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<title>Left Termination proof of ../tpdb/LP/talp/maria/mmatrix.pl</title>
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<BR><B>Left Termination</B> of the query pattern
mmultiply_in_3(g, 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>mmultiply([], _, []).<BR>mmultiply(.(V0, Rest), V1, .(Result, Others))&#160;:-&#160;','(mmultiply(Rest, V1, Others), multiply(V1, V0, Result)).<BR>multiply([], _, []).<BR>multiply(.(V0, Rest), V1, .(Result, Others))&#160;:-&#160;','(multiply(Rest, V1, Others), vmul(V0, V1, Result)).<BR>vmul([], [], 0).<BR>vmul(.(H1, T1), .(H2, T2), Result)&#160;:-&#160;','(vmul(T1, T2, Newresult), ','(is(Product, *(H1, H2)), is(Result, +(Product, Newresult)))).<BR>trans_m(.([], _), []).<BR>trans_m(M, .(C1, Cn))&#160;:-&#160;','(trans_v(M, C1, R), trans_m(R, Cn)).<BR>trans_v([], [], []).<BR>trans_v(.(.(C11, C1n), C), .(C11, X), .(C1n, Y))&#160;:-&#160;trans_v(C, X, Y).<BR>makematrix(N, Matrix)&#160;:-&#160;','(makevector(N, Vec), makematrix(N, Vec, Matrix)).<BR>makematrix(0, _, []).<BR>makematrix(Rows, Vector, .(Vector, T))&#160;:-&#160;','(>(Rows, 0), ','(is(Nextrow, -(Rows, 1)), makematrix(Nextrow, Vector, T))).<BR>makevector(0, []).<BR>makevector(Cols, .(Cols, T))&#160;:-&#160;','(>(Cols, 0), ','(is(Nextcol, -(Cols, 1)), makevector(Nextcol, T))).<BR><BR>Queries:<BR><BR>mmultiply(g,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 PrologToPiTRSProof</pre><BR>Clauses:<BR><BR>mmultiply([], X, []).<BR>mmultiply(.(V0, Rest), V1, .(Result, Others))&#160;:-&#160;','(mmultiply(Rest, V1, Others), multiply(V1, V0, Result)).<BR>multiply([], X, []).<BR>multiply(.(V0, Rest), V1, .(Result, Others))&#160;:-&#160;','(multiply(Rest, V1, Others), vmul(V0, V1, Result)).<BR>vmul([], [], zero).<BR>vmul(.(H1, T1), .(H2, T2), Result)&#160;:-&#160;','(vmul(T1, T2, Newresult), ','(isTimes(H1, H2, U), ','(=(Product, U), ','(isPlus(Product, Newresult, U), =(Result, U))))).<BR>trans_m(.([], X), []).<BR>trans_m(M, .(C1, Cn))&#160;:-&#160;','(trans_v(M, C1, R), trans_m(R, Cn)).<BR>trans_v([], [], []).<BR>trans_v(.(.(C11, C1n), C), .(C11, X), .(C1n, Y))&#160;:-&#160;trans_v(C, X, Y).<BR>makematrix(N, Matrix)&#160;:-&#160;','(makevector(N, Vec), makematrix(N, Vec, Matrix)).<BR>makematrix(zero, X, []).<BR>makematrix(Rows, Vector, .(Vector, T))&#160;:-&#160;','(=(X, Rows), ','(=(X1, zero), ','(isGreater(X, X1), ','(isMinus(Rows, succ(zero), U), ','(=(Nextrow, U), makematrix(Nextrow, Vector, T)))))).<BR>makevector(zero, []).<BR>makevector(Cols, .(Cols, T))&#160;:-&#160;','(=(X, Cols), ','(=(X1, zero), ','(isGreater(X, X1), ','(isMinus(Cols, succ(zero), U), ','(=(Nextcol, U), makevector(Nextcol, 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>mmultiply(g,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>mmultiply_in</font>: (b,b,f)
<BR><FONT COLOR=#0000cc>multiply_in</font>: (b,b,f)
<BR><FONT COLOR=#0000cc>vmul_in</font>: (b,b,f)
<BR><FONT COLOR=#0000cc>isTimes_in</font>: (b,b,f)
<BR><FONT COLOR=#0000cc>isMinus_in</font>: (b,b,f)
<BR><FONT COLOR=#0000cc>isPlus_in</font>: (b,b,f) (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>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</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 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>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</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>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)
<BR><FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)
<BR><FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)
<BR><FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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>U37_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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>U43_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U41_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U27_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U29_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U39_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U37_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U8_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U8_GGA</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_GGA</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_GGA</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>U42_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>U42_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U32_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GGA</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U9_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_GGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_GGA</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</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>U38_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>U38_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</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>U41_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>U41_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_GGA</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>U7_GGA</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U1_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U37_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>U37_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_GGA</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>U31_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</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 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>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)
<BR><FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)
<BR><FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)
<BR><FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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>U37_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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>U43_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U43_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U41_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U41_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U27_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U29_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U39_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISMINUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U37_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)
<BR><FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGG</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U8_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U8_GGA</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>=_IN_AG</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U8_GGA</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_GGA</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_GGA</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>U42_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>U42_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U32_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GGA</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U9_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_GGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_GGA</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</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>U38_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>U38_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</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>U41_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>U41_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_GGA</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>U7_GGA</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_GGA</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U1_GGA</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_GGG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U37_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>U37_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U6_GGA</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_GGA</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>U31_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_GGA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_GGA</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>The approximation of the Dependency Graph [30] contains 9 SCCs with 41 less nodes.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PredefinedPredicateTransformerProof</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><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>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</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 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><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 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><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 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><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_GGA</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_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_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>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISPLUS_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 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><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_GGA</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_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>ISPLUS_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>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISPLUS_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 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><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_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>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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>ISPLUS_IN_GGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISPLUS_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>ISPLUS_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>ISPLUS_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>ISPLUS_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>ISPLUS_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>ISPLUS_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>ISPLUS_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>ISPLUS_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>ISPLUS_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>ISPLUS_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 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><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>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</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 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><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 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><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 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><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>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</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 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><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 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><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 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><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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISTIMES_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 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><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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISTIMES_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 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><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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>pred</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 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><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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISTIMES_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 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><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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>ISTIMES_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ISTIMES_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 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><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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</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>ISTIMES_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>ISTIMES_IN_GGA</font>(<FONT COLOR=#0000cc>succ</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 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 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>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>VMUL_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 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 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>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)</BLOCKQUOTE><BR>R is empty.<BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>VMUL_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 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 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>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>)) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</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>VMUL_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>)) &#8594; <FONT COLOR=#0000cc>VMUL_IN_GGA</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</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 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 <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>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MULTIPLY_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 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 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>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)</BLOCKQUOTE><BR>R is empty.<BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MULTIPLY_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 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 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>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</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>MULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>) &#8594; <FONT COLOR=#0000cc>MULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</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 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 PiDP</pre><pre>                  &#8627 <B>PiDP</B></pre><pre>                    &#8627 UsableRulesProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>))
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>) &#8594; <FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>))
<BR><FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Newresult</font>)) &#8594; <FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>) &#8594; <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>)
<BR><FONT COLOR=#0000cc>isTimes_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>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>isTimes_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>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>))
<BR><FONT COLOR=#0000cc>U43_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</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>U31_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>U32_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>U33_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>U34_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>U35_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>U36_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>U36_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>U35_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>U34_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>U33_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>U32_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>U31_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>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>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U41_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#0000cc>zero</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_in_gga</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_gga</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_gga</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>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>))) &#8594; <FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U30_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>pred</font>(<FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U29_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U28_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U27_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isPlus_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=#0000cc>succ</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>Z</font>)))
<BR><FONT COLOR=#0000cc>U42_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>pred</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U39_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U40_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>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U37_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>A</font>)) &#8594; <FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U38_gga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>succ</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>isTimes_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>U6_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</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>U7_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_in_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</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>U27_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>U28_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>U29_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>U30_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>U30_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>U29_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>U28_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>U27_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>U8_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>, <FONT COLOR=#0000cc>isPlus_out_ggg</font>(<FONT COLOR=#cc0000>Product</font>, <FONT COLOR=#cc0000>Newresult</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_in_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>))
<BR><FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>, <FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#0000cc>=_out_ag</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>U</font>)) &#8594; <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H1</font>, <FONT COLOR=#cc0000>T1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H2</font>, <FONT COLOR=#cc0000>T2</font>), <FONT COLOR=#cc0000>Result</font>)
<BR><FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))
<BR><FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>, <FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Result</font>)) &#8594; <FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>mmultiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U2_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>multiply_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_gga</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>vmul_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)<BR>
<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>zero</font>&#160; = &#160;<FONT COLOR=#0000cc>zero</font><BR>
<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isTimes_out_gga</font>(<FONT COLOR=#cc0000>x3</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>U37_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>U37_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U39_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>U39_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U41_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>U41_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U43_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>U43_gga</font>(<FONT COLOR=#cc0000>x1</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>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>U31_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U33_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>U33_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_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>U34_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U35_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>U35_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U36_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>U36_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U42_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>U42_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_in_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>isPlus_out_gga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U27_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>U27_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U40_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>U40_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U38_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>U38_gga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U7_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>, <FONT COLOR=#cc0000>x8</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>U8_gga</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>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_gga</font>(<FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x7</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>U27_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>U27_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U28_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>U28_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U29_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>U29_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_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>U30_ggg</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U9_gga</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>, <FONT COLOR=#cc0000>x6</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_gga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MMULTIPLY_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 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 PiDP</pre><pre>                  &#8627 PiDP</pre><pre>                    &#8627 UsableRulesProof</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>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>Result</font>, <FONT COLOR=#cc0000>Others</font>)) &#8594; <FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>, <FONT COLOR=#cc0000>Others</font>)</BLOCKQUOTE><BR>R is empty.<BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>MMULTIPLY_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 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 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><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>) &#8594; <FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</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>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V0</font>, <FONT COLOR=#cc0000>Rest</font>), <FONT COLOR=#cc0000>V1</font>) &#8594; <FONT COLOR=#0000cc>MMULTIPLY_IN_GGA</font>(<FONT COLOR=#cc0000>Rest</font>, <FONT COLOR=#cc0000>V1</font>)<BR>The graph contains the following edges 1 > 1, 2 >= 2<P></LI></UL><BR><BR></body>

