YES
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<title>Left Termination proof of ../tpdb/LP/terminweb/old-terminweb/untupled_bal_tree.pl</title>
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<BR><B>Left Termination</B> of the query pattern
balance_in_2(g, a)
w.r.t. the given <I>Prolog program</I> could successfully be <font color=#00ff00>proven</font>:<BR><BR><BR><BR><pre>&#8627 <B>Prolog</B></pre><pre>  &#8627 PrologToPiTRSProof</pre><BR>Clauses:<BR><BR>balance(T, TB)&#160;:-&#160;balance55(T, XX0, XX1, [], .(','(nil, -(XX0, XX0)), XX1), [], .(','(TB, -(I, [])), X), X, I, []).<BR>balance55(nil, C, T, T, A, B, A, B, X, X).<BR>balance55(tree(L, V, R), XX0, XX1, NT, HR, TR, .(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T)), IH, IT)&#160;:-&#160;','(balance55(L, XX0, XX1, .(','(nil, -(XX2, XX2)), XX3), HR1, TR1, H, T, IH, .(V, IT1)), balance55(R, XX2, XX3, NT, HR, TR, HR1, TR1, IT1, IT)).<BR>balance5(nil, C, T, T, A, B, A, B, X, X)&#160;:-&#160;balance55(nil, C, T, T, A, B, A, B, X, X).<BR>balance5(tree(L, V, R), XX0, XX1, NT, HR, TR, .(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T)), IH, IT)&#160;:-&#160;balance55(tree(L, V, R), XX0, XX1, NT, HR, TR, .(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T)), IH, IT).<BR>balance(nil, -(X, X), -(A, B), -(A, B), -(.(','(nil, -(C, C)), T), T))&#160;:-&#160;balance5(nil, C, T, T, A, B, A, B, X, X).<BR>balance(tree(L, V, R), -(IH, IT), -(.(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T))), -(HR, TR), -(.(','(nil, -(XX0, XX0)), XX1), NT))&#160;:-&#160;balance5(tree(L, V, R), XX0, XX1, NT, HR, TR, .(','(tree(LB, VB, RB), -(A, D)), H), .(','(LB, -(A, .(VB, X))), .(','(RB, -(X, D)), T)), IH, IT).<BR><BR>Queries:<BR><BR>balance(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>balance_in</font>: (b,f)
<BR><FONT COLOR=#0000cc>balance55_in</font>: (b,f,f,b,f,b,f,f,f,b) (b,f,f,f,f,f,f,f,f,f)
<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>balance_in_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)) &#8594; <FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_out_ga</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><BR>Pi-finite rewrite system:<BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)) &#8594; <FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_out_ga</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>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))
<BR><FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)) &#8594; <FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_out_ga</font><BR>
<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U3_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U3_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x3</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))
<BR><FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)) &#8594; <FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_out_ga</font><BR>
<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U3_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE_IN_GA</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U3_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_GA</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>The approximation of the Dependency Graph [30] contains 2 SCCs with 5 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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)) &#8594; <FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_out_ga</font><BR>
<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>x1</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><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>)) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>)
<BR><FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>)
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>)) &#8594; <FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font></BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><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>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>)<BR>The graph contains the following edges 1 >= 1<P></LI>
<LI><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>)) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>L</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>BALANCE55_IN_GAAAAAAAAA</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>)) &#8594; <FONT COLOR=#0000cc>U2_GAAAAAAAAA</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>) &#8594; <FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>))
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX0</font>)), <FONT COLOR=#cc0000>XX1</font>), <FONT COLOR=#0000cc>[]</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>TB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)), <FONT COLOR=#cc0000>X</font>), <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>I</font>, <FONT COLOR=#0000cc>[]</font>)) &#8594; <FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>TB</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_in_ga</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_ga</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</font>)<BR>
<FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaagagaaag</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaagagaaag</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaagagaaag</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>[]</font>&#160; = &#160;<FONT COLOR=#0000cc>[]</font><BR>
<FONT COLOR=#0000cc>balance_out_ga</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance_out_ga</font><BR>
<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</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><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)
<BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#cc0000>C</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>B</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>)))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>nil</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX2</font>)), <FONT COLOR=#cc0000>XX3</font>), <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>IT1</font>))) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>, <FONT COLOR=#cc0000>H</font>, <FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>T</font>, <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>XX2</font>, <FONT COLOR=#cc0000>XX3</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>HR1</font>, <FONT COLOR=#cc0000>TR1</font>, <FONT COLOR=#cc0000>IT1</font>, <FONT COLOR=#cc0000>IT</font>)) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>XX0</font>, <FONT COLOR=#cc0000>XX1</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>HR</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>RB</font>), <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>H</font>), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>LB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>A</font>, <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#cc0000>VB</font>, <FONT COLOR=#cc0000>X</font>))), <FONT COLOR=#0000cc>.</font>(<FONT COLOR=#0000cc>','</font>(<FONT COLOR=#cc0000>RB</font>, <FONT COLOR=#0000cc>-</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>D</font>)), <FONT COLOR=#cc0000>T</font>)), <FONT COLOR=#cc0000>IH</font>, <FONT COLOR=#cc0000>IT</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>nil</font>&#160; = &#160;<FONT COLOR=#0000cc>nil</font><BR>
<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font><BR>
<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>, <FONT COLOR=#cc0000>x11</font>, <FONT COLOR=#cc0000>x12</font>, <FONT COLOR=#cc0000>x13</font>, <FONT COLOR=#cc0000>x14</font>, <FONT COLOR=#cc0000>x15</font>, <FONT COLOR=#cc0000>x16</font>, <FONT COLOR=#cc0000>x17</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x8</font>, <FONT COLOR=#cc0000>x18</font>, <FONT COLOR=#cc0000>x19</font>)<BR>
<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT 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>, <FONT COLOR=#cc0000>x9</font>, <FONT COLOR=#cc0000>x10</font>)&#160; = &#160;<FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x4</font>, <FONT COLOR=#cc0000>x6</font>, <FONT COLOR=#cc0000>x10</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 QDPSizeChangeProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>nil</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>
<BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>)) &#8594; <FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>))
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>R</font>))
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font></BLOCKQUOTE><BR>The set Q consists of the following terms:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x0</font>)
<BR><FONT COLOR=#0000cc>U2_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x0</font>, <FONT COLOR=#cc0000>x1</font>)
<BR><FONT COLOR=#0000cc>U3_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>x0</font>)</BLOCKQUOTE><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>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#0000cc>tree</font>(<FONT COLOR=#cc0000>L</font>, <FONT COLOR=#cc0000>V</font>, <FONT COLOR=#cc0000>R</font>), <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>) &#8594; <FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_in_gaaaaaaaaa</font>(<FONT COLOR=#cc0000>L</font>))<BR>The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4<P></LI>
<LI><FONT COLOR=#0000cc>U2_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>, <FONT COLOR=#0000cc>balance55_out_gaaaaaaaaa</font>) &#8594; <FONT COLOR=#0000cc>BALANCE55_IN_GAAGAGAAAG</font>(<FONT COLOR=#cc0000>R</font>, <FONT COLOR=#cc0000>NT</font>, <FONT COLOR=#cc0000>TR</font>, <FONT COLOR=#cc0000>IT</font>)<BR>The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4<P></LI></UL><BR><BR></body>

