>: (b,b,b)
<BR>Transforming <I>Prolog</I> into the following <B>Term Rewriting System</B>:
<BR>Pi-finite rewrite system:<BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<BR>
<P><B>Infinitary Constructor Rewriting Termination</B> of PiTRS implies <B>Termination</B> of Prolog<P>
<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 <B>PiTRS</B></pre><pre>              &#8627 DependencyPairsProof</pre><BR>Pi-finite rewrite system:<BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<BR><BR>Using Dependency Pairs [1,30] we result in the following initial DP problem:<BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_GGG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_GGG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)
<BR><FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U45_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U44_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U71_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_GG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U41_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U43_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_GGG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U40_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_GGG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U46_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U44_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U72_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_GG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U47_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_GA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 <B>PiDP</B></pre><pre>                  &#8627 DependencyGraphProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_GGG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_GGG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)
<BR><FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U45_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U44_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U71_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_GG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U41_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U43_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_GGG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U40_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_GGG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U46_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U44_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U72_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_GG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U47_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_GA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>The approximation of the Dependency Graph [30] contains 7 SCCs with 30 less nodes.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 <B>PiDP</B></pre><pre>                        &#8627 UsableRulesProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 <B>PiDP</B></pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Pi is empty.<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 PiDP</pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 QDPSizeChangeProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 > 3<P></LI>
<LI><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3<P></LI>
<LI><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3<P></LI>
<LI><FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 > 3<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 <B>PiDP</B></pre><pre>                        &#8627 UsableRulesProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 <B>PiDP</B></pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Pi is empty.<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 PiDP</pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 QDPSizeChangeProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 <B>PiDP</B></pre><pre>                        &#8627 UsableRulesProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 <B>PiDP</B></pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Pi is empty.<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 PiDP</pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 QDPSizeChangeProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 > 3<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 > 3<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 <B>PiDP</B></pre><pre>                        &#8627 UsableRulesProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 <B>PiDP</B></pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 PiDP</pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 QDPSizeChangeProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 >= 1, 2 > 2<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 >= 1, 2 > 2<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 <B>PiDP</B></pre><pre>                        &#8627 UsableRulesProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 <B>PiDP</B></pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 PiDP</pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 QDPSizeChangeProof</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2<P></LI>
<LI><FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 <B>PiDP</B></pre><pre>                        &#8627 UsableRulesProof</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 <B>PiDP</B></pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                      &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)</BLOCKQUOTE><BR>R is empty.<BR>Pi is empty.<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 UsableRulesProof</pre><pre>                          &#8627 PiDP</pre><pre>                            &#8627 PiDPToQDPProof</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 QDPSizeChangeProof</pre><pre>                      &#8627 PiDP</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2<P></LI>
<LI><FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>ISGREATER_IN_GG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)<BR>The graph contains the following edges 1 > 1, 2 > 2<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 <B>PiDP</B></pre><pre>                        &#8627 PiDPToQDPProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>M</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isGreater_out_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>isGreater_out_gg</font><BR>
<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isMinus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isMinus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_ggg</font><BR>
<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)<BR>
<FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 <B>QDP</B></pre><pre>                            &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>)) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 <B>QDP</B></pre><pre>                                    &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>)) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 <B>QDP</B></pre><pre>                                        &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>)) at position [1] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 <B>QDP</B></pre><pre>                                            &#8627 Narrowing</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>)) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 <B>QDP</B></pre><pre>                                                &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>))) at position [2,1] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 <B>QDP</B></pre><pre>                                                    &#8627 Narrowing</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>)) at position [1] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>)
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>)
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>)
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 <B>QDP</B></pre><pre>                                                        &#8627 DependencyGraphProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>)
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>)
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 4 less nodes.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 <B>QDP</B></pre><pre>                                                            &#8627 Narrowing</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) at position [1] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 <B>QDP</B></pre><pre>                                                                &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>))) at position [1,0] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 <B>QDP</B></pre><pre>                                                                    &#8627 Narrowing</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>)) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 <B>QDP</B></pre><pre>                                                                        &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>))) at position [1,0] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 <B>QDP</B></pre><pre>                                                                            &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>))) at position [1,0] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 <B>QDP</B></pre><pre>                                                                                &#8627 Instantiation</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 <B>QDP</B></pre><pre>                                                                                    &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))) at position [1] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>))))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 <B>QDP</B></pre><pre>                                                                                        &#8627 Rewriting</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>))))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By rewriting [15] the rule <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))) at position [1] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 Rewriting</pre><pre>                                                                                          &#8627 <B>QDP</B></pre><pre>                                                                                            &#8627 Instantiation</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>))))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>))) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>zero</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 Rewriting</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 Instantiation</pre><pre>                                                                                              &#8627 <B>QDP</B></pre><pre>                                                                                                &#8627 DependencyGraphProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>))))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 Rewriting</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 Instantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 DependencyGraphProof</pre><pre>                                                                                                  &#8627 <B>QDP</B></pre><pre>                                                                                                    &#8627 Instantiation</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 Rewriting</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 Instantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 DependencyGraphProof</pre><pre>                                                                                                  &#8627 QDP</pre><pre>                                                                                                    &#8627 Instantiation</pre><pre>                                                                                                      &#8627 <B>QDP</B></pre><pre>                                                                                                        &#8627 DependencyGraphProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 Rewriting</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 Instantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 DependencyGraphProof</pre><pre>                                                                                                  &#8627 QDP</pre><pre>                                                                                                    &#8627 Instantiation</pre><pre>                                                                                                      &#8627 QDP</pre><pre>                                                                                                        &#8627 DependencyGraphProof</pre><pre>                                                                                                          &#8627 <B>QDP</B></pre><pre>                                                                                                            &#8627 Instantiation</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>x2</font>))) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>z0</font>)))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 Rewriting</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 Instantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 DependencyGraphProof</pre><pre>                                                                                                  &#8627 QDP</pre><pre>                                                                                                    &#8627 Instantiation</pre><pre>                                                                                                      &#8627 QDP</pre><pre>                                                                                                        &#8627 DependencyGraphProof</pre><pre>                                                                                                          &#8627 QDP</pre><pre>                                                                                                            &#8627 Instantiation</pre><pre>                                                                                                              &#8627 <B>QDP</B></pre><pre>                                                                                                                &#8627 Narrowing</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>z0</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#cc0000>z0</font>))) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>)), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>))) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>)))))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>))), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)))) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>x2</font>))))</BLOCKQUOTE><BR><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</pre><pre>    &#8627 Prolog</pre><pre>      &#8627 UndefinedPredicateHandlerProof</pre><pre>        &#8627 Prolog</pre><pre>          &#8627 PrologToPiTRSProof</pre><pre>            &#8627 PiTRS</pre><pre>              &#8627 DependencyPairsProof</pre><pre>                &#8627 PiDP</pre><pre>                  &#8627 DependencyGraphProof</pre><pre>                    &#8627 AND</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                      &#8627 PiDP</pre><pre>                        &#8627 PiDPToQDPProof</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Rewriting</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Rewriting</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Rewriting</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Rewriting</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Narrowing</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Rewriting</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Narrowing</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 DependencyGraphProof</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Narrowing</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Rewriting</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Narrowing</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Rewriting</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Rewriting</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Rewriting</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 Rewriting</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 Instantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 DependencyGraphProof</pre><pre>                                                                                                  &#8627 QDP</pre><pre>                                                                                                    &#8627 Instantiation</pre><pre>                                                                                                      &#8627 QDP</pre><pre>                                                                                                        &#8627 DependencyGraphProof</pre><pre>                                                                                                          &#8627 QDP</pre><pre>                                                                                                            &#8627 Instantiation</pre><pre>                                                                                                              &#8627 QDP</pre><pre>                                                                                                                &#8627 Narrowing</pre><pre>                                                                                                                  &#8627 <B>QDP</B></pre><pre>                                                                                                                    &#8627 DependencyGraphProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M2</font>)
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>FIB_IN_GA</font>(<FONT COLOR=#cc0000>M1</font>)
<BR><FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))) &#8594; <FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U2_GA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>))), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)))) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>x2</font>))))
<BR><FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)))
<BR><FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>)), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>))) &#8594; <FONT COLOR=#0000cc>U6_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>)))))
<BR><FONT COLOR=#0000cc>U3_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>x0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U7_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>), <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>y2</font>)) &#8594; <FONT COLOR=#0000cc>U8_GA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U4_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>z0</font>)) &#8594; <FONT COLOR=#0000cc>U5_GA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>z0</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>))
<BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>M</font>))
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>X1</font>)) &#8594; <FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X1</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>isGreater_out_gg</font>
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isGreater_out_gg</font>) &#8594; <FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>isMinus_out_gga</font>(<FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M1</font>)) &#8594; <FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>M</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>zero</font>)), <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isMinus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>isMinus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M1</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>M2</font>)) &#8594; <FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M1</font>))
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>M2</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N1</font>)) &#8594; <FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>M2</font>))
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N2</font>)) &#8594; <FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>N1</font>, <FONT COLOR=#cc0000>N2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_ggg</font>
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>) &#8594; <FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>N</font>)) &#8594; <FONT COLOR=#0000cc>fib_out_ga</font>(<FONT COLOR=#cc0000>N</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>fib_in_ga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U2_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isGreater_in_gg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U72_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U71_gg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U3_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_gga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U47_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U4_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U5_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isMinus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U47_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U46_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U45_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U44_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U43_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U42_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U6_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U7_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U8_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U9_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)
<BR><FONT COLOR=#0000cc>U41_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U40_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U39_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U38_ggg</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U10_ga</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U11_ga</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 13 less nodes.<BR><BR></body>

