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<title>Left Termination proof of ../tpdb/LP/talp/plumer/pl5.2.2.pl</title>
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<BR><B>Left Termination</B> of the query pattern
turing_in_4(g, g, g, a)
w.r.t. the given <I>Prolog program</I> could not be shown:<BR><BR><BR><BR><pre>&#8627 <B>Prolog</B></pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Clauses:<BR><BR>member(H, .(H, L)).<BR>member(X, .(H, L))&#160;:-&#160;member(X, L).<BR>turing(t(X, Y, Z), S, P, t(X, Y, Z))&#160;:-&#160;member(p(S, Y, halt, W, D), P).<BR>turing(t(X, Y, .(R, L)), S, P, T)&#160;:-&#160;','(member(p(S, Y, S1, W, r), P), turing(t(.(W, X), R, L), S1, P, T)).<BR>turing(t(X, Y, []), S, P, T)&#160;:-&#160;','(member(p(S, Y, S1, W, r), P), turing(t(.(W, X), space, []), S1, P, T)).<BR>turing(t(.(X, L), Y, R), S, P, T)&#160;:-&#160;','(member(p(S, Y, S1, W, l), P), turing(t(L, X, .(W, R)), S1, P, T)).<BR>turing(t([], Y, R), S, P, T)&#160;:-&#160;','(member(p(S, Y, S1, W, l), P), turing(t([], space, .(W, R)), S1, P, T)).<BR><BR>Queries:<BR><BR>turing(g,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>turing_in</font>: (b,b,b,f) (b,f,b,f)
<BR><FONT COLOR=#0000cc>member_in</font>: (f,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>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</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 PrologToPiTRSProof</pre><pre>    &#8627 <B>PiTRS</B></pre><pre>      &#8627 DependencyPairsProof</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Pi-finite rewrite system:<BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</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>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GAGA</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>U6_GAGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GGGA</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>U6_GGGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U7_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GAGA</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>U4_GAGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GAGA</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>U10_GAGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U3_GGGA</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>U3_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_GGGA</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>U8_GGGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GGGA</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>U10_GGGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U9_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U8_GAGA</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>U8_GAGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GGGA</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>U4_GGGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR><BR><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><pre>  &#8627 PrologToPiTRSProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GAGA</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>U6_GAGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GGGA</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>U6_GGGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U7_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GAGA</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>U4_GAGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GAGA</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>U10_GAGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U3_GGGA</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>U3_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_GGGA</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>U8_GGGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GGGA</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>U10_GGGA</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U9_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U8_GAGA</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>U8_GAGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GGGA</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>U4_GGGA</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>The approximation of the Dependency Graph [30] contains 2 SCCs with 29 less nodes.<BR><BR><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 PrologToPiTRSProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</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 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 PrologToPiTRSProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</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>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</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 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 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>L</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>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>L</font>)<BR>The graph contains the following edges 1 > 1<P></LI></UL><BR><BR><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 PrologToPiTRSProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</font>(<FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</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 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 PrologToPiTRSProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</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 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 Narrowing</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>)) at position [4] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 <B>QDP</B></pre><pre>                            &#8627 Narrowing</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>)) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 <B>QDP</B></pre><pre>                                &#8627 Narrowing</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>)) at position [4] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 <B>QDP</B></pre><pre>                                    &#8627 Narrowing</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By narrowing [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>)) at position [2] we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 <B>QDP</B></pre><pre>                                        &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 <B>QDP</B></pre><pre>                                            &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 <B>QDP</B></pre><pre>                                                &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 <B>QDP</B></pre><pre>                                                    &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 <B>QDP</B></pre><pre>                                                        &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>))) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 <B>QDP</B></pre><pre>                                                            &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 <B>QDP</B></pre><pre>                                                                &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 <B>QDP</B></pre><pre>                                                                    &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>))) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 <B>QDP</B></pre><pre>                                                                        &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 <B>QDP</B></pre><pre>                                                                            &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 <B>QDP</B></pre><pre>                                                                                &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#cc0000>z3</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 <B>QDP</B></pre><pre>                                                                                    &#8627 Instantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By instantiating [15] the rule <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Instantiation</pre><pre>                                                                                      &#8627 <B>QDP</B></pre><pre>                                                                                        &#8627 ForwardInstantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By forward instantiating [14] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Instantiation</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                          &#8627 <B>QDP</B></pre><pre>                                                                                            &#8627 ForwardInstantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By forward instantiating [14] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x0</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Instantiation</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 ForwardInstantiation</pre><pre>                                                                                              &#8627 <B>QDP</B></pre><pre>                                                                                                &#8627 ForwardInstantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By forward instantiating [14] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Instantiation</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 ForwardInstantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 ForwardInstantiation</pre><pre>                                                                                                  &#8627 <B>QDP</B></pre><pre>                                                                                                    &#8627 ForwardInstantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By forward instantiating [14] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Instantiation</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 ForwardInstantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 ForwardInstantiation</pre><pre>                                                                                                  &#8627 QDP</pre><pre>                                                                                                    &#8627 ForwardInstantiation</pre><pre>                                                                                                      &#8627 <B>QDP</B></pre><pre>                                                                                                        &#8627 ForwardInstantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By forward instantiating [14] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z1</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Instantiation</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 ForwardInstantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 ForwardInstantiation</pre><pre>                                                                                                  &#8627 QDP</pre><pre>                                                                                                    &#8627 ForwardInstantiation</pre><pre>                                                                                                      &#8627 QDP</pre><pre>                                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                                          &#8627 <B>QDP</B></pre><pre>                                                                                                            &#8627 ForwardInstantiation</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>By forward instantiating [14] the rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>z3</font>)) we obtained the following new rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))</BLOCKQUOTE><BR><BR><BR><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 QDP</pre><pre>                        &#8627 Narrowing</pre><pre>                          &#8627 QDP</pre><pre>                            &#8627 Narrowing</pre><pre>                              &#8627 QDP</pre><pre>                                &#8627 Narrowing</pre><pre>                                  &#8627 QDP</pre><pre>                                    &#8627 Narrowing</pre><pre>                                      &#8627 QDP</pre><pre>                                        &#8627 Instantiation</pre><pre>                                          &#8627 QDP</pre><pre>                                            &#8627 Instantiation</pre><pre>                                              &#8627 QDP</pre><pre>                                                &#8627 Instantiation</pre><pre>                                                  &#8627 QDP</pre><pre>                                                    &#8627 Instantiation</pre><pre>                                                      &#8627 QDP</pre><pre>                                                        &#8627 Instantiation</pre><pre>                                                          &#8627 QDP</pre><pre>                                                            &#8627 Instantiation</pre><pre>                                                              &#8627 QDP</pre><pre>                                                                &#8627 Instantiation</pre><pre>                                                                  &#8627 QDP</pre><pre>                                                                    &#8627 Instantiation</pre><pre>                                                                      &#8627 QDP</pre><pre>                                                                        &#8627 Instantiation</pre><pre>                                                                          &#8627 QDP</pre><pre>                                                                            &#8627 Instantiation</pre><pre>                                                                              &#8627 QDP</pre><pre>                                                                                &#8627 Instantiation</pre><pre>                                                                                  &#8627 QDP</pre><pre>                                                                                    &#8627 Instantiation</pre><pre>                                                                                      &#8627 QDP</pre><pre>                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                          &#8627 QDP</pre><pre>                                                                                            &#8627 ForwardInstantiation</pre><pre>                                                                                              &#8627 QDP</pre><pre>                                                                                                &#8627 ForwardInstantiation</pre><pre>                                                                                                  &#8627 QDP</pre><pre>                                                                                                    &#8627 ForwardInstantiation</pre><pre>                                                                                                      &#8627 QDP</pre><pre>                                                                                                        &#8627 ForwardInstantiation</pre><pre>                                                                                                          &#8627 QDP</pre><pre>                                                                                                            &#8627 ForwardInstantiation</pre><pre>                                                                                                              &#8627 <B>QDP</B></pre><pre>                                                                                                                &#8627 NonTerminationProof</pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR>We used the non-termination processor [17] to show that the DP problem is infinite.<BR>Found a loop by narrowing to the left:<BR><BR>The TRS P consists of the following rules:<BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>), <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_5</font>, <FONT COLOR=#cc0000>y_6</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z5</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z6</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z4</font>)))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#cc0000>z5</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>z4</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>y0</font>, <FONT COLOR=#cc0000>y2</font>, <FONT COLOR=#cc0000>y3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>)) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>z3</font>)))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>)) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>), <FONT COLOR=#cc0000>x5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>y_4</font>)))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z3</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font>)))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>z0</font>), <FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z4</font>, <FONT COLOR=#cc0000>z5</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>)
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR><BR>s = <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4'</font>))) evaluates to  t =<FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4'</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))<BR><BR>Thus s starts an infinite chain as s semiunifies with t with the following substitutions:<BR><UL><LI> Matcher: [<FONT COLOR=#cc0000>x4'</font> / <FONT COLOR=#cc0000>y_3</font>, <FONT COLOR=#cc0000>z1</font> / <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#cc0000>x3</font> / <FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>z0</font> / <FONT COLOR=#cc0000>x4'</font>]</LI>
<LI> Semiunifier: [ ]</LI></UL><BR><BR><hr><BR><B>Rewriting sequence</B><BR><BR><B><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4'</font>)))</B> &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4'</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>z3</font>))<BR>with rule <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0'</font>, <FONT COLOR=#cc0000>z1'</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3'</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x3'</font>, <FONT COLOR=#cc0000>x4''</font>))) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4''</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0'</font>, <FONT COLOR=#cc0000>z1'</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z2</font>, <FONT COLOR=#cc0000>z3'</font>)) at position [] and matcher [<FONT COLOR=#cc0000>z3'</font> / <FONT COLOR=#cc0000>z3</font>, <FONT COLOR=#cc0000>x3'</font> / <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>z1'</font> / <FONT COLOR=#cc0000>z1</font>, <FONT COLOR=#cc0000>z2</font> / <FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>z0'</font> / <FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>x4''</font> / <FONT COLOR=#cc0000>x4'</font>]<BR><BR><B><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4'</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>z3</font>))</B> &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x4'</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>z0</font>, <FONT COLOR=#cc0000>z1</font>)), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>z3</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))<BR>with rule <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>)) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>), <FONT COLOR=#cc0000>x4</font>), <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>y_2</font>, <FONT COLOR=#cc0000>y_3</font>)))<BR><BR>Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence<BR><BR><BR>All these steps are and every following step will be a correct step w.r.t to Q.<BR><BR><BR><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>turing_in</font>: (b,b,b,f) (b,f,b,f)
<BR><FONT COLOR=#0000cc>member_in</font>: (f,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>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</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>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</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 PrologToPiTRSProof</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>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</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>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</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>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</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>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GAGA</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>U6_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GGGA</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>U6_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U7_GGGA</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_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GAGA</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>U4_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GAGA</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>U10_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U3_GGGA</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>U3_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_GGGA</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>U8_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GGGA</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>U10_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U9_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U8_GAGA</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>U8_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GGGA</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>U4_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GGGA</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_GGGA</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>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</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>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U5_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U7_GGGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U9_GGGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</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>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GAGA</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>U6_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U6_GGGA</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>U6_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U7_GGGA</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_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_AG</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U5_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GAGA</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>U4_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GAGA</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>U10_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U3_GGGA</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>U3_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_GGGA</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>U8_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U10_GGGA</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>U10_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U9_GGGA</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_GGGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U8_GAGA</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>U8_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U4_GGGA</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>U4_GGGA</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U2_GGGA</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_GGGA</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>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>The approximation of the Dependency Graph [30] contains 2 SCCs with 29 less nodes.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</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>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</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 PrologToPiTRSProof</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</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>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>MEMBER_IN_AG</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 PrologToPiTRSProof</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><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>L</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>MEMBER_IN_AG</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>MEMBER_IN_AG</font>(<FONT COLOR=#cc0000>L</font>)<BR>The graph contains the following edges 1 > 1<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U2_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>halt</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>D</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_gaga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U8_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U6_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_gaga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U4_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U5_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U6_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U8_ggga</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>))
<BR><FONT COLOR=#0000cc>U10_ggga</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)) &#8594; <FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_ggga</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_ggga</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>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>halt</font>&#160; = &#160;<FONT COLOR=#0000cc>halt</font><BR>
<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_ggga</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>U3_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_ggga</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>U4_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_in_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x5</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>turing_out_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U3_gaga</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>U3_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U4_gaga</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>U4_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>U5_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_gaga</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>U6_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_gaga</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>U8_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_gaga</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_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_gaga</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>U10_gaga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>U5_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U6_ggga</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>U6_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_ggga</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_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U8_ggga</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>U8_ggga</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>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_ggga</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_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U10_ggga</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>U10_ggga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</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 PrologToPiTRSProof</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>r</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>S</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>W</font>, <FONT COLOR=#0000cc>l</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>S1</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#cc0000>T</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x5</font>)&#160; = &#160;<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</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>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>space</font>&#160; = &#160;<FONT COLOR=#0000cc>space</font><BR>
<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>)<BR>
<FONT COLOR=#0000cc>U7_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U3_GAGA</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>U3_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>)<BR>
<FONT COLOR=#0000cc>U9_GAGA</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_GAGA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</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 PrologToPiTRSProof</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><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>)), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>space</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>U7_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>R</font>)), <FONT COLOR=#cc0000>P</font>)
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U9_GAGA</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>[]</font>), <FONT COLOR=#cc0000>P</font>) &#8594; <FONT COLOR=#0000cc>U5_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>P</font>))
<BR><FONT COLOR=#0000cc>U3_GAGA</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>P</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#0000cc>p</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>W</font>), <FONT COLOR=#cc0000>P</font>)) &#8594; <FONT COLOR=#0000cc>TURING_IN_GAGA</font>(<FONT COLOR=#0000cc>t</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>W</font>, <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>L</font>), <FONT COLOR=#cc0000>P</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>, <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>L</font>)) &#8594; <FONT COLOR=#0000cc>member_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>L</font>))</BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>member_in_ag</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U1_ag</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)</BLOCKQUOTE><BR>We have to consider all (P,Q,R)-chains.<BR><BR></body>

