YES
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<title>Left Termination proof of ../tpdb/LP/talp/talp/binary2.pl</title>
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<BR><B>Left Termination</B> of the query pattern
add_in_3(a, a, g)
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>add(b, b, b).<BR>add(X, b, X)&#160;:-&#160;binaryZ(X).<BR>add(b, Y, Y)&#160;:-&#160;binaryZ(Y).<BR>add(X, Y, Z)&#160;:-&#160;addz(X, Y, Z).<BR>addx(one(X), b, one(X))&#160;:-&#160;binary(X).<BR>addx(zero(X), b, zero(X))&#160;:-&#160;binaryZ(X).<BR>addx(X, Y, Z)&#160;:-&#160;addz(X, Y, Z).<BR>addy(b, one(Y), one(Y))&#160;:-&#160;binary(Y).<BR>addy(b, zero(Y), zero(Y))&#160;:-&#160;binaryZ(Y).<BR>addy(X, Y, Z)&#160;:-&#160;addz(X, Y, Z).<BR>addz(zero(X), zero(Y), zero(Z))&#160;:-&#160;addz(X, Y, Z).<BR>addz(zero(X), one(Y), one(Z))&#160;:-&#160;addx(X, Y, Z).<BR>addz(one(X), zero(Y), one(Z))&#160;:-&#160;addy(X, Y, Z).<BR>addz(one(X), one(Y), zero(Z))&#160;:-&#160;addc(X, Y, Z).<BR>addc(b, b, one(b)).<BR>addc(X, b, Z)&#160;:-&#160;succZ(X, Z).<BR>addc(b, Y, Z)&#160;:-&#160;succZ(Y, Z).<BR>addc(X, Y, Z)&#160;:-&#160;addC(X, Y, Z).<BR>addX(zero(X), b, one(X))&#160;:-&#160;binaryZ(X).<BR>addX(one(X), b, zero(Z))&#160;:-&#160;succ(X, Z).<BR>addX(X, Y, Z)&#160;:-&#160;addC(X, Y, Z).<BR>addY(b, zero(Y), one(Y))&#160;:-&#160;binaryZ(Y).<BR>addY(b, one(Y), zero(Z))&#160;:-&#160;succ(Y, Z).<BR>addY(X, Y, Z)&#160;:-&#160;addC(X, Y, Z).<BR>addC(zero(X), zero(Y), one(Z))&#160;:-&#160;addz(X, Y, Z).<BR>addC(zero(X), one(Y), zero(Z))&#160;:-&#160;addX(X, Y, Z).<BR>addC(one(X), zero(Y), zero(Z))&#160;:-&#160;addY(X, Y, Z).<BR>addC(one(X), one(Y), one(Z))&#160;:-&#160;addc(X, Y, Z).<BR>binary(b).<BR>binary(zero(X))&#160;:-&#160;binaryZ(X).<BR>binary(one(X))&#160;:-&#160;binary(X).<BR>binaryZ(zero(X))&#160;:-&#160;binaryZ(X).<BR>binaryZ(one(X))&#160;:-&#160;binary(X).<BR>succ(b, one(b)).<BR>succ(zero(X), one(X))&#160;:-&#160;binaryZ(X).<BR>succ(one(X), zero(Z))&#160;:-&#160;succ(X, Z).<BR>succZ(zero(X), one(X))&#160;:-&#160;binaryZ(X).<BR>succZ(one(X), zero(Z))&#160;:-&#160;succ(X, Z).<BR>times(one(b), X, X).<BR>times(zero(R), S, zero(RS))&#160;:-&#160;times(R, S, RS).<BR>times(one(R), S, RSS)&#160;:-&#160;','(times(R, S, RS), add(S, zero(RS), RSS)).<BR><BR>Queries:<BR><BR>add(a,a,g).<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>add_in</font>: (f,f,b)
<BR><FONT COLOR=#0000cc>binaryZ_in</font>: (b)
<BR><FONT COLOR=#0000cc>binary_in</font>: (b)
<BR><FONT COLOR=#0000cc>addz_in</font>: (f,f,b)
<BR><FONT COLOR=#0000cc>addx_in</font>: (f,f,b)
<BR><FONT COLOR=#0000cc>addy_in</font>: (f,f,b)
<BR><FONT COLOR=#0000cc>addc_in</font>: (f,f,b)
<BR><FONT COLOR=#0000cc>succZ_in</font>: (f,b)
<BR><FONT COLOR=#0000cc>succ_in</font>: (f,b)
<BR><FONT COLOR=#0000cc>addC_in</font>: (f,f,b)
<BR><FONT COLOR=#0000cc>addX_in</font>: (f,f,b)
<BR><FONT COLOR=#0000cc>addY_in</font>: (f,f,b)
<BR>Transforming <I>Prolog</I> into the following <B>Term Rewriting System</B>:
<BR>Pi-finite rewrite system:<BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>b</font>&#160; = &#160;<FONT COLOR=#0000cc>b</font><BR>
<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_out_g</font><BR>
<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_out_g</font><BR>
<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x4</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>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>b</font>&#160; = &#160;<FONT COLOR=#0000cc>b</font><BR>
<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_out_g</font><BR>
<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_out_g</font><BR>
<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x4</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>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>b</font>&#160; = &#160;<FONT COLOR=#0000cc>b</font><BR>
<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_out_g</font><BR>
<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_out_g</font><BR>
<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U16_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U20_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U22_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U21_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U28_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U26_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_AG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U13_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U12_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U8_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U17_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U25_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U23_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U24_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U11_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U1_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U4_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U32_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_AG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U14_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U31_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U27_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</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>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_G</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_AAG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>b</font>&#160; = &#160;<FONT COLOR=#0000cc>b</font><BR>
<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_out_g</font><BR>
<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_out_g</font><BR>
<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADD_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U5_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U16_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U20_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U22_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U21_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U2_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U28_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U26_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U34_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_AG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>SUCCZ_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U13_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U30_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U12_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U8_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U17_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U25_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U23_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U24_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U11_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U1_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U4_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U32_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_AG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U14_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U31_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U3_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_AAG</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U27_G</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_G</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>The approximation of the Dependency Graph [30] contains 3 SCCs with 50 less nodes.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>    &#8627 PiTRS</pre><pre>      &#8627 DependencyPairsProof</pre><pre>        &#8627 PiDP</pre><pre>          &#8627 DependencyGraphProof</pre><pre>            &#8627 AND</pre><pre>              &#8627 <B>PiDP</B></pre><pre>                &#8627 UsableRulesProof</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>b</font>&#160; = &#160;<FONT COLOR=#0000cc>b</font><BR>
<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_out_g</font><BR>
<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_out_g</font><BR>
<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>BINARY_IN_G</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><pre>              &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>R is empty.<BR>Pi is empty.<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>    &#8627 PiTRS</pre><pre>      &#8627 DependencyPairsProof</pre><pre>        &#8627 PiDP</pre><pre>          &#8627 DependencyGraphProof</pre><pre>            &#8627 AND</pre><pre>              &#8627 PiDP</pre><pre>                &#8627 UsableRulesProof</pre><pre>                  &#8627 PiDP</pre><pre>                    &#8627 PiDPToQDPProof</pre><pre>                      &#8627 <B>QDP</B></pre><pre>                        &#8627 QDPSizeChangeProof</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 PiDP</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARY_IN_G</font>(<FONT COLOR=#cc0000>X</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>BINARYZ_IN_G</font>(<FONT COLOR=#cc0000>X</font>)<BR>The graph contains the following edges 1 > 1<P></LI></UL><BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>    &#8627 PiTRS</pre><pre>      &#8627 DependencyPairsProof</pre><pre>        &#8627 PiDP</pre><pre>          &#8627 DependencyGraphProof</pre><pre>            &#8627 AND</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 <B>PiDP</B></pre><pre>                &#8627 UsableRulesProof</pre><pre>              &#8627 PiDP</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>b</font>&#160; = &#160;<FONT COLOR=#0000cc>b</font><BR>
<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_out_g</font><BR>
<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_out_g</font><BR>
<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>    &#8627 PiTRS</pre><pre>      &#8627 DependencyPairsProof</pre><pre>        &#8627 PiDP</pre><pre>          &#8627 DependencyGraphProof</pre><pre>            &#8627 AND</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 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>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>    &#8627 PiTRS</pre><pre>      &#8627 DependencyPairsProof</pre><pre>        &#8627 PiDP</pre><pre>          &#8627 DependencyGraphProof</pre><pre>            &#8627 AND</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 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>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>SUCC_IN_AG</font>(<FONT COLOR=#cc0000>Z</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 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>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The TRS R consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>) &#8594; <FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>b</font>) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>b</font>)
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>X</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>) &#8594; <FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Y</font>)
<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#0000cc>b</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>X</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>Y</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#0000cc>b</font>, <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>))
<BR><FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>, <FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>b</font>&#160; = &#160;<FONT COLOR=#0000cc>b</font><BR>
<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>add_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U1_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U29_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U30_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_in_g</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>binary_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binary_out_g</font><BR>
<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U27_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>binaryZ_out_g</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>binaryZ_out_g</font><BR>
<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U28_g</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U2_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U3_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U10_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U11_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U4_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addx_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U5_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U6_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U12_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U7_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addy_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U8_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U9_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U13_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addc_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U14_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U33_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succZ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U34_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_in_ag</font>(<FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>succ_out_ag</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U31_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U32_ag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U15_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U16_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U23_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addz_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addC_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U24_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U17_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addX_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U18_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U19_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U25_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_in_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)&#160; = &#160;<FONT COLOR=#0000cc>U20_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>addY_out_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>)<BR>
<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>U21_aag</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U22_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>, <FONT COLOR=#cc0000>x4</font>)&#160; = &#160;<FONT COLOR=#0000cc>U26_aag</font>(<FONT COLOR=#cc0000>x4</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>For (infinitary) constructor rewriting [30] we can delete all non-usable rules from R.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>    &#8627 PiTRS</pre><pre>      &#8627 DependencyPairsProof</pre><pre>        &#8627 PiDP</pre><pre>          &#8627 DependencyGraphProof</pre><pre>            &#8627 AND</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 PiDP</pre><pre>                &#8627 UsableRulesProof</pre><pre>                  &#8627 <B>PiDP</B></pre><pre>                    &#8627 PiDPToQDPProof</pre><BR>Pi DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>X</font>), <FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Y</font>), <FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>X</font>, <FONT COLOR=#cc0000>Y</font>, <FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>The argument filtering Pi contains the following mapping:<BR><FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)&#160; = &#160;<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>x1</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x1</font>, <FONT COLOR=#cc0000>x2</font>, <FONT COLOR=#cc0000>x3</font>)&#160; = &#160;<FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>x3</font>)<BR>
<BR>We have to consider all (P,R,Pi)-chains<BR>Transforming (infinitary) constructor rewriting Pi-DP problem [30] into ordinary QDP problem [15] by application of Pi.<BR><BR><pre>&#8627 Prolog</pre><pre>  &#8627 PrologToPiTRSProof</pre><pre>    &#8627 PiTRS</pre><pre>      &#8627 DependencyPairsProof</pre><pre>        &#8627 PiDP</pre><pre>          &#8627 DependencyGraphProof</pre><pre>            &#8627 AND</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 PiDP</pre><pre>              &#8627 PiDP</pre><pre>                &#8627 UsableRulesProof</pre><pre>                  &#8627 PiDP</pre><pre>                    &#8627 PiDPToQDPProof</pre><pre>                      &#8627 <B>QDP</B></pre><pre>                        &#8627 QDPSizeChangeProof</pre><BR>Q DP problem:<BR>The TRS P consists of the following rules:<BR><BLOCKQUOTE><BR><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)
<BR><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)</BLOCKQUOTE><BR>R is empty.<BR>Q is empty.<BR>We have to consider all (P,Q,R)-chains.<BR>By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. <P>From the DPs we obtained the following set of size-change graphs:
<UL><LI><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 >= 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDY_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 >= 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 >= 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDX_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 >= 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDY_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>) &#8594; <FONT COLOR=#0000cc>ADDZ_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 >= 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>one</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDC_IN_AAG</font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI>
<LI><FONT COLOR=#0000cc>ADDC_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#0000cc>zero</font>(<FONT COLOR=#cc0000>Z</font>)) &#8594; <FONT COLOR=#0000cc>ADDX_IN_AAG<SUP>1</SUP></font>(<FONT COLOR=#cc0000>Z</font>)<BR>The graph contains the following edges 1 > 1<P></LI></UL><BR><BR></body>

