Left Termination proof of /tmp/tmpP6xYFX/binary4.pl

Left Termination of the query pattern times_in_3(a, a, g) w.r.t. the given Prolog program could not be shown:

0 Prolog

↳1 PrologToDTProblemTransformerProof (⇐)

↳2 TRIPLES

↳3 TriplesToPiDPProof (⇐)

↳4 PiDP

↳5 DependencyGraphProof (⇔)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇔)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇔)

        ↳18 QDP

        ↳19 QDPSizeChangeProof (⇔)

        ↳20 YES

    ↳21 PiDP

        ↳22 UsableRulesProof (⇔)

        ↳23 PiDP

        ↳24 PiDPToQDPProof (⇔)

        ↳25 QDP

        ↳26 QDPSizeChangeProof (⇔)

        ↳27 YES

    ↳28 PiDP

        ↳29 UsableRulesProof (⇔)

        ↳30 PiDP

        ↳31 PiDPToQDPProof (⇐)

        ↳32 QDP

        ↳33 QDPSizeChangeProof (⇔)

        ↳34 YES

    ↳35 PiDP

        ↳36 UsableRulesProof (⇔)

        ↳37 PiDP

        ↳38 PiDPToQDPProof (⇐)

        ↳39 QDP

        ↳40 QDPSizeChangeProof (⇔)

        ↳41 YES

    ↳42 PiDP

        ↳43 UsableRulesProof (⇔)

        ↳44 PiDP

        ↳45 PiDPToQDPProof (⇐)

        ↳46 QDP

        ↳47 NonTerminationProof (⇔)

        ↳48 NO

    ↳49 PiDP

        ↳50 UsableRulesProof (⇔)

        ↳51 PiDP

        ↳52 PiDPToQDPProof (⇐)

        ↳53 QDP

        ↳54 NonTerminationProof (⇔)

        ↳55 NO

    ↳56 PiDP

        ↳57 UsableRulesProof (⇔)

        ↳58 PiDP

        ↳59 PiDPToQDPProof (⇐)

        ↳60 QDP

        ↳61 NonTerminationProof (⇔)

        ↳62 NO

    ↳63 PiDP

        ↳64 UsableRulesProof (⇔)

        ↳65 PiDP

        ↳66 PiDPToQDPProof (⇐)

        ↳67 QDP

        ↳68 NonTerminationProof (⇔)

        ↳69 NO

    ↳70 PiDP

        ↳71 UsableRulesProof (⇔)

        ↳72 PiDP

        ↳73 PiDPToQDPProof (⇐)

        ↳74 QDP

        ↳75 QDPSizeChangeProof (⇔)

        ↳76 YES

(0) Obligation:

Clauses:

add(b, b, b).
add(X, b, X) :- binaryZ(X).
add(b, Y, Y) :- binaryZ(Y).
add(X, Y, Z) :- addz(X, Y, Z).
addx(one(X), b, one(X)) :- binary(X).
addx(zero(X), b, zero(X)) :- binaryZ(X).
addx(X, Y, Z) :- addz(X, Y, Z).
addy(b, one(Y), one(Y)) :- binary(Y).
addy(b, zero(Y), zero(Y)) :- binaryZ(Y).
addy(X, Y, Z) :- addz(X, Y, Z).
addz(zero(X), zero(Y), zero(Z)) :- addz(X, Y, Z).
addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z).
addz(one(X), zero(Y), one(Z)) :- addy(X, Y, Z).
addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z).
addc(b, b, one(b)).
addc(X, b, Z) :- succZ(X, Z).
addc(b, Y, Z) :- succZ(Y, Z).
addc(X, Y, Z) :- addC(X, Y, Z).
addX(zero(X), b, one(X)) :- binaryZ(X).
addX(one(X), b, zero(Z)) :- succ(X, Z).
addX(X, Y, Z) :- addC(X, Y, Z).
addY(b, zero(Y), one(Y)) :- binaryZ(Y).
addY(b, one(Y), zero(Z)) :- succ(Y, Z).
addY(X, Y, Z) :- addC(X, Y, Z).
addC(zero(X), zero(Y), one(Z)) :- addz(X, Y, Z).
addC(zero(X), one(Y), zero(Z)) :- addX(X, Y, Z).
addC(one(X), zero(Y), zero(Z)) :- addY(X, Y, Z).
addC(one(X), one(Y), one(Z)) :- addc(X, Y, Z).
binary(b).
binary(zero(X)) :- binaryZ(X).
binary(one(X)) :- binary(X).
binaryZ(zero(X)) :- binaryZ(X).
binaryZ(one(X)) :- binary(X).
succ(b, one(b)).
succ(zero(X), one(X)) :- binaryZ(X).
succ(one(X), zero(Z)) :- succ(X, Z).
succZ(zero(X), one(X)) :- binaryZ(X).
succZ(one(X), zero(Z)) :- succ(X, Z).
times(one(b), X, X).
times(zero(R), S, zero(RS)) :- times(R, S, RS).
times(one(R), S, RSS) :- ','(times(R, S, RS), add(S, zero(RS), RSS)).

Queries:

times(a,a,g).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: times(T1, T2, T3)\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: times(T1, T2, T3), SCOPE: 1, CLAUSE: 38 | times(T1, T2, T3), SCOPE: 1, CLAUSE: 39 | times(T1, T2, T3), SCOPE: 1, CLAUSE: 40\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | times(T1, T2, T5), SCOPE: 1, CLAUSE: 39 | times(T1, T2, T5), SCOPE: 1, CLAUSE: 40\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: times(T1, T2, T3), SCOPE: 1, CLAUSE: 39 | times(T1, T2, T3), SCOPE: 1, CLAUSE: 40\n\nT3 is ground\ntimes(T1, T2, T3) !=? times(one(b), X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: times(T1, T2, T5), SCOPE: 1, CLAUSE: 39 | times(T1, T2, T5), SCOPE: 1, CLAUSE: 40\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: times(T12, T13, T11) | times(T1, T2, zero(T11)), SCOPE: 1, CLAUSE: 40\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: times(T1, T2, T5), SCOPE: 1, CLAUSE: 40\n\nT5 is ground\ntimes(T1, T2, T5) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: times(T12, T13, T11), SCOPE: 2, CLAUSE: 38 | times(T12, T13, T11), SCOPE: 2, CLAUSE: 39 | times(T12, T13, T11), SCOPE: 2, CLAUSE: 40 | ?_2 | times(T1, T2, zero(T11)), SCOPE: 1, CLAUSE: 40\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: times(T12, T13, T11), SCOPE: 2, CLAUSE: 38\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: times(T12, T13, T11), SCOPE: 2, CLAUSE: 39 | times(T12, T13, T11), SCOPE: 2, CLAUSE: 40 | ?_2 | times(T1, T2, zero(T11)), SCOPE: 1, CLAUSE: 40\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: times(T12, T13, T11), SCOPE: 2, CLAUSE: 39\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: times(T12, T13, T11), SCOPE: 2, CLAUSE: 40 | ?_2 | times(T1, T2, zero(T11)), SCOPE: 1, CLAUSE: 40\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: times(T34, T35, T33)\n\nT33 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: times(T12, T13, T11), SCOPE: 2, CLAUSE: 40\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ?_2 | times(T1, T2, zero(T11)), SCOPE: 1, CLAUSE: 40\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: ','(times(T53, T54, X56), add(T54, zero(X56), T52))\n\nT52 is ground\nX56 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: times(T53, T54, X56)\n\nX56 is free", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: add(T58, zero(T57), T52)\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: times(T53, T54, X56), SCOPE: 3, CLAUSE: 38 | times(T53, T54, X56), SCOPE: 3, CLAUSE: 39 | times(T53, T54, X56), SCOPE: 3, CLAUSE: 40\n\nX56 is free", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: times(T53, T54, X56), SCOPE: 3, CLAUSE: 38\n\nX56 is free", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: times(T53, T54, X56), SCOPE: 3, CLAUSE: 39 | times(T53, T54, X56), SCOPE: 3, CLAUSE: 40\n\nX56 is free", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: times(T53, T54, X56), SCOPE: 3, CLAUSE: 39\n\nX56 is free", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: times(T53, T54, X56), SCOPE: 3, CLAUSE: 40\n\nX56 is free", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: times(T76, T77, X89)\n\nX89 is free", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(times(T86, T87, X107), add(T87, zero(X107), X108))\n\nX108 is free\nX107 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: times(T86, T87, X107)\n\nX107 is free", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: add(T91, zero(T90), X108)\n\nX108 is free", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 0 | add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 1 | add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 2 | add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 3\n\nX108 is free", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 1 | add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 2 | add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 3\n\nX108 is free", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 2 | add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 3\n\nX108 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 2\n\nX108 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: add(T91, zero(T90), X108), SCOPE: 4, CLAUSE: 3\n\nX108 is free", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: binaryZ(zero(T102))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: binaryZ(zero(T102)), SCOPE: 5, CLAUSE: 31 | binaryZ(zero(T102)), SCOPE: 5, CLAUSE: 32\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: binaryZ(zero(T102)), SCOPE: 5, CLAUSE: 31\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: binaryZ(zero(T102)), SCOPE: 5, CLAUSE: 32\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: binaryZ(T113)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: binaryZ(T113), SCOPE: 6, CLAUSE: 31 | binaryZ(T113), SCOPE: 6, CLAUSE: 32\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: binaryZ(T113), SCOPE: 6, CLAUSE: 31\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: binaryZ(T113), SCOPE: 6, CLAUSE: 32\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: binaryZ(T120)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: binary(T125)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: binary(T125), SCOPE: 7, CLAUSE: 28 | binary(T125), SCOPE: 7, CLAUSE: 29 | binary(T125), SCOPE: 7, CLAUSE: 30\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: binary(T125), SCOPE: 7, CLAUSE: 28\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: binary(T125), SCOPE: 7, CLAUSE: 29 | binary(T125), SCOPE: 7, CLAUSE: 30\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: binary(T125), SCOPE: 7, CLAUSE: 29\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: binary(T125), SCOPE: 7, CLAUSE: 30\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: binaryZ(T131)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: binary(T136)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: addz(T147, zero(T148), X172)\n\nX172 is free", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 10 | addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 11 | addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 12 | addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 13\n\nX172 is free", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 10\n\nX172 is free", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 11 | addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 12 | addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 13\n\nX172 is free", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: addz(T161, T162, X196)\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: addz(T161, T162, X196), SCOPE: 9, CLAUSE: 10 | addz(T161, T162, X196), SCOPE: 9, CLAUSE: 11 | addz(T161, T162, X196), SCOPE: 9, CLAUSE: 12 | addz(T161, T162, X196), SCOPE: 9, CLAUSE: 13\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: addz(T161, T162, X196), SCOPE: 9, CLAUSE: 10\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: addz(T161, T162, X196), SCOPE: 9, CLAUSE: 11 | addz(T161, T162, X196), SCOPE: 9, CLAUSE: 12 | addz(T161, T162, X196), SCOPE: 9, CLAUSE: 13\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: addz(T175, T176, X223)\n\nX223 is free", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: addz(T161, T162, X196), SCOPE: 9, CLAUSE: 11\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: addz(T161, T162, X196), SCOPE: 9, CLAUSE: 12 | addz(T161, T162, X196), SCOPE: 9, CLAUSE: 13\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: addx(T189, T190, X250)\n\nX250 is free", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: addx(T189, T190, X250), SCOPE: 10, CLAUSE: 4 | addx(T189, T190, X250), SCOPE: 10, CLAUSE: 5 | addx(T189, T190, X250), SCOPE: 10, CLAUSE: 6\n\nX250 is free", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: addx(T189, T190, X250), SCOPE: 10, CLAUSE: 4\n\nX250 is free", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: addx(T189, T190, X250), SCOPE: 10, CLAUSE: 5 | addx(T189, T190, X250), SCOPE: 10, CLAUSE: 6\n\nX250 is free", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: binary(T197)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: addx(T189, T190, X250), SCOPE: 10, CLAUSE: 5\n\nX250 is free", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: addx(T189, T190, X250), SCOPE: 10, CLAUSE: 6\n\nX250 is free", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: binaryZ(T203)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: addz(T215, T216, X283)\n\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: addz(T161, T162, X196), SCOPE: 9, CLAUSE: 12\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: addz(T161, T162, X196), SCOPE: 9, CLAUSE: 13\n\nX196 is free", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: addy(T229, T230, X307)\n\nX307 is free", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: addy(T229, T230, X307), SCOPE: 11, CLAUSE: 7 | addy(T229, T230, X307), SCOPE: 11, CLAUSE: 8 | addy(T229, T230, X307), SCOPE: 11, CLAUSE: 9\n\nX307 is free", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: addy(T229, T230, X307), SCOPE: 11, CLAUSE: 7\n\nX307 is free", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: addy(T229, T230, X307), SCOPE: 11, CLAUSE: 8 | addy(T229, T230, X307), SCOPE: 11, CLAUSE: 9\n\nX307 is free", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: binary(T237)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: addy(T229, T230, X307), SCOPE: 11, CLAUSE: 8\n\nX307 is free", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: addy(T229, T230, X307), SCOPE: 11, CLAUSE: 9\n\nX307 is free", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: binaryZ(T243)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: addz(T255, T256, X340)\n\nX340 is free", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: addc(T265, T266, X356)\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: addc(T265, T266, X356), SCOPE: 12, CLAUSE: 14 | addc(T265, T266, X356), SCOPE: 12, CLAUSE: 15 | addc(T265, T266, X356), SCOPE: 12, CLAUSE: 16 | addc(T265, T266, X356), SCOPE: 12, CLAUSE: 17\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: addc(T265, T266, X356), SCOPE: 12, CLAUSE: 14\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: addc(T265, T266, X356), SCOPE: 12, CLAUSE: 15 | addc(T265, T266, X356), SCOPE: 12, CLAUSE: 16 | addc(T265, T266, X356), SCOPE: 12, CLAUSE: 17\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: addc(T265, T266, X356), SCOPE: 12, CLAUSE: 15\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: addc(T265, T266, X356), SCOPE: 12, CLAUSE: 16 | addc(T265, T266, X356), SCOPE: 12, CLAUSE: 17\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: succZ(T272, X374)\n\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: succZ(T272, X374), SCOPE: 13, CLAUSE: 36 | succZ(T272, X374), SCOPE: 13, CLAUSE: 37\n\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: succZ(T272, X374), SCOPE: 13, CLAUSE: 36\n\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: succZ(T272, X374), SCOPE: 13, CLAUSE: 37\n\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: binaryZ(T279)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: succ(T284, X393)\n\nX393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: succ(T284, X393), SCOPE: 14, CLAUSE: 33 | succ(T284, X393), SCOPE: 14, CLAUSE: 34 | succ(T284, X393), SCOPE: 14, CLAUSE: 35\n\nX393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: succ(T284, X393), SCOPE: 14, CLAUSE: 33\n\nX393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: succ(T284, X393), SCOPE: 14, CLAUSE: 34 | succ(T284, X393), SCOPE: 14, CLAUSE: 35\n\nX393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: succ(T284, X393), SCOPE: 14, CLAUSE: 34\n\nX393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: succ(T284, X393), SCOPE: 14, CLAUSE: 35\n\nX393 is free", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: binaryZ(T290)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: succ(T295, X411)\n\nX411 is free", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: addc(T265, T266, X356), SCOPE: 12, CLAUSE: 16\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: addc(T265, T266, X356), SCOPE: 12, CLAUSE: 17\n\nX356 is free", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: succZ(T301, X428)\n\nX428 is free", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: addC(T313, T314, X447)\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: addC(T313, T314, X447), SCOPE: 15, CLAUSE: 24 | addC(T313, T314, X447), SCOPE: 15, CLAUSE: 25 | addC(T313, T314, X447), SCOPE: 15, CLAUSE: 26 | addC(T313, T314, X447), SCOPE: 15, CLAUSE: 27\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: addC(T313, T314, X447), SCOPE: 15, CLAUSE: 24\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: addC(T313, T314, X447), SCOPE: 15, CLAUSE: 25 | addC(T313, T314, X447), SCOPE: 15, CLAUSE: 26 | addC(T313, T314, X447), SCOPE: 15, CLAUSE: 27\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: addz(T327, T328, X471)\n\nX471 is free", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: addC(T313, T314, X447), SCOPE: 15, CLAUSE: 25\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: addC(T313, T314, X447), SCOPE: 15, CLAUSE: 26 | addC(T313, T314, X447), SCOPE: 15, CLAUSE: 27\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: addX(T341, T342, X498)\n\nX498 is free", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: addX(T341, T342, X498), SCOPE: 16, CLAUSE: 18 | addX(T341, T342, X498), SCOPE: 16, CLAUSE: 19 | addX(T341, T342, X498), SCOPE: 16, CLAUSE: 20\n\nX498 is free", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: addX(T341, T342, X498), SCOPE: 16, CLAUSE: 18\n\nX498 is free", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: addX(T341, T342, X498), SCOPE: 16, CLAUSE: 19 | addX(T341, T342, X498), SCOPE: 16, CLAUSE: 20\n\nX498 is free", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: binaryZ(T349)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: addX(T341, T342, X498), SCOPE: 16, CLAUSE: 19\n\nX498 is free", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: addX(T341, T342, X498), SCOPE: 16, CLAUSE: 20\n\nX498 is free", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: succ(T356, X524)\n\nX524 is free", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: addC(T367, T368, X542)\n\nX542 is free", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: addC(T313, T314, X447), SCOPE: 15, CLAUSE: 26\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: addC(T313, T314, X447), SCOPE: 15, CLAUSE: 27\n\nX447 is free", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: addY(T381, T382, X566)\n\nX566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: addY(T381, T382, X566), SCOPE: 17, CLAUSE: 21 | addY(T381, T382, X566), SCOPE: 17, CLAUSE: 22 | addY(T381, T382, X566), SCOPE: 17, CLAUSE: 23\n\nX566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: addY(T381, T382, X566), SCOPE: 17, CLAUSE: 21\n\nX566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: addY(T381, T382, X566), SCOPE: 17, CLAUSE: 22 | addY(T381, T382, X566), SCOPE: 17, CLAUSE: 23\n\nX566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: binaryZ(T389)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: addY(T381, T382, X566), SCOPE: 17, CLAUSE: 22\n\nX566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: addY(T381, T382, X566), SCOPE: 17, CLAUSE: 23\n\nX566 is free", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: succ(T396, X592)\n\nX592 is free", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: addC(T407, T408, X610)\n\nX610 is free", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: addc(T417, T418, X626)\n\nX626 is free", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 12 | addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 13\n\nX172 is free", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 12\n\nX172 is free", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: addz(T147, zero(T148), X172), SCOPE: 8, CLAUSE: 13\n\nX172 is free", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: addy(T430, T431, X652)\n\nX652 is free", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 0 | add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 1 | add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 2 | add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 3\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 1 | add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 2 | add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 3\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 2 | add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 3\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 2\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: add(T58, zero(T57), T52), SCOPE: 18, CLAUSE: 3\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: binaryZ(zero(T441))\n\nT441 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: addz(T457, zero(T458), T456)\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 10 | addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 11 | addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 12 | addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 13\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 10\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 11 | addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 12 | addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 13\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: addz(T477, T478, T476)\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: addz(T477, T478, T476), SCOPE: 20, CLAUSE: 10 | addz(T477, T478, T476), SCOPE: 20, CLAUSE: 11 | addz(T477, T478, T476), SCOPE: 20, CLAUSE: 12 | addz(T477, T478, T476), SCOPE: 20, CLAUSE: 13\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: addz(T477, T478, T476), SCOPE: 20, CLAUSE: 10\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: addz(T477, T478, T476), SCOPE: 20, CLAUSE: 11 | addz(T477, T478, T476), SCOPE: 20, CLAUSE: 12 | addz(T477, T478, T476), SCOPE: 20, CLAUSE: 13\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: addz(T497, T498, T496)\n\nT496 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: addz(T477, T478, T476), SCOPE: 20, CLAUSE: 11\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: addz(T477, T478, T476), SCOPE: 20, CLAUSE: 12 | addz(T477, T478, T476), SCOPE: 20, CLAUSE: 13\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: addx(T517, T518, T516)\n\nT516 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: addx(T517, T518, T516), SCOPE: 21, CLAUSE: 4 | addx(T517, T518, T516), SCOPE: 21, CLAUSE: 5 | addx(T517, T518, T516), SCOPE: 21, CLAUSE: 6\n\nT516 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: addx(T517, T518, T516), SCOPE: 21, CLAUSE: 4\n\nT516 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: addx(T517, T518, T516), SCOPE: 21, CLAUSE: 5 | addx(T517, T518, T516), SCOPE: 21, CLAUSE: 6\n\nT516 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: binary(T524)\n\nT524 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: addx(T517, T518, T516), SCOPE: 21, CLAUSE: 5\n\nT516 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: addx(T517, T518, T516), SCOPE: 21, CLAUSE: 6\n\nT516 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: binaryZ(T529)\n\nT529 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: addz(T545, T546, T544)\n\nT544 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: addz(T477, T478, T476), SCOPE: 20, CLAUSE: 12\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: addz(T477, T478, T476), SCOPE: 20, CLAUSE: 13\n\nT476 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: addy(T565, T566, T564)\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: addy(T565, T566, T564), SCOPE: 22, CLAUSE: 7 | addy(T565, T566, T564), SCOPE: 22, CLAUSE: 8 | addy(T565, T566, T564), SCOPE: 22, CLAUSE: 9\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: addy(T565, T566, T564), SCOPE: 22, CLAUSE: 7\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: addy(T565, T566, T564), SCOPE: 22, CLAUSE: 8 | addy(T565, T566, T564), SCOPE: 22, CLAUSE: 9\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: binary(T572)\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: addy(T565, T566, T564), SCOPE: 22, CLAUSE: 8\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: addy(T565, T566, T564), SCOPE: 22, CLAUSE: 9\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: binaryZ(T577)\n\nT577 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: addz(T593, T594, T592)\n\nT592 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: addc(T607, T608, T606)\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: addc(T607, T608, T606), SCOPE: 23, CLAUSE: 14 | addc(T607, T608, T606), SCOPE: 23, CLAUSE: 15 | addc(T607, T608, T606), SCOPE: 23, CLAUSE: 16 | addc(T607, T608, T606), SCOPE: 23, CLAUSE: 17\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: addc(T607, T608, T606), SCOPE: 23, CLAUSE: 14\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: addc(T607, T608, T606), SCOPE: 23, CLAUSE: 15 | addc(T607, T608, T606), SCOPE: 23, CLAUSE: 16 | addc(T607, T608, T606), SCOPE: 23, CLAUSE: 17\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: addc(T607, T608, T606), SCOPE: 23, CLAUSE: 15\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: addc(T607, T608, T606), SCOPE: 23, CLAUSE: 16 | addc(T607, T608, T606), SCOPE: 23, CLAUSE: 17\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: succZ(T619, T618)\n\nT618 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: succZ(T619, T618), SCOPE: 24, CLAUSE: 36 | succZ(T619, T618), SCOPE: 24, CLAUSE: 37\n\nT618 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: succZ(T619, T618), SCOPE: 24, CLAUSE: 36\n\nT618 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: succZ(T619, T618), SCOPE: 24, CLAUSE: 37\n\nT618 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: binaryZ(T625)\n\nT625 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: succ(T633, T632)\n\nT632 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: succ(T633, T632), SCOPE: 25, CLAUSE: 33 | succ(T633, T632), SCOPE: 25, CLAUSE: 34 | succ(T633, T632), SCOPE: 25, CLAUSE: 35\n\nT632 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: succ(T633, T632), SCOPE: 25, CLAUSE: 33\n\nT632 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: succ(T633, T632), SCOPE: 25, CLAUSE: 34 | succ(T633, T632), SCOPE: 25, CLAUSE: 35\n\nT632 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: succ(T633, T632), SCOPE: 25, CLAUSE: 34\n\nT632 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: succ(T633, T632), SCOPE: 25, CLAUSE: 35\n\nT632 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: binaryZ(T638)\n\nT638 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: succ(T646, T645)\n\nT645 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: addc(T607, T608, T606), SCOPE: 23, CLAUSE: 16\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: addc(T607, T608, T606), SCOPE: 23, CLAUSE: 17\n\nT606 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: succZ(T657, T656)\n\nT656 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: addC(T673, T674, T672)\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: addC(T673, T674, T672), SCOPE: 26, CLAUSE: 24 | addC(T673, T674, T672), SCOPE: 26, CLAUSE: 25 | addC(T673, T674, T672), SCOPE: 26, CLAUSE: 26 | addC(T673, T674, T672), SCOPE: 26, CLAUSE: 27\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: addC(T673, T674, T672), SCOPE: 26, CLAUSE: 24\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: addC(T673, T674, T672), SCOPE: 26, CLAUSE: 25 | addC(T673, T674, T672), SCOPE: 26, CLAUSE: 26 | addC(T673, T674, T672), SCOPE: 26, CLAUSE: 27\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: addz(T693, T694, T692)\n\nT692 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: addC(T673, T674, T672), SCOPE: 26, CLAUSE: 25\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: addC(T673, T674, T672), SCOPE: 26, CLAUSE: 26 | addC(T673, T674, T672), SCOPE: 26, CLAUSE: 27\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: addX(T713, T714, T712)\n\nT712 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: addX(T713, T714, T712), SCOPE: 27, CLAUSE: 18 | addX(T713, T714, T712), SCOPE: 27, CLAUSE: 19 | addX(T713, T714, T712), SCOPE: 27, CLAUSE: 20\n\nT712 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: addX(T713, T714, T712), SCOPE: 27, CLAUSE: 18\n\nT712 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: addX(T713, T714, T712), SCOPE: 27, CLAUSE: 19 | addX(T713, T714, T712), SCOPE: 27, CLAUSE: 20\n\nT712 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: binaryZ(T720)\n\nT720 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: addX(T713, T714, T712), SCOPE: 27, CLAUSE: 19\n\nT712 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: addX(T713, T714, T712), SCOPE: 27, CLAUSE: 20\n\nT712 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: succ(T732, T731)\n\nT731 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: addC(T747, T748, T746)\n\nT746 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: addC(T673, T674, T672), SCOPE: 26, CLAUSE: 26\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: addC(T673, T674, T672), SCOPE: 26, CLAUSE: 27\n\nT672 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: addY(T767, T768, T766)\n\nT766 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: addY(T767, T768, T766), SCOPE: 28, CLAUSE: 21 | addY(T767, T768, T766), SCOPE: 28, CLAUSE: 22 | addY(T767, T768, T766), SCOPE: 28, CLAUSE: 23\n\nT766 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: addY(T767, T768, T766), SCOPE: 28, CLAUSE: 21\n\nT766 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: addY(T767, T768, T766), SCOPE: 28, CLAUSE: 22 | addY(T767, T768, T766), SCOPE: 28, CLAUSE: 23\n\nT766 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: binaryZ(T774)\n\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: addY(T767, T768, T766), SCOPE: 28, CLAUSE: 22\n\nT766 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: addY(T767, T768, T766), SCOPE: 28, CLAUSE: 23\n\nT766 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: succ(T786, T785)\n\nT785 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: addC(T801, T802, T800)\n\nT800 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: addc(T815, T816, T814)\n\nT814 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 12 | addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 13\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 12\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: addz(T457, zero(T458), T456), SCOPE: 19, CLAUSE: 13\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: addy(T833, T834, T832)\n\nT832 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: times(T1, T2, zero(T11)), SCOPE: 1, CLAUSE: 40\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: ','(times(T846, T847, X1078), add(T847, zero(X1078), zero(T845)))\n\nT845 is ground\nX1078 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: ','(times(T856, T857, X1090), add(T857, zero(X1090), T855))\n\nT855 is ground\nX1090 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="312: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 38 | ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 39 | ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 40\n\nT855 is ground\nX1090 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 38\n\nT855 is ground\nX1090 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 39 | ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 40\n\nT855 is ground\nX1090 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: add(T863, zero(T863), T855)\n\nT855 is ground\ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 39\n\nT855 is ground\nX1090 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: ','(times(T856, T857, X1090), add(T857, zero(X1090), T855)), SCOPE: 29, CLAUSE: 40\n\nT855 is ground\nX1090 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: ','(times(T875, T876, X1121), add(T876, zero(zero(X1121)), T855))\n\nT855 is ground\nX1121 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: times(T875, T876, X1121)\n\nX1121 is free", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: add(T880, zero(zero(T879)), T855)\n\nT855 is ground\ntimes(T881, T882, T855) !=? times(zero(T883), T884, zero(T885))", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: ','(times(T896, T897, X1143), ','(add(T897, zero(X1143), X1144), add(T897, zero(X1144), T855)))\n\nT855 is ground\nX1144 is free; \nX1143 is free; \ntimes(T1, T2, T855) !=? times(zero(X7), X8, zero(X9))", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
326 [label="326: times(T896, T897, X1143)\n\nX1143 is free", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: ','(add(T901, zero(T900), X1144), add(T901, zero(X1144), T855))\n\nT855 is ground\nX1144 is free; \ntimes(T902, T903, T855) !=? times(zero(T904), T905, zero(T906))", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: add(T901, zero(T900), X1144)\n\nX1144 is free", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: add(T912, zero(T911), T855)\n\nT855 is ground\nT912 is ground\nT911 is ground\ntimes(T913, T914, T855) !=? times(zero(T915), T916, zero(T917))", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: times(T928, T929, T927) | times(T1, T2, zero(T927)), SCOPE: 1, CLAUSE: 40\n\nT927 is ground\ntimes(T1, T2, zero(T927)) !=? times(one(b), X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: times(T1, T2, T3), SCOPE: 1, CLAUSE: 40\n\nT3 is ground\ntimes(T1, T2, T3) !=? times(one(b), X2, X2)\ntimes(T1, T2, T3) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: times(T928, T929, T927), SCOPE: 30, CLAUSE: 38 | times(T928, T929, T927), SCOPE: 30, CLAUSE: 39 | times(T928, T929, T927), SCOPE: 30, CLAUSE: 40 | ?_30 | times(T1, T2, zero(T927)), SCOPE: 1, CLAUSE: 40\n\nT927 is ground\ntimes(T1, T2, zero(T927)) !=? times(one(b), X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: times(T928, T929, T927), SCOPE: 30, CLAUSE: 38\n\nT927 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: times(T928, T929, T927), SCOPE: 30, CLAUSE: 39 | times(T928, T929, T927), SCOPE: 30, CLAUSE: 40 | ?_30 | times(T1, T2, zero(T927)), SCOPE: 1, CLAUSE: 40\n\nT927 is ground\ntimes(T1, T2, zero(T927)) !=? times(one(b), X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="335: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="336: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
337 [label="337: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: times(T928, T929, T927), SCOPE: 30, CLAUSE: 39\n\nT927 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: times(T928, T929, T927), SCOPE: 30, CLAUSE: 40 | ?_30 | times(T1, T2, zero(T927)), SCOPE: 1, CLAUSE: 40\n\nT927 is ground\ntimes(T1, T2, zero(T927)) !=? times(one(b), X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: times(T950, T951, T949)\n\nT949 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: times(T928, T929, T927), SCOPE: 30, CLAUSE: 40\n\nT927 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: ?_30 | times(T1, T2, zero(T927)), SCOPE: 1, CLAUSE: 40\n\nT927 is ground\ntimes(T1, T2, zero(T927)) !=? times(one(b), X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: ','(times(T969, T970, X1210), add(T970, zero(X1210), T968))\n\nT968 is ground\nX1210 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
345 [label="345: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
346 [label="346: times(T1, T2, zero(T927)), SCOPE: 1, CLAUSE: 40\n\nT927 is ground\ntimes(T1, T2, zero(T927)) !=? times(one(b), X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
347 [label="347: ','(times(T982, T983, X1226), add(T983, zero(X1226), zero(T981)))\n\nT981 is ground\nX1226 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: ','(times(T992, T993, X1238), add(T993, zero(X1238), T991))\n\nT991 is ground\nX1238 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="350: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
351 [label="351: ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 38 | ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 39 | ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 40\n\nT991 is ground\nX1238 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 38\n\nT991 is ground\nX1238 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
353 [label="353: ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 39 | ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 40\n\nT991 is ground\nX1238 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
354 [label="354: add(T999, zero(T999), T991)\n\nT991 is ground\ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
356 [label="356: ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 39\n\nT991 is ground\nX1238 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: ','(times(T992, T993, X1238), add(T993, zero(X1238), T991)), SCOPE: 31, CLAUSE: 40\n\nT991 is ground\nX1238 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: ','(times(T1011, T1012, X1269), add(T1012, zero(zero(X1269)), T991))\n\nT991 is ground\nX1269 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="359: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
360 [label="360: ','(times(T1021, T1022, X1287), ','(add(T1022, zero(X1287), X1288), add(T1022, zero(X1288), T991)))\n\nT991 is ground\nX1288 is free; \nX1287 is free; \ntimes(T1, T2, T991) !=? times(one(b), X2, X2)\ntimes(T1, T2, T991) !=? times(zero(X1161), X1162, zero(X1163))", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 362 [arrowhead = none ];
362 -> 2;

363 [label="EVAL with clause\ntimes(one(b), X2, X2).\nand substitution\nT1 -> one(b)\nT2 -> T5\nX2 -> T5\nT3 -> T5", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 363 [arrowhead = none ];
363 -> 3;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 364 [arrowhead = none ];
364 -> 4;

365 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 365 [arrowhead = none ];
365 -> 5;

366 [label="EVAL with clause\ntimes(zero(X1161), X1162, zero(X1163)) :- times(X1161, X1162, X1163).\nand substitution\nX1161 -> T928\nT1 -> zero(T928)\nT2 -> T929\nX1162 -> T929\nX1163 -> T927\nT3 -> zero(T927)\nT925 -> T928\nT926 -> T929", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 366 [arrowhead = none ];
366 -> 330;

367 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 367 [arrowhead = none ];
367 -> 331;

368 [label="EVAL with clause\ntimes(zero(X7), X8, zero(X9)) :- times(X7, X8, X9).\nand substitution\nX7 -> T12\nT1 -> zero(T12)\nT2 -> T13\nX8 -> T13\nX9 -> T11\nT5 -> zero(T11)\nT9 -> T12\nT10 -> T13", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 368 [arrowhead = none ];
368 -> 6;

369 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 369 [arrowhead = none ];
369 -> 7;

370 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
6 -> 370 [arrowhead = none ];
370 -> 8;

371 [label="EVAL with clause\ntimes(one(X1087), X1088, X1089) :- ','(times(X1087, X1088, X1090), add(X1088, zero(X1090), X1089)).\nand substitution\nX1087 -> T856\nT1 -> one(T856)\nT2 -> T857\nX1088 -> T857\nT5 -> T855\nX1089 -> T855\nT853 -> T856\nT854 -> T857", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 371 [arrowhead = none ];
371 -> 311;

372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 372 [arrowhead = none ];
372 -> 312;

373 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 373 [arrowhead = none ];
373 -> 9;

374 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 374 [arrowhead = none ];
374 -> 10;

375 [label="EVAL with clause\ntimes(one(b), X17, X17).\nand substitution\nT12 -> one(b)\nT13 -> T18\nX17 -> T18\nT11 -> T18", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 375 [arrowhead = none ];
375 -> 11;

376 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 376 [arrowhead = none ];
376 -> 12;

377 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 377 [arrowhead = none ];
377 -> 14;

378 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 378 [arrowhead = none ];
378 -> 15;

379 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 379 [arrowhead = none ];
379 -> 13;

380 [label="EVAL with clause\ntimes(zero(X31), X32, zero(X33)) :- times(X31, X32, X33).\nand substitution\nX31 -> T34\nT12 -> zero(T34)\nT13 -> T35\nX32 -> T35\nX33 -> T33\nT11 -> zero(T33)\nT31 -> T34\nT32 -> T35", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 380 [arrowhead = none ];
380 -> 16;

381 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 381 [arrowhead = none ];
381 -> 17;

382 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 382 [arrowhead = none ];
382 -> 18;

383 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 383 [arrowhead = none ];
383 -> 19;

384 [label="INSTANCE with matching:\nT1 -> T34\nT2 -> T35\nT3 -> T33", fontsize=14, style = filled, fillcolor = lightgrey];
16 -> 384 [arrowhead = none , style=dashed];
384 -> 1[style=dashed];

385 [label="EVAL with clause\ntimes(one(X53), X54, X55) :- ','(times(X53, X54, X56), add(X54, zero(X56), X55)).\nand substitution\nX53 -> T53\nT12 -> one(T53)\nT13 -> T54\nX54 -> T54\nT11 -> T52\nX55 -> T52\nT50 -> T53\nT51 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 385 [arrowhead = none ];
385 -> 20;

386 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
18 -> 386 [arrowhead = none ];
386 -> 21;

387 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 387 [arrowhead = none ];
387 -> 308;

388 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
20 -> 388 [arrowhead = none ];
388 -> 22;

389 [label="SPLIT 2\nnew knowledge:\nT53 is ground\nreplacements:\nX56 -> T57\nT54 -> T58", fontsize=14, style = filled, fillcolor = violet];
20 -> 389 [arrowhead = none ];
389 -> 23;

390 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 390 [arrowhead = none ];
390 -> 24;

391 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
23 -> 391 [arrowhead = none ];
391 -> 185;

392 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 392 [arrowhead = none ];
392 -> 25;

393 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 393 [arrowhead = none ];
393 -> 26;

394 [label="EVAL with clause\ntimes(one(b), X68, X68).\nand substitution\nT53 -> one(b)\nT54 -> T65\nX68 -> T65\nX56 -> T65", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 394 [arrowhead = none ];
394 -> 27;

395 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 395 [arrowhead = none ];
395 -> 28;

396 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 396 [arrowhead = none ];
396 -> 30;

397 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 397 [arrowhead = none ];
397 -> 31;

398 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 398 [arrowhead = none ];
398 -> 29;

399 [label="EVAL with clause\ntimes(zero(X86), X87, zero(X88)) :- times(X86, X87, X88).\nand substitution\nX86 -> T76\nT53 -> zero(T76)\nT54 -> T77\nX87 -> T77\nX88 -> X89\nX56 -> zero(X89)\nT74 -> T76\nT75 -> T77", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 399 [arrowhead = none ];
399 -> 32;

400 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 400 [arrowhead = none ];
400 -> 33;

401 [label="EVAL with clause\ntimes(one(X104), X105, X106) :- ','(times(X104, X105, X107), add(X105, zero(X107), X106)).\nand substitution\nX104 -> T86\nT53 -> one(T86)\nT54 -> T87\nX105 -> T87\nX56 -> X108\nX106 -> X108\nT84 -> T86\nT85 -> T87", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 401 [arrowhead = none ];
401 -> 34;

402 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 402 [arrowhead = none ];
402 -> 35;

403 [label="INSTANCE with matching:\nT53 -> T76\nT54 -> T77\nX56 -> X89", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 403 [arrowhead = none , style=dashed];
403 -> 22[style=dashed];

404 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
34 -> 404 [arrowhead = none ];
404 -> 36;

405 [label="SPLIT 2\nnew knowledge:\nT86 is ground\nreplacements:\nX107 -> T90\nT87 -> T91", fontsize=14, style = filled, fillcolor = violet];
34 -> 405 [arrowhead = none ];
405 -> 37;

406 [label="INSTANCE with matching:\nT53 -> T86\nT54 -> T87\nX56 -> X107", fontsize=14, style = filled, fillcolor = lightgrey];
36 -> 406 [arrowhead = none , style=dashed];
406 -> 22[style=dashed];

407 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
37 -> 407 [arrowhead = none ];
407 -> 38;

408 [label="BACKTRACK\nfor clause: add(b, b, b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
38 -> 408 [arrowhead = none ];
408 -> 39;

409 [label="BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
39 -> 409 [arrowhead = none ];
409 -> 40;

410 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 410 [arrowhead = none ];
410 -> 41;

411 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 411 [arrowhead = none ];
411 -> 42;

412 [label="EVAL with clause\nadd(b, X123, X123) :- binaryZ(X123).\nand substitution\nT91 -> b\nT90 -> T102\nX123 -> zero(T102)\nX108 -> zero(T102)\nT101 -> T102", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 412 [arrowhead = none ];
412 -> 43;

413 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 413 [arrowhead = none ];
413 -> 44;

414 [label="ONLY EVAL with clause\nadd(X169, X170, X171) :- addz(X169, X170, X171).\nand substitution\nT91 -> T147\nX169 -> T147\nT90 -> T148\nX170 -> zero(T148)\nX108 -> X172\nX171 -> X172\nT145 -> T147\nT146 -> T148", fontsize=14, style = filled, fillcolor = white];
42 -> 414 [arrowhead = none ];
414 -> 69;

415 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
43 -> 415 [arrowhead = none ];
415 -> 45;

416 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 416 [arrowhead = none ];
416 -> 46;

417 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 417 [arrowhead = none ];
417 -> 47;

418 [label="ONLY EVAL with clause\nbinaryZ(zero(X132)) :- binaryZ(X132).\nand substitution\nT102 -> T113\nX132 -> T113\nT112 -> T113", fontsize=14, style = filled, fillcolor = white];
46 -> 418 [arrowhead = none ];
418 -> 48;

419 [label="BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
47 -> 419 [arrowhead = none ];
419 -> 68;

420 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
48 -> 420 [arrowhead = none ];
420 -> 49;

421 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
49 -> 421 [arrowhead = none ];
421 -> 50;

422 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
49 -> 422 [arrowhead = none ];
422 -> 51;

423 [label="EVAL with clause\nbinaryZ(zero(X138)) :- binaryZ(X138).\nand substitution\nX138 -> T120\nT113 -> zero(T120)\nT119 -> T120", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 423 [arrowhead = none ];
423 -> 52;

424 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 424 [arrowhead = none ];
424 -> 53;

425 [label="EVAL with clause\nbinaryZ(one(X143)) :- binary(X143).\nand substitution\nX143 -> T125\nT113 -> one(T125)\nT124 -> T125", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 425 [arrowhead = none ];
425 -> 54;

426 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 426 [arrowhead = none ];
426 -> 55;

427 [label="INSTANCE with matching:\nT113 -> T120", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 427 [arrowhead = none , style=dashed];
427 -> 48[style=dashed];

428 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 428 [arrowhead = none ];
428 -> 56;

429 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 429 [arrowhead = none ];
429 -> 57;

430 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 430 [arrowhead = none ];
430 -> 58;

431 [label="EVAL with clause\nbinary(b).\nand substitution\nT125 -> b", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 431 [arrowhead = none ];
431 -> 59;

432 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 432 [arrowhead = none ];
432 -> 60;

433 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 433 [arrowhead = none ];
433 -> 62;

434 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 434 [arrowhead = none ];
434 -> 63;

435 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 435 [arrowhead = none ];
435 -> 61;

436 [label="EVAL with clause\nbinary(zero(X149)) :- binaryZ(X149).\nand substitution\nX149 -> T131\nT125 -> zero(T131)\nT130 -> T131", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 436 [arrowhead = none ];
436 -> 64;

437 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 437 [arrowhead = none ];
437 -> 65;

438 [label="EVAL with clause\nbinary(one(X154)) :- binary(X154).\nand substitution\nX154 -> T136\nT125 -> one(T136)\nT135 -> T136", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 438 [arrowhead = none ];
438 -> 66;

439 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 439 [arrowhead = none ];
439 -> 67;

440 [label="INSTANCE with matching:\nT113 -> T131", fontsize=14, style = filled, fillcolor = lightgrey];
64 -> 440 [arrowhead = none , style=dashed];
440 -> 48[style=dashed];

441 [label="INSTANCE with matching:\nT125 -> T136", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 441 [arrowhead = none , style=dashed];
441 -> 54[style=dashed];

442 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
69 -> 442 [arrowhead = none ];
442 -> 70;

443 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 443 [arrowhead = none ];
443 -> 71;

444 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 444 [arrowhead = none ];
444 -> 72;

445 [label="EVAL with clause\naddz(zero(X193), zero(X194), zero(X195)) :- addz(X193, X194, X195).\nand substitution\nX193 -> T161\nT147 -> zero(T161)\nT148 -> T162\nX194 -> T162\nX195 -> X196\nX172 -> zero(X196)\nT159 -> T161\nT160 -> T162", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 445 [arrowhead = none ];
445 -> 73;

446 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 446 [arrowhead = none ];
446 -> 74;

447 [label="BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = white];
72 -> 447 [arrowhead = none ];
447 -> 179;

448 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
73 -> 448 [arrowhead = none ];
448 -> 75;

449 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
75 -> 449 [arrowhead = none ];
449 -> 76;

450 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
75 -> 450 [arrowhead = none ];
450 -> 77;

451 [label="EVAL with clause\naddz(zero(X220), zero(X221), zero(X222)) :- addz(X220, X221, X222).\nand substitution\nX220 -> T175\nT161 -> zero(T175)\nX221 -> T176\nT162 -> zero(T176)\nX222 -> X223\nX196 -> zero(X223)\nT173 -> T175\nT174 -> T176", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 451 [arrowhead = none ];
451 -> 78;

452 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 452 [arrowhead = none ];
452 -> 79;

453 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 453 [arrowhead = none ];
453 -> 80;

454 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 454 [arrowhead = none ];
454 -> 81;

455 [label="INSTANCE with matching:\nT161 -> T175\nT162 -> T176\nX196 -> X223", fontsize=14, style = filled, fillcolor = lightgrey];
78 -> 455 [arrowhead = none , style=dashed];
455 -> 73[style=dashed];

456 [label="EVAL with clause\naddz(zero(X247), one(X248), one(X249)) :- addx(X247, X248, X249).\nand substitution\nX247 -> T189\nT161 -> zero(T189)\nX248 -> T190\nT162 -> one(T190)\nX249 -> X250\nX196 -> one(X250)\nT187 -> T189\nT188 -> T190", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 456 [arrowhead = none ];
456 -> 82;

457 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 457 [arrowhead = none ];
457 -> 83;

458 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 458 [arrowhead = none ];
458 -> 94;

459 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 459 [arrowhead = none ];
459 -> 95;

460 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
82 -> 460 [arrowhead = none ];
460 -> 84;

461 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 461 [arrowhead = none ];
461 -> 85;

462 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 462 [arrowhead = none ];
462 -> 86;

463 [label="EVAL with clause\naddx(one(X259), b, one(X259)) :- binary(X259).\nand substitution\nX259 -> T197\nT189 -> one(T197)\nT190 -> b\nX250 -> one(T197)\nT196 -> T197", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 463 [arrowhead = none ];
463 -> 87;

464 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 464 [arrowhead = none ];
464 -> 88;

465 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 465 [arrowhead = none ];
465 -> 89;

466 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 466 [arrowhead = none ];
466 -> 90;

467 [label="INSTANCE with matching:\nT125 -> T197", fontsize=14, style = filled, fillcolor = lightgrey];
87 -> 467 [arrowhead = none , style=dashed];
467 -> 54[style=dashed];

468 [label="EVAL with clause\naddx(zero(X265), b, zero(X265)) :- binaryZ(X265).\nand substitution\nX265 -> T203\nT189 -> zero(T203)\nT190 -> b\nX250 -> zero(T203)\nT202 -> T203", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 468 [arrowhead = none ];
468 -> 91;

469 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 469 [arrowhead = none ];
469 -> 92;

470 [label="ONLY EVAL with clause\naddx(X280, X281, X282) :- addz(X280, X281, X282).\nand substitution\nT189 -> T215\nX280 -> T215\nT190 -> T216\nX281 -> T216\nX250 -> X283\nX282 -> X283\nT213 -> T215\nT214 -> T216", fontsize=14, style = filled, fillcolor = white];
90 -> 470 [arrowhead = none ];
470 -> 93;

471 [label="INSTANCE with matching:\nT113 -> T203", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 471 [arrowhead = none , style=dashed];
471 -> 48[style=dashed];

472 [label="INSTANCE with matching:\nT161 -> T215\nT162 -> T216\nX196 -> X283", fontsize=14, style = filled, fillcolor = lightgrey];
93 -> 472 [arrowhead = none , style=dashed];
472 -> 73[style=dashed];

473 [label="EVAL with clause\naddz(one(X304), zero(X305), one(X306)) :- addy(X304, X305, X306).\nand substitution\nX304 -> T229\nT161 -> one(T229)\nX305 -> T230\nT162 -> zero(T230)\nX306 -> X307\nX196 -> one(X307)\nT227 -> T229\nT228 -> T230", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 473 [arrowhead = none ];
473 -> 96;

474 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 474 [arrowhead = none ];
474 -> 97;

475 [label="EVAL with clause\naddz(one(X353), one(X354), zero(X355)) :- addc(X353, X354, X355).\nand substitution\nX353 -> T265\nT161 -> one(T265)\nX354 -> T266\nT162 -> one(T266)\nX355 -> X356\nX196 -> zero(X356)\nT263 -> T265\nT264 -> T266", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 475 [arrowhead = none ];
475 -> 108;

476 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 476 [arrowhead = none ];
476 -> 109;

477 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
96 -> 477 [arrowhead = none ];
477 -> 98;

478 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 478 [arrowhead = none ];
478 -> 99;

479 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 479 [arrowhead = none ];
479 -> 100;

480 [label="EVAL with clause\naddy(b, one(X316), one(X316)) :- binary(X316).\nand substitution\nT229 -> b\nX316 -> T237\nT230 -> one(T237)\nX307 -> one(T237)\nT236 -> T237", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 480 [arrowhead = none ];
480 -> 101;

481 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 481 [arrowhead = none ];
481 -> 102;

482 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
100 -> 482 [arrowhead = none ];
482 -> 103;

483 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
100 -> 483 [arrowhead = none ];
483 -> 104;

484 [label="INSTANCE with matching:\nT125 -> T237", fontsize=14, style = filled, fillcolor = lightgrey];
101 -> 484 [arrowhead = none , style=dashed];
484 -> 54[style=dashed];

485 [label="EVAL with clause\naddy(b, zero(X322), zero(X322)) :- binaryZ(X322).\nand substitution\nT229 -> b\nX322 -> T243\nT230 -> zero(T243)\nX307 -> zero(T243)\nT242 -> T243", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 485 [arrowhead = none ];
485 -> 105;

486 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 486 [arrowhead = none ];
486 -> 106;

487 [label="ONLY EVAL with clause\naddy(X337, X338, X339) :- addz(X337, X338, X339).\nand substitution\nT229 -> T255\nX337 -> T255\nT230 -> T256\nX338 -> T256\nX307 -> X340\nX339 -> X340\nT253 -> T255\nT254 -> T256", fontsize=14, style = filled, fillcolor = white];
104 -> 487 [arrowhead = none ];
487 -> 107;

488 [label="INSTANCE with matching:\nT203 -> T243", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 488 [arrowhead = none , style=dashed];
488 -> 91[style=dashed];

489 [label="INSTANCE with matching:\nT161 -> T255\nT162 -> T256\nX196 -> X340", fontsize=14, style = filled, fillcolor = lightgrey];
107 -> 489 [arrowhead = none , style=dashed];
489 -> 73[style=dashed];

490 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
108 -> 490 [arrowhead = none ];
490 -> 110;

491 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
110 -> 491 [arrowhead = none ];
491 -> 111;

492 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
110 -> 492 [arrowhead = none ];
492 -> 112;

493 [label="EVAL with clause\naddc(b, b, one(b)).\nand substitution\nT265 -> b\nT266 -> b\nX356 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 493 [arrowhead = none ];
493 -> 113;

494 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 494 [arrowhead = none ];
494 -> 114;

495 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
112 -> 495 [arrowhead = none ];
495 -> 116;

496 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
112 -> 496 [arrowhead = none ];
496 -> 117;

497 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 497 [arrowhead = none ];
497 -> 115;

498 [label="EVAL with clause\naddc(X372, b, X373) :- succZ(X372, X373).\nand substitution\nT265 -> T272\nX372 -> T272\nT266 -> b\nX356 -> X374\nX373 -> X374\nT271 -> T272", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 498 [arrowhead = none ];
498 -> 118;

499 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 499 [arrowhead = none ];
499 -> 119;

500 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
117 -> 500 [arrowhead = none ];
500 -> 139;

501 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
117 -> 501 [arrowhead = none ];
501 -> 140;

502 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 502 [arrowhead = none ];
502 -> 120;

503 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
120 -> 503 [arrowhead = none ];
503 -> 121;

504 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
120 -> 504 [arrowhead = none ];
504 -> 122;

505 [label="EVAL with clause\nsuccZ(zero(X382), one(X382)) :- binaryZ(X382).\nand substitution\nX382 -> T279\nT272 -> zero(T279)\nX374 -> one(T279)\nT278 -> T279", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 505 [arrowhead = none ];
505 -> 123;

506 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 506 [arrowhead = none ];
506 -> 124;

507 [label="EVAL with clause\nsuccZ(one(X391), zero(X392)) :- succ(X391, X392).\nand substitution\nX391 -> T284\nT272 -> one(T284)\nX392 -> X393\nX374 -> zero(X393)\nT283 -> T284", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 507 [arrowhead = none ];
507 -> 125;

508 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 508 [arrowhead = none ];
508 -> 126;

509 [label="INSTANCE with matching:\nT203 -> T279", fontsize=14, style = filled, fillcolor = lightgrey];
123 -> 509 [arrowhead = none , style=dashed];
509 -> 91[style=dashed];

510 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 510 [arrowhead = none ];
510 -> 127;

511 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
127 -> 511 [arrowhead = none ];
511 -> 128;

512 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
127 -> 512 [arrowhead = none ];
512 -> 129;

513 [label="EVAL with clause\nsucc(b, one(b)).\nand substitution\nT284 -> b\nX393 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 513 [arrowhead = none ];
513 -> 130;

514 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 514 [arrowhead = none ];
514 -> 131;

515 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 515 [arrowhead = none ];
515 -> 133;

516 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 516 [arrowhead = none ];
516 -> 134;

517 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
130 -> 517 [arrowhead = none ];
517 -> 132;

518 [label="EVAL with clause\nsucc(zero(X400), one(X400)) :- binaryZ(X400).\nand substitution\nX400 -> T290\nT284 -> zero(T290)\nX393 -> one(T290)\nT289 -> T290", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 518 [arrowhead = none ];
518 -> 135;

519 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 519 [arrowhead = none ];
519 -> 136;

520 [label="EVAL with clause\nsucc(one(X409), zero(X410)) :- succ(X409, X410).\nand substitution\nX409 -> T295\nT284 -> one(T295)\nX410 -> X411\nX393 -> zero(X411)\nT294 -> T295", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 520 [arrowhead = none ];
520 -> 137;

521 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 521 [arrowhead = none ];
521 -> 138;

522 [label="INSTANCE with matching:\nT203 -> T290", fontsize=14, style = filled, fillcolor = lightgrey];
135 -> 522 [arrowhead = none , style=dashed];
522 -> 91[style=dashed];

523 [label="INSTANCE with matching:\nT284 -> T295\nX393 -> X411", fontsize=14, style = filled, fillcolor = lightgrey];
137 -> 523 [arrowhead = none , style=dashed];
523 -> 125[style=dashed];

524 [label="EVAL with clause\naddc(b, X426, X427) :- succZ(X426, X427).\nand substitution\nT265 -> b\nT266 -> T301\nX426 -> T301\nX356 -> X428\nX427 -> X428\nT300 -> T301", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 524 [arrowhead = none ];
524 -> 141;

525 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 525 [arrowhead = none ];
525 -> 142;

526 [label="ONLY EVAL with clause\naddc(X444, X445, X446) :- addC(X444, X445, X446).\nand substitution\nT265 -> T313\nX444 -> T313\nT266 -> T314\nX445 -> T314\nX356 -> X447\nX446 -> X447\nT311 -> T313\nT312 -> T314", fontsize=14, style = filled, fillcolor = white];
140 -> 526 [arrowhead = none ];
526 -> 143;

527 [label="INSTANCE with matching:\nT272 -> T301\nX374 -> X428", fontsize=14, style = filled, fillcolor = lightgrey];
141 -> 527 [arrowhead = none , style=dashed];
527 -> 118[style=dashed];

528 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
143 -> 528 [arrowhead = none ];
528 -> 144;

529 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
144 -> 529 [arrowhead = none ];
529 -> 145;

530 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
144 -> 530 [arrowhead = none ];
530 -> 146;

531 [label="EVAL with clause\naddC(zero(X468), zero(X469), one(X470)) :- addz(X468, X469, X470).\nand substitution\nX468 -> T327\nT313 -> zero(T327)\nX469 -> T328\nT314 -> zero(T328)\nX470 -> X471\nX447 -> one(X471)\nT325 -> T327\nT326 -> T328", fontsize=14, style = filled, fillcolor = lightblue];
145 -> 531 [arrowhead = none ];
531 -> 147;

532 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
145 -> 532 [arrowhead = none ];
532 -> 148;

533 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
146 -> 533 [arrowhead = none ];
533 -> 149;

534 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
146 -> 534 [arrowhead = none ];
534 -> 150;

535 [label="INSTANCE with matching:\nT161 -> T327\nT162 -> T328\nX196 -> X471", fontsize=14, style = filled, fillcolor = lightgrey];
147 -> 535 [arrowhead = none , style=dashed];
535 -> 73[style=dashed];

536 [label="EVAL with clause\naddC(zero(X495), one(X496), zero(X497)) :- addX(X495, X496, X497).\nand substitution\nX495 -> T341\nT313 -> zero(T341)\nX496 -> T342\nT314 -> one(T342)\nX497 -> X498\nX447 -> zero(X498)\nT339 -> T341\nT340 -> T342", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 536 [arrowhead = none ];
536 -> 151;

537 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 537 [arrowhead = none ];
537 -> 152;

538 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 538 [arrowhead = none ];
538 -> 163;

539 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 539 [arrowhead = none ];
539 -> 164;

540 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
151 -> 540 [arrowhead = none ];
540 -> 153;

541 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 541 [arrowhead = none ];
541 -> 154;

542 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 542 [arrowhead = none ];
542 -> 155;

543 [label="EVAL with clause\naddX(zero(X507), b, one(X507)) :- binaryZ(X507).\nand substitution\nX507 -> T349\nT341 -> zero(T349)\nT342 -> b\nX498 -> one(T349)\nT348 -> T349", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 543 [arrowhead = none ];
543 -> 156;

544 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 544 [arrowhead = none ];
544 -> 157;

545 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 545 [arrowhead = none ];
545 -> 158;

546 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 546 [arrowhead = none ];
546 -> 159;

547 [label="INSTANCE with matching:\nT203 -> T349", fontsize=14, style = filled, fillcolor = lightgrey];
156 -> 547 [arrowhead = none , style=dashed];
547 -> 91[style=dashed];

548 [label="EVAL with clause\naddX(one(X522), b, zero(X523)) :- succ(X522, X523).\nand substitution\nX522 -> T356\nT341 -> one(T356)\nT342 -> b\nX523 -> X524\nX498 -> zero(X524)\nT355 -> T356", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 548 [arrowhead = none ];
548 -> 160;

549 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 549 [arrowhead = none ];
549 -> 161;

550 [label="ONLY EVAL with clause\naddX(X539, X540, X541) :- addC(X539, X540, X541).\nand substitution\nT341 -> T367\nX539 -> T367\nT342 -> T368\nX540 -> T368\nX498 -> X542\nX541 -> X542\nT365 -> T367\nT366 -> T368", fontsize=14, style = filled, fillcolor = white];
159 -> 550 [arrowhead = none ];
550 -> 162;

551 [label="INSTANCE with matching:\nT284 -> T356\nX393 -> X524", fontsize=14, style = filled, fillcolor = lightgrey];
160 -> 551 [arrowhead = none , style=dashed];
551 -> 125[style=dashed];

552 [label="INSTANCE with matching:\nT313 -> T367\nT314 -> T368\nX447 -> X542", fontsize=14, style = filled, fillcolor = lightgrey];
162 -> 552 [arrowhead = none , style=dashed];
552 -> 143[style=dashed];

553 [label="EVAL with clause\naddC(one(X563), zero(X564), zero(X565)) :- addY(X563, X564, X565).\nand substitution\nX563 -> T381\nT313 -> one(T381)\nX564 -> T382\nT314 -> zero(T382)\nX565 -> X566\nX447 -> zero(X566)\nT379 -> T381\nT380 -> T382", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 553 [arrowhead = none ];
553 -> 165;

554 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 554 [arrowhead = none ];
554 -> 166;

555 [label="EVAL with clause\naddC(one(X623), one(X624), one(X625)) :- addc(X623, X624, X625).\nand substitution\nX623 -> T417\nT313 -> one(T417)\nX624 -> T418\nT314 -> one(T418)\nX625 -> X626\nX447 -> one(X626)\nT415 -> T417\nT416 -> T418", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 555 [arrowhead = none ];
555 -> 177;

556 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 556 [arrowhead = none ];
556 -> 178;

557 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
165 -> 557 [arrowhead = none ];
557 -> 167;

558 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
167 -> 558 [arrowhead = none ];
558 -> 168;

559 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
167 -> 559 [arrowhead = none ];
559 -> 169;

560 [label="EVAL with clause\naddY(b, zero(X575), one(X575)) :- binaryZ(X575).\nand substitution\nT381 -> b\nX575 -> T389\nT382 -> zero(T389)\nX566 -> one(T389)\nT388 -> T389", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 560 [arrowhead = none ];
560 -> 170;

561 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 561 [arrowhead = none ];
561 -> 171;

562 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
169 -> 562 [arrowhead = none ];
562 -> 172;

563 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
169 -> 563 [arrowhead = none ];
563 -> 173;

564 [label="INSTANCE with matching:\nT203 -> T389", fontsize=14, style = filled, fillcolor = lightgrey];
170 -> 564 [arrowhead = none , style=dashed];
564 -> 91[style=dashed];

565 [label="EVAL with clause\naddY(b, one(X590), zero(X591)) :- succ(X590, X591).\nand substitution\nT381 -> b\nX590 -> T396\nT382 -> one(T396)\nX591 -> X592\nX566 -> zero(X592)\nT395 -> T396", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 565 [arrowhead = none ];
565 -> 174;

566 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 566 [arrowhead = none ];
566 -> 175;

567 [label="ONLY EVAL with clause\naddY(X607, X608, X609) :- addC(X607, X608, X609).\nand substitution\nT381 -> T407\nX607 -> T407\nT382 -> T408\nX608 -> T408\nX566 -> X610\nX609 -> X610\nT405 -> T407\nT406 -> T408", fontsize=14, style = filled, fillcolor = white];
173 -> 567 [arrowhead = none ];
567 -> 176;

568 [label="INSTANCE with matching:\nT284 -> T396\nX393 -> X592", fontsize=14, style = filled, fillcolor = lightgrey];
174 -> 568 [arrowhead = none , style=dashed];
568 -> 125[style=dashed];

569 [label="INSTANCE with matching:\nT313 -> T407\nT314 -> T408\nX447 -> X610", fontsize=14, style = filled, fillcolor = lightgrey];
176 -> 569 [arrowhead = none , style=dashed];
569 -> 143[style=dashed];

570 [label="INSTANCE with matching:\nT265 -> T417\nT266 -> T418\nX356 -> X626", fontsize=14, style = filled, fillcolor = lightgrey];
177 -> 570 [arrowhead = none , style=dashed];
570 -> 108[style=dashed];

571 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
179 -> 571 [arrowhead = none ];
571 -> 180;

572 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
179 -> 572 [arrowhead = none ];
572 -> 181;

573 [label="EVAL with clause\naddz(one(X649), zero(X650), one(X651)) :- addy(X649, X650, X651).\nand substitution\nX649 -> T430\nT147 -> one(T430)\nT148 -> T431\nX650 -> T431\nX651 -> X652\nX172 -> one(X652)\nT428 -> T430\nT429 -> T431", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 573 [arrowhead = none ];
573 -> 182;

574 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 574 [arrowhead = none ];
574 -> 183;

575 [label="BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = white];
181 -> 575 [arrowhead = none ];
575 -> 184;

576 [label="INSTANCE with matching:\nT229 -> T430\nT230 -> T431\nX307 -> X652", fontsize=14, style = filled, fillcolor = lightgrey];
182 -> 576 [arrowhead = none , style=dashed];
576 -> 96[style=dashed];

577 [label="BACKTRACK\nfor clause: add(b, b, b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
185 -> 577 [arrowhead = none ];
577 -> 186;

578 [label="BACKTRACK\nfor clause: add(X, b, X) :- binaryZ(X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
186 -> 578 [arrowhead = none ];
578 -> 187;

579 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
187 -> 579 [arrowhead = none ];
579 -> 188;

580 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
187 -> 580 [arrowhead = none ];
580 -> 189;

581 [label="EVAL with clause\nadd(b, X667, X667) :- binaryZ(X667).\nand substitution\nT58 -> b\nT57 -> T441\nX667 -> zero(T441)\nT52 -> zero(T441)", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 581 [arrowhead = none ];
581 -> 190;

582 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 582 [arrowhead = none ];
582 -> 191;

583 [label="ONLY EVAL with clause\nadd(X679, X680, X681) :- addz(X679, X680, X681).\nand substitution\nT58 -> T457\nX679 -> T457\nT57 -> T458\nX680 -> zero(T458)\nT52 -> T456\nX681 -> T456\nT454 -> T457\nT455 -> T458", fontsize=14, style = filled, fillcolor = white];
189 -> 583 [arrowhead = none ];
583 -> 192;

584 [label="INSTANCE with matching:\nT102 -> T441", fontsize=14, style = filled, fillcolor = lightgrey];
190 -> 584 [arrowhead = none , style=dashed];
584 -> 43[style=dashed];

585 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
192 -> 585 [arrowhead = none ];
585 -> 193;

586 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 586 [arrowhead = none ];
586 -> 194;

587 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 587 [arrowhead = none ];
587 -> 195;

588 [label="EVAL with clause\naddz(zero(X697), zero(X698), zero(X699)) :- addz(X697, X698, X699).\nand substitution\nX697 -> T477\nT457 -> zero(T477)\nT458 -> T478\nX698 -> T478\nX699 -> T476\nT456 -> zero(T476)\nT474 -> T477\nT475 -> T478", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 588 [arrowhead = none ];
588 -> 196;

589 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 589 [arrowhead = none ];
589 -> 197;

590 [label="BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = white];
195 -> 590 [arrowhead = none ];
590 -> 302;

591 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
196 -> 591 [arrowhead = none ];
591 -> 198;

592 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
198 -> 592 [arrowhead = none ];
592 -> 199;

593 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
198 -> 593 [arrowhead = none ];
593 -> 200;

594 [label="EVAL with clause\naddz(zero(X718), zero(X719), zero(X720)) :- addz(X718, X719, X720).\nand substitution\nX718 -> T497\nT477 -> zero(T497)\nX719 -> T498\nT478 -> zero(T498)\nX720 -> T496\nT476 -> zero(T496)\nT494 -> T497\nT495 -> T498", fontsize=14, style = filled, fillcolor = lightblue];
199 -> 594 [arrowhead = none ];
594 -> 201;

595 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
199 -> 595 [arrowhead = none ];
595 -> 202;

596 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
200 -> 596 [arrowhead = none ];
596 -> 203;

597 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
200 -> 597 [arrowhead = none ];
597 -> 204;

598 [label="INSTANCE with matching:\nT477 -> T497\nT478 -> T498\nT476 -> T496", fontsize=14, style = filled, fillcolor = lightgrey];
201 -> 598 [arrowhead = none , style=dashed];
598 -> 196[style=dashed];

599 [label="EVAL with clause\naddz(zero(X739), one(X740), one(X741)) :- addx(X739, X740, X741).\nand substitution\nX739 -> T517\nT477 -> zero(T517)\nX740 -> T518\nT478 -> one(T518)\nX741 -> T516\nT476 -> one(T516)\nT514 -> T517\nT515 -> T518", fontsize=14, style = filled, fillcolor = lightblue];
203 -> 599 [arrowhead = none ];
599 -> 205;

600 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
203 -> 600 [arrowhead = none ];
600 -> 206;

601 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 601 [arrowhead = none ];
601 -> 217;

602 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 602 [arrowhead = none ];
602 -> 218;

603 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
205 -> 603 [arrowhead = none ];
603 -> 207;

604 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
207 -> 604 [arrowhead = none ];
604 -> 208;

605 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
207 -> 605 [arrowhead = none ];
605 -> 209;

606 [label="EVAL with clause\naddx(one(X750), b, one(X750)) :- binary(X750).\nand substitution\nX750 -> T524\nT517 -> one(T524)\nT518 -> b\nT516 -> one(T524)", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 606 [arrowhead = none ];
606 -> 210;

607 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 607 [arrowhead = none ];
607 -> 211;

608 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
209 -> 608 [arrowhead = none ];
608 -> 212;

609 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
209 -> 609 [arrowhead = none ];
609 -> 213;

610 [label="INSTANCE with matching:\nT125 -> T524", fontsize=14, style = filled, fillcolor = lightgrey];
210 -> 610 [arrowhead = none , style=dashed];
610 -> 54[style=dashed];

611 [label="EVAL with clause\naddx(zero(X756), b, zero(X756)) :- binaryZ(X756).\nand substitution\nX756 -> T529\nT517 -> zero(T529)\nT518 -> b\nT516 -> zero(T529)", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 611 [arrowhead = none ];
611 -> 214;

612 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 612 [arrowhead = none ];
612 -> 215;

613 [label="ONLY EVAL with clause\naddx(X768, X769, X770) :- addz(X768, X769, X770).\nand substitution\nT517 -> T545\nX768 -> T545\nT518 -> T546\nX769 -> T546\nT516 -> T544\nX770 -> T544\nT542 -> T545\nT543 -> T546", fontsize=14, style = filled, fillcolor = white];
213 -> 613 [arrowhead = none ];
613 -> 216;

614 [label="INSTANCE with matching:\nT203 -> T529", fontsize=14, style = filled, fillcolor = lightgrey];
214 -> 614 [arrowhead = none , style=dashed];
614 -> 91[style=dashed];

615 [label="INSTANCE with matching:\nT477 -> T545\nT478 -> T546\nT476 -> T544", fontsize=14, style = filled, fillcolor = lightgrey];
216 -> 615 [arrowhead = none , style=dashed];
615 -> 196[style=dashed];

616 [label="EVAL with clause\naddz(one(X786), zero(X787), one(X788)) :- addy(X786, X787, X788).\nand substitution\nX786 -> T565\nT477 -> one(T565)\nX787 -> T566\nT478 -> zero(T566)\nX788 -> T564\nT476 -> one(T564)\nT562 -> T565\nT563 -> T566", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 616 [arrowhead = none ];
616 -> 219;

617 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 617 [arrowhead = none ];
617 -> 220;

618 [label="EVAL with clause\naddz(one(X827), one(X828), zero(X829)) :- addc(X827, X828, X829).\nand substitution\nX827 -> T607\nT477 -> one(T607)\nX828 -> T608\nT478 -> one(T608)\nX829 -> T606\nT476 -> zero(T606)\nT604 -> T607\nT605 -> T608", fontsize=14, style = filled, fillcolor = lightblue];
218 -> 618 [arrowhead = none ];
618 -> 231;

619 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
218 -> 619 [arrowhead = none ];
619 -> 232;

620 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
219 -> 620 [arrowhead = none ];
620 -> 221;

621 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
221 -> 621 [arrowhead = none ];
621 -> 222;

622 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
221 -> 622 [arrowhead = none ];
622 -> 223;

623 [label="EVAL with clause\naddy(b, one(X797), one(X797)) :- binary(X797).\nand substitution\nT565 -> b\nX797 -> T572\nT566 -> one(T572)\nT564 -> one(T572)", fontsize=14, style = filled, fillcolor = lightblue];
222 -> 623 [arrowhead = none ];
623 -> 224;

624 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
222 -> 624 [arrowhead = none ];
624 -> 225;

625 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
223 -> 625 [arrowhead = none ];
625 -> 226;

626 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
223 -> 626 [arrowhead = none ];
626 -> 227;

627 [label="INSTANCE with matching:\nT524 -> T572", fontsize=14, style = filled, fillcolor = lightgrey];
224 -> 627 [arrowhead = none , style=dashed];
627 -> 210[style=dashed];

628 [label="EVAL with clause\naddy(b, zero(X803), zero(X803)) :- binaryZ(X803).\nand substitution\nT565 -> b\nX803 -> T577\nT566 -> zero(T577)\nT564 -> zero(T577)", fontsize=14, style = filled, fillcolor = lightblue];
226 -> 628 [arrowhead = none ];
628 -> 228;

629 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
226 -> 629 [arrowhead = none ];
629 -> 229;

630 [label="ONLY EVAL with clause\naddy(X815, X816, X817) :- addz(X815, X816, X817).\nand substitution\nT565 -> T593\nX815 -> T593\nT566 -> T594\nX816 -> T594\nT564 -> T592\nX817 -> T592\nT590 -> T593\nT591 -> T594", fontsize=14, style = filled, fillcolor = white];
227 -> 630 [arrowhead = none ];
630 -> 230;

631 [label="INSTANCE with matching:\nT529 -> T577", fontsize=14, style = filled, fillcolor = lightgrey];
228 -> 631 [arrowhead = none , style=dashed];
631 -> 214[style=dashed];

632 [label="INSTANCE with matching:\nT477 -> T593\nT478 -> T594\nT476 -> T592", fontsize=14, style = filled, fillcolor = lightgrey];
230 -> 632 [arrowhead = none , style=dashed];
632 -> 196[style=dashed];

633 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
231 -> 633 [arrowhead = none ];
633 -> 233;

634 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
233 -> 634 [arrowhead = none ];
634 -> 234;

635 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
233 -> 635 [arrowhead = none ];
635 -> 235;

636 [label="EVAL with clause\naddc(b, b, one(b)).\nand substitution\nT607 -> b\nT608 -> b\nT606 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
234 -> 636 [arrowhead = none ];
636 -> 236;

637 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
234 -> 637 [arrowhead = none ];
637 -> 237;

638 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
235 -> 638 [arrowhead = none ];
638 -> 239;

639 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
235 -> 639 [arrowhead = none ];
639 -> 240;

640 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
236 -> 640 [arrowhead = none ];
640 -> 238;

641 [label="EVAL with clause\naddc(X841, b, X842) :- succZ(X841, X842).\nand substitution\nT607 -> T619\nX841 -> T619\nT608 -> b\nT606 -> T618\nX842 -> T618\nT617 -> T619", fontsize=14, style = filled, fillcolor = lightblue];
239 -> 641 [arrowhead = none ];
641 -> 241;

642 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
239 -> 642 [arrowhead = none ];
642 -> 242;

643 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 643 [arrowhead = none ];
643 -> 262;

644 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 644 [arrowhead = none ];
644 -> 263;

645 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
241 -> 645 [arrowhead = none ];
645 -> 243;

646 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
243 -> 646 [arrowhead = none ];
646 -> 244;

647 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
243 -> 647 [arrowhead = none ];
647 -> 245;

648 [label="EVAL with clause\nsuccZ(zero(X850), one(X850)) :- binaryZ(X850).\nand substitution\nX850 -> T625\nT619 -> zero(T625)\nT618 -> one(T625)", fontsize=14, style = filled, fillcolor = lightblue];
244 -> 648 [arrowhead = none ];
648 -> 246;

649 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
244 -> 649 [arrowhead = none ];
649 -> 247;

650 [label="EVAL with clause\nsuccZ(one(X857), zero(X858)) :- succ(X857, X858).\nand substitution\nX857 -> T633\nT619 -> one(T633)\nX858 -> T632\nT618 -> zero(T632)\nT631 -> T633", fontsize=14, style = filled, fillcolor = lightblue];
245 -> 650 [arrowhead = none ];
650 -> 248;

651 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
245 -> 651 [arrowhead = none ];
651 -> 249;

652 [label="INSTANCE with matching:\nT529 -> T625", fontsize=14, style = filled, fillcolor = lightgrey];
246 -> 652 [arrowhead = none , style=dashed];
652 -> 214[style=dashed];

653 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
248 -> 653 [arrowhead = none ];
653 -> 250;

654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
250 -> 654 [arrowhead = none ];
654 -> 251;

655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
250 -> 655 [arrowhead = none ];
655 -> 252;

656 [label="EVAL with clause\nsucc(b, one(b)).\nand substitution\nT633 -> b\nT632 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
251 -> 656 [arrowhead = none ];
656 -> 253;

657 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
251 -> 657 [arrowhead = none ];
657 -> 254;

658 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
252 -> 658 [arrowhead = none ];
658 -> 256;

659 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
252 -> 659 [arrowhead = none ];
659 -> 257;

660 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
253 -> 660 [arrowhead = none ];
660 -> 255;

661 [label="EVAL with clause\nsucc(zero(X865), one(X865)) :- binaryZ(X865).\nand substitution\nX865 -> T638\nT633 -> zero(T638)\nT632 -> one(T638)", fontsize=14, style = filled, fillcolor = lightblue];
256 -> 661 [arrowhead = none ];
661 -> 258;

662 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
256 -> 662 [arrowhead = none ];
662 -> 259;

663 [label="EVAL with clause\nsucc(one(X872), zero(X873)) :- succ(X872, X873).\nand substitution\nX872 -> T646\nT633 -> one(T646)\nX873 -> T645\nT632 -> zero(T645)\nT644 -> T646", fontsize=14, style = filled, fillcolor = lightblue];
257 -> 663 [arrowhead = none ];
663 -> 260;

664 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
257 -> 664 [arrowhead = none ];
664 -> 261;

665 [label="INSTANCE with matching:\nT529 -> T638", fontsize=14, style = filled, fillcolor = lightgrey];
258 -> 665 [arrowhead = none , style=dashed];
665 -> 214[style=dashed];

666 [label="INSTANCE with matching:\nT633 -> T646\nT632 -> T645", fontsize=14, style = filled, fillcolor = lightgrey];
260 -> 666 [arrowhead = none , style=dashed];
666 -> 248[style=dashed];

667 [label="EVAL with clause\naddc(b, X884, X885) :- succZ(X884, X885).\nand substitution\nT607 -> b\nT608 -> T657\nX884 -> T657\nT606 -> T656\nX885 -> T656\nT655 -> T657", fontsize=14, style = filled, fillcolor = lightblue];
262 -> 667 [arrowhead = none ];
667 -> 264;

668 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
262 -> 668 [arrowhead = none ];
668 -> 265;

669 [label="ONLY EVAL with clause\naddc(X898, X899, X900) :- addC(X898, X899, X900).\nand substitution\nT607 -> T673\nX898 -> T673\nT608 -> T674\nX899 -> T674\nT606 -> T672\nX900 -> T672\nT670 -> T673\nT671 -> T674", fontsize=14, style = filled, fillcolor = white];
263 -> 669 [arrowhead = none ];
669 -> 266;

670 [label="INSTANCE with matching:\nT619 -> T657\nT618 -> T656", fontsize=14, style = filled, fillcolor = lightgrey];
264 -> 670 [arrowhead = none , style=dashed];
670 -> 241[style=dashed];

671 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
266 -> 671 [arrowhead = none ];
671 -> 267;

672 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
267 -> 672 [arrowhead = none ];
672 -> 268;

673 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
267 -> 673 [arrowhead = none ];
673 -> 269;

674 [label="EVAL with clause\naddC(zero(X916), zero(X917), one(X918)) :- addz(X916, X917, X918).\nand substitution\nX916 -> T693\nT673 -> zero(T693)\nX917 -> T694\nT674 -> zero(T694)\nX918 -> T692\nT672 -> one(T692)\nT690 -> T693\nT691 -> T694", fontsize=14, style = filled, fillcolor = lightblue];
268 -> 674 [arrowhead = none ];
674 -> 270;

675 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
268 -> 675 [arrowhead = none ];
675 -> 271;

676 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
269 -> 676 [arrowhead = none ];
676 -> 272;

677 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
269 -> 677 [arrowhead = none ];
677 -> 273;

678 [label="INSTANCE with matching:\nT477 -> T693\nT478 -> T694\nT476 -> T692", fontsize=14, style = filled, fillcolor = lightgrey];
270 -> 678 [arrowhead = none , style=dashed];
678 -> 196[style=dashed];

679 [label="EVAL with clause\naddC(zero(X937), one(X938), zero(X939)) :- addX(X937, X938, X939).\nand substitution\nX937 -> T713\nT673 -> zero(T713)\nX938 -> T714\nT674 -> one(T714)\nX939 -> T712\nT672 -> zero(T712)\nT710 -> T713\nT711 -> T714", fontsize=14, style = filled, fillcolor = lightblue];
272 -> 679 [arrowhead = none ];
679 -> 274;

680 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
272 -> 680 [arrowhead = none ];
680 -> 275;

681 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
273 -> 681 [arrowhead = none ];
681 -> 286;

682 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
273 -> 682 [arrowhead = none ];
682 -> 287;

683 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
274 -> 683 [arrowhead = none ];
683 -> 276;

684 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 684 [arrowhead = none ];
684 -> 277;

685 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 685 [arrowhead = none ];
685 -> 278;

686 [label="EVAL with clause\naddX(zero(X948), b, one(X948)) :- binaryZ(X948).\nand substitution\nX948 -> T720\nT713 -> zero(T720)\nT714 -> b\nT712 -> one(T720)", fontsize=14, style = filled, fillcolor = lightblue];
277 -> 686 [arrowhead = none ];
686 -> 279;

687 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
277 -> 687 [arrowhead = none ];
687 -> 280;

688 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 688 [arrowhead = none ];
688 -> 281;

689 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 689 [arrowhead = none ];
689 -> 282;

690 [label="INSTANCE with matching:\nT529 -> T720", fontsize=14, style = filled, fillcolor = lightgrey];
279 -> 690 [arrowhead = none , style=dashed];
690 -> 214[style=dashed];

691 [label="EVAL with clause\naddX(one(X959), b, zero(X960)) :- succ(X959, X960).\nand substitution\nX959 -> T732\nT713 -> one(T732)\nT714 -> b\nX960 -> T731\nT712 -> zero(T731)\nT730 -> T732", fontsize=14, style = filled, fillcolor = lightblue];
281 -> 691 [arrowhead = none ];
691 -> 283;

692 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
281 -> 692 [arrowhead = none ];
692 -> 284;

693 [label="ONLY EVAL with clause\naddX(X972, X973, X974) :- addC(X972, X973, X974).\nand substitution\nT713 -> T747\nX972 -> T747\nT714 -> T748\nX973 -> T748\nT712 -> T746\nX974 -> T746\nT744 -> T747\nT745 -> T748", fontsize=14, style = filled, fillcolor = white];
282 -> 693 [arrowhead = none ];
693 -> 285;

694 [label="INSTANCE with matching:\nT633 -> T732\nT632 -> T731", fontsize=14, style = filled, fillcolor = lightgrey];
283 -> 694 [arrowhead = none , style=dashed];
694 -> 248[style=dashed];

695 [label="INSTANCE with matching:\nT673 -> T747\nT674 -> T748\nT672 -> T746", fontsize=14, style = filled, fillcolor = lightgrey];
285 -> 695 [arrowhead = none , style=dashed];
695 -> 266[style=dashed];

696 [label="EVAL with clause\naddC(one(X990), zero(X991), zero(X992)) :- addY(X990, X991, X992).\nand substitution\nX990 -> T767\nT673 -> one(T767)\nX991 -> T768\nT674 -> zero(T768)\nX992 -> T766\nT672 -> zero(T766)\nT764 -> T767\nT765 -> T768", fontsize=14, style = filled, fillcolor = lightblue];
286 -> 696 [arrowhead = none ];
696 -> 288;

697 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
286 -> 697 [arrowhead = none ];
697 -> 289;

698 [label="EVAL with clause\naddC(one(X1037), one(X1038), one(X1039)) :- addc(X1037, X1038, X1039).\nand substitution\nX1037 -> T815\nT673 -> one(T815)\nX1038 -> T816\nT674 -> one(T816)\nX1039 -> T814\nT672 -> one(T814)\nT812 -> T815\nT813 -> T816", fontsize=14, style = filled, fillcolor = lightblue];
287 -> 698 [arrowhead = none ];
698 -> 300;

699 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
287 -> 699 [arrowhead = none ];
699 -> 301;

700 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
288 -> 700 [arrowhead = none ];
700 -> 290;

701 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
290 -> 701 [arrowhead = none ];
701 -> 291;

702 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
290 -> 702 [arrowhead = none ];
702 -> 292;

703 [label="EVAL with clause\naddY(b, zero(X1001), one(X1001)) :- binaryZ(X1001).\nand substitution\nT767 -> b\nX1001 -> T774\nT768 -> zero(T774)\nT766 -> one(T774)", fontsize=14, style = filled, fillcolor = lightblue];
291 -> 703 [arrowhead = none ];
703 -> 293;

704 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
291 -> 704 [arrowhead = none ];
704 -> 294;

705 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
292 -> 705 [arrowhead = none ];
705 -> 295;

706 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
292 -> 706 [arrowhead = none ];
706 -> 296;

707 [label="INSTANCE with matching:\nT529 -> T774", fontsize=14, style = filled, fillcolor = lightgrey];
293 -> 707 [arrowhead = none , style=dashed];
707 -> 214[style=dashed];

708 [label="EVAL with clause\naddY(b, one(X1012), zero(X1013)) :- succ(X1012, X1013).\nand substitution\nT767 -> b\nX1012 -> T786\nT768 -> one(T786)\nX1013 -> T785\nT766 -> zero(T785)\nT784 -> T786", fontsize=14, style = filled, fillcolor = lightblue];
295 -> 708 [arrowhead = none ];
708 -> 297;

709 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
295 -> 709 [arrowhead = none ];
709 -> 298;

710 [label="ONLY EVAL with clause\naddY(X1025, X1026, X1027) :- addC(X1025, X1026, X1027).\nand substitution\nT767 -> T801\nX1025 -> T801\nT768 -> T802\nX1026 -> T802\nT766 -> T800\nX1027 -> T800\nT798 -> T801\nT799 -> T802", fontsize=14, style = filled, fillcolor = white];
296 -> 710 [arrowhead = none ];
710 -> 299;

711 [label="INSTANCE with matching:\nT633 -> T786\nT632 -> T785", fontsize=14, style = filled, fillcolor = lightgrey];
297 -> 711 [arrowhead = none , style=dashed];
711 -> 248[style=dashed];

712 [label="INSTANCE with matching:\nT673 -> T801\nT674 -> T802\nT672 -> T800", fontsize=14, style = filled, fillcolor = lightgrey];
299 -> 712 [arrowhead = none , style=dashed];
712 -> 266[style=dashed];

713 [label="INSTANCE with matching:\nT607 -> T815\nT608 -> T816\nT606 -> T814", fontsize=14, style = filled, fillcolor = lightgrey];
300 -> 713 [arrowhead = none , style=dashed];
713 -> 231[style=dashed];

714 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
302 -> 714 [arrowhead = none ];
714 -> 303;

715 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
302 -> 715 [arrowhead = none ];
715 -> 304;

716 [label="EVAL with clause\naddz(one(X1058), zero(X1059), one(X1060)) :- addy(X1058, X1059, X1060).\nand substitution\nX1058 -> T833\nT457 -> one(T833)\nT458 -> T834\nX1059 -> T834\nX1060 -> T832\nT456 -> one(T832)\nT830 -> T833\nT831 -> T834", fontsize=14, style = filled, fillcolor = lightblue];
303 -> 716 [arrowhead = none ];
716 -> 305;

717 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
303 -> 717 [arrowhead = none ];
717 -> 306;

718 [label="BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = white];
304 -> 718 [arrowhead = none ];
718 -> 307;

719 [label="INSTANCE with matching:\nT565 -> T833\nT566 -> T834\nT564 -> T832", fontsize=14, style = filled, fillcolor = lightgrey];
305 -> 719 [arrowhead = none , style=dashed];
719 -> 219[style=dashed];

720 [label="EVAL with clause\ntimes(one(X1075), X1076, X1077) :- ','(times(X1075, X1076, X1078), add(X1076, zero(X1078), X1077)).\nand substitution\nX1075 -> T846\nT1 -> one(T846)\nT2 -> T847\nX1076 -> T847\nT11 -> T845\nX1077 -> zero(T845)\nT843 -> T846\nT844 -> T847", fontsize=14, style = filled, fillcolor = lightblue];
308 -> 720 [arrowhead = none ];
720 -> 309;

721 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
308 -> 721 [arrowhead = none ];
721 -> 310;

722 [label="INSTANCE with matching:\nT53 -> T846\nT54 -> T847\nX56 -> X1078\nT52 -> zero(T845)", fontsize=14, style = filled, fillcolor = lightgrey];
309 -> 722 [arrowhead = none , style=dashed];
722 -> 20[style=dashed];

723 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
311 -> 723 [arrowhead = none ];
723 -> 313;

724 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
313 -> 724 [arrowhead = none ];
724 -> 314;

725 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
313 -> 725 [arrowhead = none ];
725 -> 315;

726 [label="EVAL with clause\ntimes(one(b), X1098, X1098).\nand substitution\nT856 -> one(b)\nT857 -> T863\nX1098 -> T863\nX1090 -> T863\nT862 -> T863", fontsize=14, style = filled, fillcolor = lightblue];
314 -> 726 [arrowhead = none ];
726 -> 316;

727 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
314 -> 727 [arrowhead = none ];
727 -> 317;

728 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
315 -> 728 [arrowhead = none ];
728 -> 318;

729 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
315 -> 729 [arrowhead = none ];
729 -> 319;

730 [label="INSTANCE with matching:\nT58 -> T863\nT57 -> T863\nT52 -> T855", fontsize=14, style = filled, fillcolor = lightgrey];
316 -> 730 [arrowhead = none , style=dashed];
730 -> 23[style=dashed];

731 [label="EVAL with clause\ntimes(zero(X1118), X1119, zero(X1120)) :- times(X1118, X1119, X1120).\nand substitution\nX1118 -> T875\nT856 -> zero(T875)\nT857 -> T876\nX1119 -> T876\nX1120 -> X1121\nX1090 -> zero(X1121)\nT873 -> T875\nT874 -> T876", fontsize=14, style = filled, fillcolor = lightblue];
318 -> 731 [arrowhead = none ];
731 -> 320;

732 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
318 -> 732 [arrowhead = none ];
732 -> 321;

733 [label="EVAL with clause\ntimes(one(X1140), X1141, X1142) :- ','(times(X1140, X1141, X1143), add(X1141, zero(X1143), X1142)).\nand substitution\nX1140 -> T896\nT856 -> one(T896)\nT857 -> T897\nX1141 -> T897\nX1090 -> X1144\nX1142 -> X1144\nT894 -> T896\nT895 -> T897", fontsize=14, style = filled, fillcolor = lightblue];
319 -> 733 [arrowhead = none ];
733 -> 324;

734 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
319 -> 734 [arrowhead = none ];
734 -> 325;

735 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
320 -> 735 [arrowhead = none ];
735 -> 322;

736 [label="SPLIT 2\nnew knowledge:\nT875 is ground\nreplacements:\nX1121 -> T879\nT876 -> T880\nT1 -> T881\nT2 -> T882\nX7 -> T883\nX8 -> T884\nX9 -> T885", fontsize=14, style = filled, fillcolor = violet];
320 -> 736 [arrowhead = none ];
736 -> 323;

737 [label="INSTANCE with matching:\nT53 -> T875\nT54 -> T876\nX56 -> X1121", fontsize=14, style = filled, fillcolor = lightgrey];
322 -> 737 [arrowhead = none , style=dashed];
737 -> 22[style=dashed];

738 [label="INSTANCE with matching:\nT58 -> T880\nT57 -> zero(T879)\nT52 -> T855", fontsize=14, style = filled, fillcolor = lightgrey];
323 -> 738 [arrowhead = none , style=dashed];
738 -> 23[style=dashed];

739 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
324 -> 739 [arrowhead = none ];
739 -> 326;

740 [label="SPLIT 2\nnew knowledge:\nT896 is ground\nreplacements:\nX1143 -> T900\nT897 -> T901\nT1 -> T902\nT2 -> T903\nX7 -> T904\nX8 -> T905\nX9 -> T906", fontsize=14, style = filled, fillcolor = violet];
324 -> 740 [arrowhead = none ];
740 -> 327;

741 [label="INSTANCE with matching:\nT53 -> T896\nT54 -> T897\nX56 -> X1143", fontsize=14, style = filled, fillcolor = lightgrey];
326 -> 741 [arrowhead = none , style=dashed];
741 -> 22[style=dashed];

742 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
327 -> 742 [arrowhead = none ];
742 -> 328;

743 [label="SPLIT 2\nnew knowledge:\nT912 is ground\nT900 is ground\nT911 is ground\nreplacements:\nX1144 -> T911\nT901 -> T912\nT902 -> T913\nT903 -> T914\nT904 -> T915\nT905 -> T916\nT906 -> T917", fontsize=14, style = filled, fillcolor = violet];
327 -> 743 [arrowhead = none ];
743 -> 329;

744 [label="INSTANCE with matching:\nT91 -> T901\nT90 -> T900\nX108 -> X1144", fontsize=14, style = filled, fillcolor = lightgrey];
328 -> 744 [arrowhead = none , style=dashed];
744 -> 37[style=dashed];

745 [label="INSTANCE with matching:\nT58 -> T912\nT57 -> T911\nT52 -> T855", fontsize=14, style = filled, fillcolor = lightgrey];
329 -> 745 [arrowhead = none , style=dashed];
745 -> 23[style=dashed];

746 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
330 -> 746 [arrowhead = none ];
746 -> 332;

747 [label="EVAL with clause\ntimes(one(X1235), X1236, X1237) :- ','(times(X1235, X1236, X1238), add(X1236, zero(X1238), X1237)).\nand substitution\nX1235 -> T992\nT1 -> one(T992)\nT2 -> T993\nX1236 -> T993\nT3 -> T991\nX1237 -> T991\nT989 -> T992\nT990 -> T993", fontsize=14, style = filled, fillcolor = lightblue];
331 -> 747 [arrowhead = none ];
747 -> 349;

748 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
331 -> 748 [arrowhead = none ];
748 -> 350;

749 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 749 [arrowhead = none ];
749 -> 333;

750 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 750 [arrowhead = none ];
750 -> 334;

751 [label="EVAL with clause\ntimes(one(b), X1171, X1171).\nand substitution\nT928 -> one(b)\nT929 -> T934\nX1171 -> T934\nT927 -> T934", fontsize=14, style = filled, fillcolor = lightblue];
333 -> 751 [arrowhead = none ];
751 -> 335;

752 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
333 -> 752 [arrowhead = none ];
752 -> 336;

753 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
334 -> 753 [arrowhead = none ];
753 -> 338;

754 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
334 -> 754 [arrowhead = none ];
754 -> 339;

755 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
335 -> 755 [arrowhead = none ];
755 -> 337;

756 [label="EVAL with clause\ntimes(zero(X1185), X1186, zero(X1187)) :- times(X1185, X1186, X1187).\nand substitution\nX1185 -> T950\nT928 -> zero(T950)\nT929 -> T951\nX1186 -> T951\nX1187 -> T949\nT927 -> zero(T949)\nT947 -> T950\nT948 -> T951", fontsize=14, style = filled, fillcolor = lightblue];
338 -> 756 [arrowhead = none ];
756 -> 340;

757 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
338 -> 757 [arrowhead = none ];
757 -> 341;

758 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
339 -> 758 [arrowhead = none ];
758 -> 342;

759 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
339 -> 759 [arrowhead = none ];
759 -> 343;

760 [label="INSTANCE with matching:\nT1 -> T950\nT2 -> T951\nT3 -> T949", fontsize=14, style = filled, fillcolor = lightgrey];
340 -> 760 [arrowhead = none , style=dashed];
760 -> 1[style=dashed];

761 [label="EVAL with clause\ntimes(one(X1207), X1208, X1209) :- ','(times(X1207, X1208, X1210), add(X1208, zero(X1210), X1209)).\nand substitution\nX1207 -> T969\nT928 -> one(T969)\nT929 -> T970\nX1208 -> T970\nT927 -> T968\nX1209 -> T968\nT966 -> T969\nT967 -> T970", fontsize=14, style = filled, fillcolor = lightblue];
342 -> 761 [arrowhead = none ];
761 -> 344;

762 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
342 -> 762 [arrowhead = none ];
762 -> 345;

763 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
343 -> 763 [arrowhead = none ];
763 -> 346;

764 [label="INSTANCE with matching:\nT53 -> T969\nT54 -> T970\nX56 -> X1210\nT52 -> T968", fontsize=14, style = filled, fillcolor = lightgrey];
344 -> 764 [arrowhead = none , style=dashed];
764 -> 20[style=dashed];

765 [label="EVAL with clause\ntimes(one(X1223), X1224, X1225) :- ','(times(X1223, X1224, X1226), add(X1224, zero(X1226), X1225)).\nand substitution\nX1223 -> T982\nT1 -> one(T982)\nT2 -> T983\nX1224 -> T983\nT927 -> T981\nX1225 -> zero(T981)\nT979 -> T982\nT980 -> T983", fontsize=14, style = filled, fillcolor = lightblue];
346 -> 765 [arrowhead = none ];
765 -> 347;

766 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
346 -> 766 [arrowhead = none ];
766 -> 348;

767 [label="INSTANCE with matching:\nT969 -> T982\nT970 -> T983\nX1210 -> X1226\nT968 -> zero(T981)", fontsize=14, style = filled, fillcolor = lightgrey];
347 -> 767 [arrowhead = none , style=dashed];
767 -> 344[style=dashed];

768 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
349 -> 768 [arrowhead = none ];
768 -> 351;

769 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
351 -> 769 [arrowhead = none ];
769 -> 352;

770 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
351 -> 770 [arrowhead = none ];
770 -> 353;

771 [label="EVAL with clause\ntimes(one(b), X1246, X1246).\nand substitution\nT992 -> one(b)\nT993 -> T999\nX1246 -> T999\nX1238 -> T999\nT998 -> T999", fontsize=14, style = filled, fillcolor = lightblue];
352 -> 771 [arrowhead = none ];
771 -> 354;

772 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
352 -> 772 [arrowhead = none ];
772 -> 355;

773 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
353 -> 773 [arrowhead = none ];
773 -> 356;

774 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
353 -> 774 [arrowhead = none ];
774 -> 357;

775 [label="INSTANCE with matching:\nT863 -> T999\nT855 -> T991\nX7 -> X1161\nX8 -> X1162\nX9 -> X1163", fontsize=14, style = filled, fillcolor = lightgrey];
354 -> 775 [arrowhead = none , style=dashed];
775 -> 316[style=dashed];

776 [label="EVAL with clause\ntimes(zero(X1266), X1267, zero(X1268)) :- times(X1266, X1267, X1268).\nand substitution\nX1266 -> T1011\nT992 -> zero(T1011)\nT993 -> T1012\nX1267 -> T1012\nX1268 -> X1269\nX1238 -> zero(X1269)\nT1009 -> T1011\nT1010 -> T1012", fontsize=14, style = filled, fillcolor = lightblue];
356 -> 776 [arrowhead = none ];
776 -> 358;

777 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
356 -> 777 [arrowhead = none ];
777 -> 359;

778 [label="EVAL with clause\ntimes(one(X1284), X1285, X1286) :- ','(times(X1284, X1285, X1287), add(X1285, zero(X1287), X1286)).\nand substitution\nX1284 -> T1021\nT992 -> one(T1021)\nT993 -> T1022\nX1285 -> T1022\nX1238 -> X1288\nX1286 -> X1288\nT1019 -> T1021\nT1020 -> T1022", fontsize=14, style = filled, fillcolor = lightblue];
357 -> 778 [arrowhead = none ];
778 -> 360;

779 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
357 -> 779 [arrowhead = none ];
779 -> 361;

780 [label="INSTANCE with matching:\nT875 -> T1011\nT876 -> T1012\nX1121 -> X1269\nT855 -> T991\nX7 -> X1161\nX8 -> X1162\nX9 -> X1163", fontsize=14, style = filled, fillcolor = lightgrey];
358 -> 780 [arrowhead = none , style=dashed];
780 -> 320[style=dashed];

781 [label="INSTANCE with matching:\nT896 -> T1021\nT897 -> T1022\nX1143 -> X1287\nX1144 -> X1288\nT855 -> T991\nX7 -> X1161\nX8 -> X1162\nX9 -> X1163", fontsize=14, style = filled, fillcolor = lightgrey];
360 -> 781 [arrowhead = none , style=dashed];
781 -> 324[style=dashed];

}

(2) Obligation:

Triples:

times22(zero(T76), T77, zero(X89)) :- times22(T76, T77, X89).
times22(one(T86), T87, X108) :- times22(T86, T87, X107).
times22(one(T86), T91, X108) :- ','(timesc22(T86, T91, T90), add37(T91, T90, X108)).
binaryZ48(zero(T120)) :- binaryZ48(T120).
binaryZ48(one(T125)) :- binary54(T125).
binary54(zero(T131)) :- binaryZ48(T131).
binary54(one(T136)) :- binary54(T136).
addz73(zero(T175), zero(T176), zero(X223)) :- addz73(T175, T176, X223).
addz73(zero(one(T197)), one(b), one(one(T197))) :- binary54(T197).
addz73(zero(zero(T203)), one(b), one(zero(T203))) :- binaryZ48(T203).
addz73(zero(T215), one(T216), one(X283)) :- addz73(T215, T216, X283).
addz73(one(T229), zero(T230), one(X307)) :- addy96(T229, T230, X307).
addz73(one(T265), one(T266), zero(X356)) :- addc108(T265, T266, X356).
succ125(zero(T290), one(T290)) :- binaryZ48(T290).
succ125(one(T295), zero(X411)) :- succ125(T295, X411).
succZ118(zero(T279), one(T279)) :- binaryZ48(T279).
succZ118(one(T284), zero(X393)) :- succ125(T284, X393).
addC143(zero(T327), zero(T328), one(X471)) :- addz73(T327, T328, X471).
addC143(zero(zero(T349)), one(b), zero(one(T349))) :- binaryZ48(T349).
addC143(zero(one(T356)), one(b), zero(zero(X524))) :- succ125(T356, X524).
addC143(zero(T367), one(T368), zero(X542)) :- addC143(T367, T368, X542).
addC143(one(b), zero(zero(T389)), zero(one(T389))) :- binaryZ48(T389).
addC143(one(b), zero(one(T396)), zero(zero(X592))) :- succ125(T396, X592).
addC143(one(T407), zero(T408), zero(X610)) :- addC143(T407, T408, X610).
addC143(one(T417), one(T418), one(X626)) :- addc108(T417, T418, X626).
addc108(T272, b, X374) :- succZ118(T272, X374).
addc108(b, T301, X428) :- succZ118(T301, X428).
addc108(T313, T314, X447) :- addC143(T313, T314, X447).
addy96(b, one(T237), one(T237)) :- binary54(T237).
addy96(b, zero(T243), zero(T243)) :- binaryZ48(T243).
addy96(T255, T256, X340) :- addz73(T255, T256, X340).
binaryZ43(T113) :- binaryZ48(T113).
addz196(zero(T497), zero(T498), zero(T496)) :- addz196(T497, T498, T496).
addz196(zero(one(T524)), one(b), one(one(T524))) :- binary54(T524).
addz196(zero(zero(T529)), one(b), one(zero(T529))) :- binaryZ48(T529).
addz196(zero(T545), one(T546), one(T544)) :- addz196(T545, T546, T544).
addz196(one(T565), zero(T566), one(T564)) :- addy219(T565, T566, T564).
addz196(one(T607), one(T608), zero(T606)) :- addc231(T607, T608, T606).
succ248(zero(T638), one(T638)) :- binaryZ48(T638).
succ248(one(T646), zero(T645)) :- succ248(T646, T645).
succZ241(zero(T625), one(T625)) :- binaryZ48(T625).
succZ241(one(T633), zero(T632)) :- succ248(T633, T632).
addC266(zero(T693), zero(T694), one(T692)) :- addz196(T693, T694, T692).
addC266(zero(zero(T720)), one(b), zero(one(T720))) :- binaryZ48(T720).
addC266(zero(one(T732)), one(b), zero(zero(T731))) :- succ248(T732, T731).
addC266(zero(T747), one(T748), zero(T746)) :- addC266(T747, T748, T746).
addC266(one(b), zero(zero(T774)), zero(one(T774))) :- binaryZ48(T774).
addC266(one(b), zero(one(T786)), zero(zero(T785))) :- succ248(T786, T785).
addC266(one(T801), zero(T802), zero(T800)) :- addC266(T801, T802, T800).
addC266(one(T815), one(T816), one(T814)) :- addc231(T815, T816, T814).
addc231(T619, b, T618) :- succZ241(T619, T618).
addc231(b, T657, T656) :- succZ241(T657, T656).
addc231(T673, T674, T672) :- addC266(T673, T674, T672).
addy219(b, one(T572), one(T572)) :- binary54(T572).
addy219(b, zero(T577), zero(T577)) :- binaryZ48(T577).
addy219(T593, T594, T592) :- addz196(T593, T594, T592).
p20(T53, T54, X56, T52) :- times22(T53, T54, X56).
p20(T53, T58, T57, T52) :- ','(timesc22(T53, T58, T57), add23(T58, T57, T52)).
add23(b, T441, zero(T441)) :- binaryZ43(T441).
add23(zero(T477), T478, zero(T476)) :- addz196(T477, T478, T476).
add23(one(T833), T834, one(T832)) :- addy219(T833, T834, T832).
add37(b, T102, zero(T102)) :- binaryZ43(T102).
add37(zero(T161), T162, zero(X196)) :- addz73(T161, T162, X196).
add37(one(T430), T431, one(X652)) :- addy96(T430, T431, X652).
p320(T875, T876, X1121, T855) :- times22(T875, T876, X1121).
p320(T875, T880, T879, T855) :- ','(timesc22(T875, T880, T879), add23(T880, zero(T879), T855)).
p324(T896, T897, X1143, X1144, T855) :- times22(T896, T897, X1143).
p324(T896, T901, T900, X1144, T855) :- ','(timesc22(T896, T901, T900), add37(T901, T900, X1144)).
p324(T896, T912, T900, T911, T855) :- ','(timesc22(T896, T912, T900), ','(addc37(T912, T900, T911), add23(T912, T911, T855))).
times1(zero(zero(T34)), T35, zero(zero(T33))) :- times1(T34, T35, T33).
times1(zero(one(T53)), T54, zero(T52)) :- p20(T53, T54, X56, T52).
times1(one(T846), T847, zero(T845)) :- p20(T846, T847, X1078, zero(T845)).
times1(one(one(b)), T863, T855) :- add23(T863, T863, T855).
times1(one(zero(T875)), T876, T855) :- p320(T875, T876, X1121, T855).
times1(one(one(T896)), T897, T855) :- p324(T896, T897, X1143, X1144, T855).
times1(zero(zero(T950)), T951, zero(zero(T949))) :- times1(T950, T951, T949).
times1(zero(one(T969)), T970, zero(T968)) :- p20(T969, T970, X1210, T968).
times1(one(T982), T983, zero(T981)) :- p20(T982, T983, X1226, zero(T981)).
times1(one(one(b)), T999, T991) :- add23(T999, T999, T991).
times1(one(zero(T1011)), T1012, T991) :- p320(T1011, T1012, X1269, T991).
times1(one(one(T1021)), T1022, T991) :- p324(T1021, T1022, X1287, X1288, T991).

Clauses:

timesc1(one(b), T5, T5).
timesc1(zero(one(b)), T18, zero(T18)).
timesc1(zero(zero(T34)), T35, zero(zero(T33))) :- timesc1(T34, T35, T33).
timesc1(zero(one(T53)), T54, zero(T52)) :- qc20(T53, T54, X56, T52).
timesc1(one(T846), T847, zero(T845)) :- qc20(T846, T847, X1078, zero(T845)).
timesc1(one(one(b)), T863, T855) :- addc23(T863, T863, T855).
timesc1(one(zero(T875)), T876, T855) :- qc320(T875, T876, X1121, T855).
timesc1(one(one(T896)), T897, T855) :- qc324(T896, T897, X1143, X1144, T855).
timesc1(zero(one(b)), T934, zero(T934)).
timesc1(zero(zero(T950)), T951, zero(zero(T949))) :- timesc1(T950, T951, T949).
timesc1(zero(one(T969)), T970, zero(T968)) :- qc20(T969, T970, X1210, T968).
timesc1(one(T982), T983, zero(T981)) :- qc20(T982, T983, X1226, zero(T981)).
timesc1(one(one(b)), T999, T991) :- addc23(T999, T999, T991).
timesc1(one(zero(T1011)), T1012, T991) :- qc320(T1011, T1012, X1269, T991).
timesc1(one(one(T1021)), T1022, T991) :- qc324(T1021, T1022, X1287, X1288, T991).
timesc22(one(b), T65, T65).
timesc22(zero(T76), T77, zero(X89)) :- timesc22(T76, T77, X89).
timesc22(one(T86), T91, X108) :- ','(timesc22(T86, T91, T90), addc37(T91, T90, X108)).
binaryZc48(zero(T120)) :- binaryZc48(T120).
binaryZc48(one(T125)) :- binaryc54(T125).
binaryc54(b).
binaryc54(zero(T131)) :- binaryZc48(T131).
binaryc54(one(T136)) :- binaryc54(T136).
addzc73(zero(T175), zero(T176), zero(X223)) :- addzc73(T175, T176, X223).
addzc73(zero(one(T197)), one(b), one(one(T197))) :- binaryc54(T197).
addzc73(zero(zero(T203)), one(b), one(zero(T203))) :- binaryZc48(T203).
addzc73(zero(T215), one(T216), one(X283)) :- addzc73(T215, T216, X283).
addzc73(one(T229), zero(T230), one(X307)) :- addyc96(T229, T230, X307).
addzc73(one(T265), one(T266), zero(X356)) :- addcc108(T265, T266, X356).
succc125(b, one(b)).
succc125(zero(T290), one(T290)) :- binaryZc48(T290).
succc125(one(T295), zero(X411)) :- succc125(T295, X411).
succZc118(zero(T279), one(T279)) :- binaryZc48(T279).
succZc118(one(T284), zero(X393)) :- succc125(T284, X393).
addCc143(zero(T327), zero(T328), one(X471)) :- addzc73(T327, T328, X471).
addCc143(zero(zero(T349)), one(b), zero(one(T349))) :- binaryZc48(T349).
addCc143(zero(one(T356)), one(b), zero(zero(X524))) :- succc125(T356, X524).
addCc143(zero(T367), one(T368), zero(X542)) :- addCc143(T367, T368, X542).
addCc143(one(b), zero(zero(T389)), zero(one(T389))) :- binaryZc48(T389).
addCc143(one(b), zero(one(T396)), zero(zero(X592))) :- succc125(T396, X592).
addCc143(one(T407), zero(T408), zero(X610)) :- addCc143(T407, T408, X610).
addCc143(one(T417), one(T418), one(X626)) :- addcc108(T417, T418, X626).
addcc108(b, b, one(b)).
addcc108(T272, b, X374) :- succZc118(T272, X374).
addcc108(b, T301, X428) :- succZc118(T301, X428).
addcc108(T313, T314, X447) :- addCc143(T313, T314, X447).
addyc96(b, one(T237), one(T237)) :- binaryc54(T237).
addyc96(b, zero(T243), zero(T243)) :- binaryZc48(T243).
addyc96(T255, T256, X340) :- addzc73(T255, T256, X340).
binaryZc43(T113) :- binaryZc48(T113).
addzc196(zero(T497), zero(T498), zero(T496)) :- addzc196(T497, T498, T496).
addzc196(zero(one(T524)), one(b), one(one(T524))) :- binaryc54(T524).
addzc196(zero(zero(T529)), one(b), one(zero(T529))) :- binaryZc48(T529).
addzc196(zero(T545), one(T546), one(T544)) :- addzc196(T545, T546, T544).
addzc196(one(T565), zero(T566), one(T564)) :- addyc219(T565, T566, T564).
addzc196(one(T607), one(T608), zero(T606)) :- addcc231(T607, T608, T606).
succc248(b, one(b)).
succc248(zero(T638), one(T638)) :- binaryZc48(T638).
succc248(one(T646), zero(T645)) :- succc248(T646, T645).
succZc241(zero(T625), one(T625)) :- binaryZc48(T625).
succZc241(one(T633), zero(T632)) :- succc248(T633, T632).
addCc266(zero(T693), zero(T694), one(T692)) :- addzc196(T693, T694, T692).
addCc266(zero(zero(T720)), one(b), zero(one(T720))) :- binaryZc48(T720).
addCc266(zero(one(T732)), one(b), zero(zero(T731))) :- succc248(T732, T731).
addCc266(zero(T747), one(T748), zero(T746)) :- addCc266(T747, T748, T746).
addCc266(one(b), zero(zero(T774)), zero(one(T774))) :- binaryZc48(T774).
addCc266(one(b), zero(one(T786)), zero(zero(T785))) :- succc248(T786, T785).
addCc266(one(T801), zero(T802), zero(T800)) :- addCc266(T801, T802, T800).
addCc266(one(T815), one(T816), one(T814)) :- addcc231(T815, T816, T814).
addcc231(b, b, one(b)).
addcc231(T619, b, T618) :- succZc241(T619, T618).
addcc231(b, T657, T656) :- succZc241(T657, T656).
addcc231(T673, T674, T672) :- addCc266(T673, T674, T672).
addyc219(b, one(T572), one(T572)) :- binaryc54(T572).
addyc219(b, zero(T577), zero(T577)) :- binaryZc48(T577).
addyc219(T593, T594, T592) :- addzc196(T593, T594, T592).
qc20(T53, T58, T57, T52) :- ','(timesc22(T53, T58, T57), addc23(T58, T57, T52)).
addc23(b, T441, zero(T441)) :- binaryZc43(T441).
addc23(zero(T477), T478, zero(T476)) :- addzc196(T477, T478, T476).
addc23(one(T833), T834, one(T832)) :- addyc219(T833, T834, T832).
addc37(b, T102, zero(T102)) :- binaryZc43(T102).
addc37(zero(T161), T162, zero(X196)) :- addzc73(T161, T162, X196).
addc37(one(T430), T431, one(X652)) :- addyc96(T430, T431, X652).
qc320(T875, T880, T879, T855) :- ','(timesc22(T875, T880, T879), addc23(T880, zero(T879), T855)).
qc324(T896, T912, T900, T911, T855) :- ','(timesc22(T896, T912, T900), ','(addc37(T912, T900, T911), addc23(T912, T911, T855))).

Afs:

times1(x1, x2, x3) = times1(x3)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
times1_in: (f,f,b)
p20_in: (f,f,f,b)
times22_in: (f,f,f)
timesc22_in: (f,f,f)
addc37_in: (f,f,f)
binaryZc43_in: (f)
binaryZc48_in: (f)
binaryc54_in: (f)
addzc73_in: (f,f,f)
addyc96_in: (f,f,f)
addcc108_in: (f,f,f)
succZc118_in: (f,f)
succc125_in: (f,f)
addCc143_in: (f,f,f)
add37_in: (f,f,f)
binaryZ43_in: (f) (b)
binaryZ48_in: (f) (b)
binary54_in: (f) (b)
addz73_in: (f,f,f)
addy96_in: (f,f,f)
addc108_in: (f,f,f)
succZ118_in: (f,f)
succ125_in: (f,f)
addC143_in: (f,f,f)
add23_in: (f,f,b) (b,b,b)
addz196_in: (f,f,b) (b,b,b)
addy219_in: (f,f,b) (b,b,b)
addc231_in: (f,f,b) (b,b,b)
succZ241_in: (f,b) (b,b)
succ248_in: (f,b) (b,b)
addC266_in: (f,f,b) (b,b,b)
p320_in: (f,f,f,b)
p324_in: (f,f,f,f,b)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

TIMES1_IN_AAG(zero(zero(T34)), T35, zero(zero(T33))) → U76_AAG(T34, T35, T33, times1_in_aag(T34, T35, T33))
TIMES1_IN_AAG(zero(zero(T34)), T35, zero(zero(T33))) → TIMES1_IN_AAG(T34, T35, T33)
TIMES1_IN_AAG(zero(one(T53)), T54, zero(T52)) → U77_AAG(T53, T54, T52, p20_in_aaag(T53, T54, X56, T52))
TIMES1_IN_AAG(zero(one(T53)), T54, zero(T52)) → P20_IN_AAAG(T53, T54, X56, T52)
P20_IN_AAAG(T53, T54, X56, T52) → U58_AAAG(T53, T54, X56, T52, times22_in_aaa(T53, T54, X56))
P20_IN_AAAG(T53, T54, X56, T52) → TIMES22_IN_AAA(T53, T54, X56)
TIMES22_IN_AAA(zero(T76), T77, zero(X89)) → U1_AAA(T76, T77, X89, times22_in_aaa(T76, T77, X89))
TIMES22_IN_AAA(zero(T76), T77, zero(X89)) → TIMES22_IN_AAA(T76, T77, X89)
TIMES22_IN_AAA(one(T86), T87, X108) → U2_AAA(T86, T87, X108, times22_in_aaa(T86, T87, X107))
TIMES22_IN_AAA(one(T86), T87, X108) → TIMES22_IN_AAA(T86, T87, X107)
TIMES22_IN_AAA(one(T86), T91, X108) → U3_AAA(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U3_AAA(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U4_AAA(T86, T91, X108, add37_in_aaa(T91, T90, X108))
U3_AAA(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → ADD37_IN_AAA(T91, T90, X108)
ADD37_IN_AAA(b, T102, zero(T102)) → U64_AAA(T102, binaryZ43_in_a(T102))
ADD37_IN_AAA(b, T102, zero(T102)) → BINARYZ43_IN_A(T102)
BINARYZ43_IN_A(T113) → U33_A(T113, binaryZ48_in_a(T113))
BINARYZ43_IN_A(T113) → BINARYZ48_IN_A(T113)
BINARYZ48_IN_A(zero(T120)) → U5_A(T120, binaryZ48_in_a(T120))
BINARYZ48_IN_A(zero(T120)) → BINARYZ48_IN_A(T120)
BINARYZ48_IN_A(one(T125)) → U6_A(T125, binary54_in_a(T125))
BINARYZ48_IN_A(one(T125)) → BINARY54_IN_A(T125)
BINARY54_IN_A(zero(T131)) → U7_A(T131, binaryZ48_in_a(T131))
BINARY54_IN_A(zero(T131)) → BINARYZ48_IN_A(T131)
BINARY54_IN_A(one(T136)) → U8_A(T136, binary54_in_a(T136))
BINARY54_IN_A(one(T136)) → BINARY54_IN_A(T136)
ADD37_IN_AAA(zero(T161), T162, zero(X196)) → U65_AAA(T161, T162, X196, addz73_in_aaa(T161, T162, X196))
ADD37_IN_AAA(zero(T161), T162, zero(X196)) → ADDZ73_IN_AAA(T161, T162, X196)
ADDZ73_IN_AAA(zero(T175), zero(T176), zero(X223)) → U9_AAA(T175, T176, X223, addz73_in_aaa(T175, T176, X223))
ADDZ73_IN_AAA(zero(T175), zero(T176), zero(X223)) → ADDZ73_IN_AAA(T175, T176, X223)
ADDZ73_IN_AAA(zero(one(T197)), one(b), one(one(T197))) → U10_AAA(T197, binary54_in_a(T197))
ADDZ73_IN_AAA(zero(one(T197)), one(b), one(one(T197))) → BINARY54_IN_A(T197)
ADDZ73_IN_AAA(zero(zero(T203)), one(b), one(zero(T203))) → U11_AAA(T203, binaryZ48_in_a(T203))
ADDZ73_IN_AAA(zero(zero(T203)), one(b), one(zero(T203))) → BINARYZ48_IN_A(T203)
ADDZ73_IN_AAA(zero(T215), one(T216), one(X283)) → U12_AAA(T215, T216, X283, addz73_in_aaa(T215, T216, X283))
ADDZ73_IN_AAA(zero(T215), one(T216), one(X283)) → ADDZ73_IN_AAA(T215, T216, X283)
ADDZ73_IN_AAA(one(T229), zero(T230), one(X307)) → U13_AAA(T229, T230, X307, addy96_in_aaa(T229, T230, X307))
ADDZ73_IN_AAA(one(T229), zero(T230), one(X307)) → ADDY96_IN_AAA(T229, T230, X307)
ADDY96_IN_AAA(b, one(T237), one(T237)) → U30_AAA(T237, binary54_in_a(T237))
ADDY96_IN_AAA(b, one(T237), one(T237)) → BINARY54_IN_A(T237)
ADDY96_IN_AAA(b, zero(T243), zero(T243)) → U31_AAA(T243, binaryZ48_in_a(T243))
ADDY96_IN_AAA(b, zero(T243), zero(T243)) → BINARYZ48_IN_A(T243)
ADDY96_IN_AAA(T255, T256, X340) → U32_AAA(T255, T256, X340, addz73_in_aaa(T255, T256, X340))
ADDY96_IN_AAA(T255, T256, X340) → ADDZ73_IN_AAA(T255, T256, X340)
ADDZ73_IN_AAA(one(T265), one(T266), zero(X356)) → U14_AAA(T265, T266, X356, addc108_in_aaa(T265, T266, X356))
ADDZ73_IN_AAA(one(T265), one(T266), zero(X356)) → ADDC108_IN_AAA(T265, T266, X356)
ADDC108_IN_AAA(T272, b, X374) → U27_AAA(T272, X374, succZ118_in_aa(T272, X374))
ADDC108_IN_AAA(T272, b, X374) → SUCCZ118_IN_AA(T272, X374)
SUCCZ118_IN_AA(zero(T279), one(T279)) → U17_AA(T279, binaryZ48_in_a(T279))
SUCCZ118_IN_AA(zero(T279), one(T279)) → BINARYZ48_IN_A(T279)
SUCCZ118_IN_AA(one(T284), zero(X393)) → U18_AA(T284, X393, succ125_in_aa(T284, X393))
SUCCZ118_IN_AA(one(T284), zero(X393)) → SUCC125_IN_AA(T284, X393)
SUCC125_IN_AA(zero(T290), one(T290)) → U15_AA(T290, binaryZ48_in_a(T290))
SUCC125_IN_AA(zero(T290), one(T290)) → BINARYZ48_IN_A(T290)
SUCC125_IN_AA(one(T295), zero(X411)) → U16_AA(T295, X411, succ125_in_aa(T295, X411))
SUCC125_IN_AA(one(T295), zero(X411)) → SUCC125_IN_AA(T295, X411)
ADDC108_IN_AAA(b, T301, X428) → U28_AAA(T301, X428, succZ118_in_aa(T301, X428))
ADDC108_IN_AAA(b, T301, X428) → SUCCZ118_IN_AA(T301, X428)
ADDC108_IN_AAA(T313, T314, X447) → U29_AAA(T313, T314, X447, addC143_in_aaa(T313, T314, X447))
ADDC108_IN_AAA(T313, T314, X447) → ADDC143_IN_AAA(T313, T314, X447)
ADDC143_IN_AAA(zero(T327), zero(T328), one(X471)) → U19_AAA(T327, T328, X471, addz73_in_aaa(T327, T328, X471))
ADDC143_IN_AAA(zero(T327), zero(T328), one(X471)) → ADDZ73_IN_AAA(T327, T328, X471)
ADDC143_IN_AAA(zero(zero(T349)), one(b), zero(one(T349))) → U20_AAA(T349, binaryZ48_in_a(T349))
ADDC143_IN_AAA(zero(zero(T349)), one(b), zero(one(T349))) → BINARYZ48_IN_A(T349)
ADDC143_IN_AAA(zero(one(T356)), one(b), zero(zero(X524))) → U21_AAA(T356, X524, succ125_in_aa(T356, X524))
ADDC143_IN_AAA(zero(one(T356)), one(b), zero(zero(X524))) → SUCC125_IN_AA(T356, X524)
ADDC143_IN_AAA(zero(T367), one(T368), zero(X542)) → U22_AAA(T367, T368, X542, addC143_in_aaa(T367, T368, X542))
ADDC143_IN_AAA(zero(T367), one(T368), zero(X542)) → ADDC143_IN_AAA(T367, T368, X542)
ADDC143_IN_AAA(one(b), zero(zero(T389)), zero(one(T389))) → U23_AAA(T389, binaryZ48_in_a(T389))
ADDC143_IN_AAA(one(b), zero(zero(T389)), zero(one(T389))) → BINARYZ48_IN_A(T389)
ADDC143_IN_AAA(one(b), zero(one(T396)), zero(zero(X592))) → U24_AAA(T396, X592, succ125_in_aa(T396, X592))
ADDC143_IN_AAA(one(b), zero(one(T396)), zero(zero(X592))) → SUCC125_IN_AA(T396, X592)
ADDC143_IN_AAA(one(T407), zero(T408), zero(X610)) → U25_AAA(T407, T408, X610, addC143_in_aaa(T407, T408, X610))
ADDC143_IN_AAA(one(T407), zero(T408), zero(X610)) → ADDC143_IN_AAA(T407, T408, X610)
ADDC143_IN_AAA(one(T417), one(T418), one(X626)) → U26_AAA(T417, T418, X626, addc108_in_aaa(T417, T418, X626))
ADDC143_IN_AAA(one(T417), one(T418), one(X626)) → ADDC108_IN_AAA(T417, T418, X626)
ADD37_IN_AAA(one(T430), T431, one(X652)) → U66_AAA(T430, T431, X652, addy96_in_aaa(T430, T431, X652))
ADD37_IN_AAA(one(T430), T431, one(X652)) → ADDY96_IN_AAA(T430, T431, X652)
P20_IN_AAAG(T53, T58, T57, T52) → U59_AAAG(T53, T58, T57, T52, timesc22_in_aaa(T53, T58, T57))
U59_AAAG(T53, T58, T57, T52, timesc22_out_aaa(T53, T58, T57)) → U60_AAAG(T53, T58, T57, T52, add23_in_aag(T58, T57, T52))
U59_AAAG(T53, T58, T57, T52, timesc22_out_aaa(T53, T58, T57)) → ADD23_IN_AAG(T58, T57, T52)
ADD23_IN_AAG(b, T441, zero(T441)) → U61_AAG(T441, binaryZ43_in_g(T441))
ADD23_IN_AAG(b, T441, zero(T441)) → BINARYZ43_IN_G(T441)
BINARYZ43_IN_G(T113) → U33_G(T113, binaryZ48_in_g(T113))
BINARYZ43_IN_G(T113) → BINARYZ48_IN_G(T113)
BINARYZ48_IN_G(zero(T120)) → U5_G(T120, binaryZ48_in_g(T120))
BINARYZ48_IN_G(zero(T120)) → BINARYZ48_IN_G(T120)
BINARYZ48_IN_G(one(T125)) → U6_G(T125, binary54_in_g(T125))
BINARYZ48_IN_G(one(T125)) → BINARY54_IN_G(T125)
BINARY54_IN_G(zero(T131)) → U7_G(T131, binaryZ48_in_g(T131))
BINARY54_IN_G(zero(T131)) → BINARYZ48_IN_G(T131)
BINARY54_IN_G(one(T136)) → U8_G(T136, binary54_in_g(T136))
BINARY54_IN_G(one(T136)) → BINARY54_IN_G(T136)
ADD23_IN_AAG(zero(T477), T478, zero(T476)) → U62_AAG(T477, T478, T476, addz196_in_aag(T477, T478, T476))
ADD23_IN_AAG(zero(T477), T478, zero(T476)) → ADDZ196_IN_AAG(T477, T478, T476)
ADDZ196_IN_AAG(zero(T497), zero(T498), zero(T496)) → U34_AAG(T497, T498, T496, addz196_in_aag(T497, T498, T496))
ADDZ196_IN_AAG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_AAG(T497, T498, T496)
ADDZ196_IN_AAG(zero(one(T524)), one(b), one(one(T524))) → U35_AAG(T524, binary54_in_g(T524))
ADDZ196_IN_AAG(zero(one(T524)), one(b), one(one(T524))) → BINARY54_IN_G(T524)
ADDZ196_IN_AAG(zero(zero(T529)), one(b), one(zero(T529))) → U36_AAG(T529, binaryZ48_in_g(T529))
ADDZ196_IN_AAG(zero(zero(T529)), one(b), one(zero(T529))) → BINARYZ48_IN_G(T529)
ADDZ196_IN_AAG(zero(T545), one(T546), one(T544)) → U37_AAG(T545, T546, T544, addz196_in_aag(T545, T546, T544))
ADDZ196_IN_AAG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_AAG(T545, T546, T544)
ADDZ196_IN_AAG(one(T565), zero(T566), one(T564)) → U38_AAG(T565, T566, T564, addy219_in_aag(T565, T566, T564))
ADDZ196_IN_AAG(one(T565), zero(T566), one(T564)) → ADDY219_IN_AAG(T565, T566, T564)
ADDY219_IN_AAG(b, one(T572), one(T572)) → U55_AAG(T572, binary54_in_g(T572))
ADDY219_IN_AAG(b, one(T572), one(T572)) → BINARY54_IN_G(T572)
ADDY219_IN_AAG(b, zero(T577), zero(T577)) → U56_AAG(T577, binaryZ48_in_g(T577))
ADDY219_IN_AAG(b, zero(T577), zero(T577)) → BINARYZ48_IN_G(T577)
ADDY219_IN_AAG(T593, T594, T592) → U57_AAG(T593, T594, T592, addz196_in_aag(T593, T594, T592))
ADDY219_IN_AAG(T593, T594, T592) → ADDZ196_IN_AAG(T593, T594, T592)
ADDZ196_IN_AAG(one(T607), one(T608), zero(T606)) → U39_AAG(T607, T608, T606, addc231_in_aag(T607, T608, T606))
ADDZ196_IN_AAG(one(T607), one(T608), zero(T606)) → ADDC231_IN_AAG(T607, T608, T606)
ADDC231_IN_AAG(T619, b, T618) → U52_AAG(T619, T618, succZ241_in_ag(T619, T618))
ADDC231_IN_AAG(T619, b, T618) → SUCCZ241_IN_AG(T619, T618)
SUCCZ241_IN_AG(zero(T625), one(T625)) → U42_AG(T625, binaryZ48_in_g(T625))
SUCCZ241_IN_AG(zero(T625), one(T625)) → BINARYZ48_IN_G(T625)
SUCCZ241_IN_AG(one(T633), zero(T632)) → U43_AG(T633, T632, succ248_in_ag(T633, T632))
SUCCZ241_IN_AG(one(T633), zero(T632)) → SUCC248_IN_AG(T633, T632)
SUCC248_IN_AG(zero(T638), one(T638)) → U40_AG(T638, binaryZ48_in_g(T638))
SUCC248_IN_AG(zero(T638), one(T638)) → BINARYZ48_IN_G(T638)
SUCC248_IN_AG(one(T646), zero(T645)) → U41_AG(T646, T645, succ248_in_ag(T646, T645))
SUCC248_IN_AG(one(T646), zero(T645)) → SUCC248_IN_AG(T646, T645)
ADDC231_IN_AAG(b, T657, T656) → U53_AAG(T657, T656, succZ241_in_ag(T657, T656))
ADDC231_IN_AAG(b, T657, T656) → SUCCZ241_IN_AG(T657, T656)
ADDC231_IN_AAG(T673, T674, T672) → U54_AAG(T673, T674, T672, addC266_in_aag(T673, T674, T672))
ADDC231_IN_AAG(T673, T674, T672) → ADDC266_IN_AAG(T673, T674, T672)
ADDC266_IN_AAG(zero(T693), zero(T694), one(T692)) → U44_AAG(T693, T694, T692, addz196_in_aag(T693, T694, T692))
ADDC266_IN_AAG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_AAG(T693, T694, T692)
ADDC266_IN_AAG(zero(zero(T720)), one(b), zero(one(T720))) → U45_AAG(T720, binaryZ48_in_g(T720))
ADDC266_IN_AAG(zero(zero(T720)), one(b), zero(one(T720))) → BINARYZ48_IN_G(T720)
ADDC266_IN_AAG(zero(one(T732)), one(b), zero(zero(T731))) → U46_AAG(T732, T731, succ248_in_ag(T732, T731))
ADDC266_IN_AAG(zero(one(T732)), one(b), zero(zero(T731))) → SUCC248_IN_AG(T732, T731)
ADDC266_IN_AAG(zero(T747), one(T748), zero(T746)) → U47_AAG(T747, T748, T746, addC266_in_aag(T747, T748, T746))
ADDC266_IN_AAG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_AAG(T747, T748, T746)
ADDC266_IN_AAG(one(b), zero(zero(T774)), zero(one(T774))) → U48_AAG(T774, binaryZ48_in_g(T774))
ADDC266_IN_AAG(one(b), zero(zero(T774)), zero(one(T774))) → BINARYZ48_IN_G(T774)
ADDC266_IN_AAG(one(b), zero(one(T786)), zero(zero(T785))) → U49_AAG(T786, T785, succ248_in_ag(T786, T785))
ADDC266_IN_AAG(one(b), zero(one(T786)), zero(zero(T785))) → SUCC248_IN_AG(T786, T785)
ADDC266_IN_AAG(one(T801), zero(T802), zero(T800)) → U50_AAG(T801, T802, T800, addC266_in_aag(T801, T802, T800))
ADDC266_IN_AAG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_AAG(T801, T802, T800)
ADDC266_IN_AAG(one(T815), one(T816), one(T814)) → U51_AAG(T815, T816, T814, addc231_in_aag(T815, T816, T814))
ADDC266_IN_AAG(one(T815), one(T816), one(T814)) → ADDC231_IN_AAG(T815, T816, T814)
ADD23_IN_AAG(one(T833), T834, one(T832)) → U63_AAG(T833, T834, T832, addy219_in_aag(T833, T834, T832))
ADD23_IN_AAG(one(T833), T834, one(T832)) → ADDY219_IN_AAG(T833, T834, T832)
TIMES1_IN_AAG(one(T846), T847, zero(T845)) → U78_AAG(T846, T847, T845, p20_in_aaag(T846, T847, X1078, zero(T845)))
TIMES1_IN_AAG(one(T846), T847, zero(T845)) → P20_IN_AAAG(T846, T847, X1078, zero(T845))
TIMES1_IN_AAG(one(one(b)), T863, T855) → U79_AAG(T863, T855, add23_in_aag(T863, T863, T855))
TIMES1_IN_AAG(one(one(b)), T863, T855) → ADD23_IN_AAG(T863, T863, T855)
TIMES1_IN_AAG(one(zero(T875)), T876, T855) → U80_AAG(T875, T876, T855, p320_in_aaag(T875, T876, X1121, T855))
TIMES1_IN_AAG(one(zero(T875)), T876, T855) → P320_IN_AAAG(T875, T876, X1121, T855)
P320_IN_AAAG(T875, T876, X1121, T855) → U67_AAAG(T875, T876, X1121, T855, times22_in_aaa(T875, T876, X1121))
P320_IN_AAAG(T875, T876, X1121, T855) → TIMES22_IN_AAA(T875, T876, X1121)
P320_IN_AAAG(T875, T880, T879, T855) → U68_AAAG(T875, T880, T879, T855, timesc22_in_aaa(T875, T880, T879))
U68_AAAG(T875, T880, T879, T855, timesc22_out_aaa(T875, T880, T879)) → U69_AAAG(T875, T880, T879, T855, add23_in_aag(T880, zero(T879), T855))
U68_AAAG(T875, T880, T879, T855, timesc22_out_aaa(T875, T880, T879)) → ADD23_IN_AAG(T880, zero(T879), T855)
TIMES1_IN_AAG(one(one(T896)), T897, T855) → U81_AAG(T896, T897, T855, p324_in_aaaag(T896, T897, X1143, X1144, T855))
TIMES1_IN_AAG(one(one(T896)), T897, T855) → P324_IN_AAAAG(T896, T897, X1143, X1144, T855)
P324_IN_AAAAG(T896, T897, X1143, X1144, T855) → U70_AAAAG(T896, T897, X1143, X1144, T855, times22_in_aaa(T896, T897, X1143))
P324_IN_AAAAG(T896, T897, X1143, X1144, T855) → TIMES22_IN_AAA(T896, T897, X1143)
P324_IN_AAAAG(T896, T901, T900, X1144, T855) → U71_AAAAG(T896, T901, T900, X1144, T855, timesc22_in_aaa(T896, T901, T900))
U71_AAAAG(T896, T901, T900, X1144, T855, timesc22_out_aaa(T896, T901, T900)) → U72_AAAAG(T896, T901, T900, X1144, T855, add37_in_aaa(T901, T900, X1144))
U71_AAAAG(T896, T901, T900, X1144, T855, timesc22_out_aaa(T896, T901, T900)) → ADD37_IN_AAA(T901, T900, X1144)
P324_IN_AAAAG(T896, T912, T900, T911, T855) → U73_AAAAG(T896, T912, T900, T911, T855, timesc22_in_aaa(T896, T912, T900))
U73_AAAAG(T896, T912, T900, T911, T855, timesc22_out_aaa(T896, T912, T900)) → U74_AAAAG(T896, T912, T900, T911, T855, addc37_in_aaa(T912, T900, T911))
U74_AAAAG(T896, T912, T900, T911, T855, addc37_out_aaa(T912, T900, T911)) → U75_AAAAG(T896, T912, T900, T911, T855, add23_in_ggg(T912, T911, T855))
U74_AAAAG(T896, T912, T900, T911, T855, addc37_out_aaa(T912, T900, T911)) → ADD23_IN_GGG(T912, T911, T855)
ADD23_IN_GGG(b, T441, zero(T441)) → U61_GGG(T441, binaryZ43_in_g(T441))
ADD23_IN_GGG(b, T441, zero(T441)) → BINARYZ43_IN_G(T441)
ADD23_IN_GGG(zero(T477), T478, zero(T476)) → U62_GGG(T477, T478, T476, addz196_in_ggg(T477, T478, T476))
ADD23_IN_GGG(zero(T477), T478, zero(T476)) → ADDZ196_IN_GGG(T477, T478, T476)
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → U34_GGG(T497, T498, T496, addz196_in_ggg(T497, T498, T496))
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_GGG(T497, T498, T496)
ADDZ196_IN_GGG(zero(one(T524)), one(b), one(one(T524))) → U35_GGG(T524, binary54_in_g(T524))
ADDZ196_IN_GGG(zero(one(T524)), one(b), one(one(T524))) → BINARY54_IN_G(T524)
ADDZ196_IN_GGG(zero(zero(T529)), one(b), one(zero(T529))) → U36_GGG(T529, binaryZ48_in_g(T529))
ADDZ196_IN_GGG(zero(zero(T529)), one(b), one(zero(T529))) → BINARYZ48_IN_G(T529)
ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → U37_GGG(T545, T546, T544, addz196_in_ggg(T545, T546, T544))
ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_GGG(T545, T546, T544)
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → U38_GGG(T565, T566, T564, addy219_in_ggg(T565, T566, T564))
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → ADDY219_IN_GGG(T565, T566, T564)
ADDY219_IN_GGG(b, one(T572), one(T572)) → U55_GGG(T572, binary54_in_g(T572))
ADDY219_IN_GGG(b, one(T572), one(T572)) → BINARY54_IN_G(T572)
ADDY219_IN_GGG(b, zero(T577), zero(T577)) → U56_GGG(T577, binaryZ48_in_g(T577))
ADDY219_IN_GGG(b, zero(T577), zero(T577)) → BINARYZ48_IN_G(T577)
ADDY219_IN_GGG(T593, T594, T592) → U57_GGG(T593, T594, T592, addz196_in_ggg(T593, T594, T592))
ADDY219_IN_GGG(T593, T594, T592) → ADDZ196_IN_GGG(T593, T594, T592)
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → U39_GGG(T607, T608, T606, addc231_in_ggg(T607, T608, T606))
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → ADDC231_IN_GGG(T607, T608, T606)
ADDC231_IN_GGG(T619, b, T618) → U52_GGG(T619, T618, succZ241_in_gg(T619, T618))
ADDC231_IN_GGG(T619, b, T618) → SUCCZ241_IN_GG(T619, T618)
SUCCZ241_IN_GG(zero(T625), one(T625)) → U42_GG(T625, binaryZ48_in_g(T625))
SUCCZ241_IN_GG(zero(T625), one(T625)) → BINARYZ48_IN_G(T625)
SUCCZ241_IN_GG(one(T633), zero(T632)) → U43_GG(T633, T632, succ248_in_gg(T633, T632))
SUCCZ241_IN_GG(one(T633), zero(T632)) → SUCC248_IN_GG(T633, T632)
SUCC248_IN_GG(zero(T638), one(T638)) → U40_GG(T638, binaryZ48_in_g(T638))
SUCC248_IN_GG(zero(T638), one(T638)) → BINARYZ48_IN_G(T638)
SUCC248_IN_GG(one(T646), zero(T645)) → U41_GG(T646, T645, succ248_in_gg(T646, T645))
SUCC248_IN_GG(one(T646), zero(T645)) → SUCC248_IN_GG(T646, T645)
ADDC231_IN_GGG(b, T657, T656) → U53_GGG(T657, T656, succZ241_in_gg(T657, T656))
ADDC231_IN_GGG(b, T657, T656) → SUCCZ241_IN_GG(T657, T656)
ADDC231_IN_GGG(T673, T674, T672) → U54_GGG(T673, T674, T672, addC266_in_ggg(T673, T674, T672))
ADDC231_IN_GGG(T673, T674, T672) → ADDC266_IN_GGG(T673, T674, T672)
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → U44_GGG(T693, T694, T692, addz196_in_ggg(T693, T694, T692))
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_GGG(T693, T694, T692)
ADDC266_IN_GGG(zero(zero(T720)), one(b), zero(one(T720))) → U45_GGG(T720, binaryZ48_in_g(T720))
ADDC266_IN_GGG(zero(zero(T720)), one(b), zero(one(T720))) → BINARYZ48_IN_G(T720)
ADDC266_IN_GGG(zero(one(T732)), one(b), zero(zero(T731))) → U46_GGG(T732, T731, succ248_in_gg(T732, T731))
ADDC266_IN_GGG(zero(one(T732)), one(b), zero(zero(T731))) → SUCC248_IN_GG(T732, T731)
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → U47_GGG(T747, T748, T746, addC266_in_ggg(T747, T748, T746))
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_GGG(T747, T748, T746)
ADDC266_IN_GGG(one(b), zero(zero(T774)), zero(one(T774))) → U48_GGG(T774, binaryZ48_in_g(T774))
ADDC266_IN_GGG(one(b), zero(zero(T774)), zero(one(T774))) → BINARYZ48_IN_G(T774)
ADDC266_IN_GGG(one(b), zero(one(T786)), zero(zero(T785))) → U49_GGG(T786, T785, succ248_in_gg(T786, T785))
ADDC266_IN_GGG(one(b), zero(one(T786)), zero(zero(T785))) → SUCC248_IN_GG(T786, T785)
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → U50_GGG(T801, T802, T800, addC266_in_ggg(T801, T802, T800))
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_GGG(T801, T802, T800)
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → U51_GGG(T815, T816, T814, addc231_in_ggg(T815, T816, T814))
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → ADDC231_IN_GGG(T815, T816, T814)
ADD23_IN_GGG(one(T833), T834, one(T832)) → U63_GGG(T833, T834, T832, addy219_in_ggg(T833, T834, T832))
ADD23_IN_GGG(one(T833), T834, one(T832)) → ADDY219_IN_GGG(T833, T834, T832)
TIMES1_IN_AAG(zero(zero(T950)), T951, zero(zero(T949))) → U82_AAG(T950, T951, T949, times1_in_aag(T950, T951, T949))
TIMES1_IN_AAG(zero(one(T969)), T970, zero(T968)) → U83_AAG(T969, T970, T968, p20_in_aaag(T969, T970, X1210, T968))
TIMES1_IN_AAG(one(T982), T983, zero(T981)) → U84_AAG(T982, T983, T981, p20_in_aaag(T982, T983, X1226, zero(T981)))
TIMES1_IN_AAG(one(one(b)), T999, T991) → U85_AAG(T999, T991, add23_in_aag(T999, T999, T991))
TIMES1_IN_AAG(one(zero(T1011)), T1012, T991) → U86_AAG(T1011, T1012, T991, p320_in_aaag(T1011, T1012, X1269, T991))
TIMES1_IN_AAG(one(one(T1021)), T1022, T991) → U87_AAG(T1021, T1022, T991, p324_in_aaaag(T1021, T1022, X1287, X1288, T991))

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
times1_in_aag(x1, x2, x3) = times1_in_aag(x3)
zero(x1) = zero(x1)
p20_in_aaag(x1, x2, x3, x4) = p20_in_aaag(x4)
times22_in_aaa(x1, x2, x3) = times22_in_aaa
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
add37_in_aaa(x1, x2, x3) = add37_in_aaa
binaryZ43_in_a(x1) = binaryZ43_in_a
binaryZ48_in_a(x1) = binaryZ48_in_a
binary54_in_a(x1) = binary54_in_a
addz73_in_aaa(x1, x2, x3) = addz73_in_aaa
addy96_in_aaa(x1, x2, x3) = addy96_in_aaa
addc108_in_aaa(x1, x2, x3) = addc108_in_aaa
succZ118_in_aa(x1, x2) = succZ118_in_aa
succ125_in_aa(x1, x2) = succ125_in_aa
addC143_in_aaa(x1, x2, x3) = addC143_in_aaa
add23_in_aag(x1, x2, x3) = add23_in_aag(x3)
binaryZ43_in_g(x1) = binaryZ43_in_g(x1)
binaryZ48_in_g(x1) = binaryZ48_in_g(x1)
one(x1) = one(x1)
binary54_in_g(x1) = binary54_in_g(x1)
addz196_in_aag(x1, x2, x3) = addz196_in_aag(x3)
addy219_in_aag(x1, x2, x3) = addy219_in_aag(x3)
addc231_in_aag(x1, x2, x3) = addc231_in_aag(x3)
succZ241_in_ag(x1, x2) = succZ241_in_ag(x2)
succ248_in_ag(x1, x2) = succ248_in_ag(x2)
addC266_in_aag(x1, x2, x3) = addC266_in_aag(x3)
p320_in_aaag(x1, x2, x3, x4) = p320_in_aaag(x4)
p324_in_aaaag(x1, x2, x3, x4, x5) = p324_in_aaaag(x5)
add23_in_ggg(x1, x2, x3) = add23_in_ggg(x1, x2, x3)
b = b
addz196_in_ggg(x1, x2, x3) = addz196_in_ggg(x1, x2, x3)
addy219_in_ggg(x1, x2, x3) = addy219_in_ggg(x1, x2, x3)
addc231_in_ggg(x1, x2, x3) = addc231_in_ggg(x1, x2, x3)
succZ241_in_gg(x1, x2) = succZ241_in_gg(x1, x2)
succ248_in_gg(x1, x2) = succ248_in_gg(x1, x2)
addC266_in_ggg(x1, x2, x3) = addC266_in_ggg(x1, x2, x3)
TIMES1_IN_AAG(x1, x2, x3) = TIMES1_IN_AAG(x3)
U76_AAG(x1, x2, x3, x4) = U76_AAG(x3, x4)
U77_AAG(x1, x2, x3, x4) = U77_AAG(x3, x4)
P20_IN_AAAG(x1, x2, x3, x4) = P20_IN_AAAG(x4)
U58_AAAG(x1, x2, x3, x4, x5) = U58_AAAG(x4, x5)
TIMES22_IN_AAA(x1, x2, x3) = TIMES22_IN_AAA
U1_AAA(x1, x2, x3, x4) = U1_AAA(x4)
U2_AAA(x1, x2, x3, x4) = U2_AAA(x4)
U3_AAA(x1, x2, x3, x4) = U3_AAA(x4)
U4_AAA(x1, x2, x3, x4) = U4_AAA(x1, x4)
ADD37_IN_AAA(x1, x2, x3) = ADD37_IN_AAA
U64_AAA(x1, x2) = U64_AAA(x2)
BINARYZ43_IN_A(x1) = BINARYZ43_IN_A
U33_A(x1, x2) = U33_A(x2)
BINARYZ48_IN_A(x1) = BINARYZ48_IN_A
U5_A(x1, x2) = U5_A(x2)
U6_A(x1, x2) = U6_A(x2)
BINARY54_IN_A(x1) = BINARY54_IN_A
U7_A(x1, x2) = U7_A(x2)
U8_A(x1, x2) = U8_A(x2)
U65_AAA(x1, x2, x3, x4) = U65_AAA(x4)
ADDZ73_IN_AAA(x1, x2, x3) = ADDZ73_IN_AAA
U9_AAA(x1, x2, x3, x4) = U9_AAA(x4)
U10_AAA(x1, x2) = U10_AAA(x2)
U11_AAA(x1, x2) = U11_AAA(x2)
U12_AAA(x1, x2, x3, x4) = U12_AAA(x4)
U13_AAA(x1, x2, x3, x4) = U13_AAA(x4)
ADDY96_IN_AAA(x1, x2, x3) = ADDY96_IN_AAA
U30_AAA(x1, x2) = U30_AAA(x2)
U31_AAA(x1, x2) = U31_AAA(x2)
U32_AAA(x1, x2, x3, x4) = U32_AAA(x4)
U14_AAA(x1, x2, x3, x4) = U14_AAA(x4)
ADDC108_IN_AAA(x1, x2, x3) = ADDC108_IN_AAA
U27_AAA(x1, x2, x3) = U27_AAA(x3)
SUCCZ118_IN_AA(x1, x2) = SUCCZ118_IN_AA
U17_AA(x1, x2) = U17_AA(x2)
U18_AA(x1, x2, x3) = U18_AA(x3)
SUCC125_IN_AA(x1, x2) = SUCC125_IN_AA
U15_AA(x1, x2) = U15_AA(x2)
U16_AA(x1, x2, x3) = U16_AA(x3)
U28_AAA(x1, x2, x3) = U28_AAA(x3)
U29_AAA(x1, x2, x3, x4) = U29_AAA(x4)
ADDC143_IN_AAA(x1, x2, x3) = ADDC143_IN_AAA
U19_AAA(x1, x2, x3, x4) = U19_AAA(x4)
U20_AAA(x1, x2) = U20_AAA(x2)
U21_AAA(x1, x2, x3) = U21_AAA(x3)
U22_AAA(x1, x2, x3, x4) = U22_AAA(x4)
U23_AAA(x1, x2) = U23_AAA(x2)
U24_AAA(x1, x2, x3) = U24_AAA(x3)
U25_AAA(x1, x2, x3, x4) = U25_AAA(x4)
U26_AAA(x1, x2, x3, x4) = U26_AAA(x4)
U66_AAA(x1, x2, x3, x4) = U66_AAA(x4)
U59_AAAG(x1, x2, x3, x4, x5) = U59_AAAG(x4, x5)
U60_AAAG(x1, x2, x3, x4, x5) = U60_AAAG(x1, x4, x5)
ADD23_IN_AAG(x1, x2, x3) = ADD23_IN_AAG(x3)
U61_AAG(x1, x2) = U61_AAG(x1, x2)
BINARYZ43_IN_G(x1) = BINARYZ43_IN_G(x1)
U33_G(x1, x2) = U33_G(x1, x2)
BINARYZ48_IN_G(x1) = BINARYZ48_IN_G(x1)
U5_G(x1, x2) = U5_G(x1, x2)
U6_G(x1, x2) = U6_G(x1, x2)
BINARY54_IN_G(x1) = BINARY54_IN_G(x1)
U7_G(x1, x2) = U7_G(x1, x2)
U8_G(x1, x2) = U8_G(x1, x2)
U62_AAG(x1, x2, x3, x4) = U62_AAG(x3, x4)
ADDZ196_IN_AAG(x1, x2, x3) = ADDZ196_IN_AAG(x3)
U34_AAG(x1, x2, x3, x4) = U34_AAG(x3, x4)
U35_AAG(x1, x2) = U35_AAG(x1, x2)
U36_AAG(x1, x2) = U36_AAG(x1, x2)
U37_AAG(x1, x2, x3, x4) = U37_AAG(x3, x4)
U38_AAG(x1, x2, x3, x4) = U38_AAG(x3, x4)
ADDY219_IN_AAG(x1, x2, x3) = ADDY219_IN_AAG(x3)
U55_AAG(x1, x2) = U55_AAG(x1, x2)
U56_AAG(x1, x2) = U56_AAG(x1, x2)
U57_AAG(x1, x2, x3, x4) = U57_AAG(x3, x4)
U39_AAG(x1, x2, x3, x4) = U39_AAG(x3, x4)
ADDC231_IN_AAG(x1, x2, x3) = ADDC231_IN_AAG(x3)
U52_AAG(x1, x2, x3) = U52_AAG(x2, x3)
SUCCZ241_IN_AG(x1, x2) = SUCCZ241_IN_AG(x2)
U42_AG(x1, x2) = U42_AG(x1, x2)
U43_AG(x1, x2, x3) = U43_AG(x2, x3)
SUCC248_IN_AG(x1, x2) = SUCC248_IN_AG(x2)
U40_AG(x1, x2) = U40_AG(x1, x2)
U41_AG(x1, x2, x3) = U41_AG(x2, x3)
U53_AAG(x1, x2, x3) = U53_AAG(x2, x3)
U54_AAG(x1, x2, x3, x4) = U54_AAG(x3, x4)
ADDC266_IN_AAG(x1, x2, x3) = ADDC266_IN_AAG(x3)
U44_AAG(x1, x2, x3, x4) = U44_AAG(x3, x4)
U45_AAG(x1, x2) = U45_AAG(x1, x2)
U46_AAG(x1, x2, x3) = U46_AAG(x2, x3)
U47_AAG(x1, x2, x3, x4) = U47_AAG(x3, x4)
U48_AAG(x1, x2) = U48_AAG(x1, x2)
U49_AAG(x1, x2, x3) = U49_AAG(x2, x3)
U50_AAG(x1, x2, x3, x4) = U50_AAG(x3, x4)
U51_AAG(x1, x2, x3, x4) = U51_AAG(x3, x4)
U63_AAG(x1, x2, x3, x4) = U63_AAG(x3, x4)
U78_AAG(x1, x2, x3, x4) = U78_AAG(x3, x4)
U79_AAG(x1, x2, x3) = U79_AAG(x2, x3)
U80_AAG(x1, x2, x3, x4) = U80_AAG(x3, x4)
P320_IN_AAAG(x1, x2, x3, x4) = P320_IN_AAAG(x4)
U67_AAAG(x1, x2, x3, x4, x5) = U67_AAAG(x4, x5)
U68_AAAG(x1, x2, x3, x4, x5) = U68_AAAG(x4, x5)
U69_AAAG(x1, x2, x3, x4, x5) = U69_AAAG(x1, x4, x5)
U81_AAG(x1, x2, x3, x4) = U81_AAG(x3, x4)
P324_IN_AAAAG(x1, x2, x3, x4, x5) = P324_IN_AAAAG(x5)
U70_AAAAG(x1, x2, x3, x4, x5, x6) = U70_AAAAG(x5, x6)
U71_AAAAG(x1, x2, x3, x4, x5, x6) = U71_AAAAG(x5, x6)
U72_AAAAG(x1, x2, x3, x4, x5, x6) = U72_AAAAG(x1, x5, x6)
U73_AAAAG(x1, x2, x3, x4, x5, x6) = U73_AAAAG(x5, x6)
U74_AAAAG(x1, x2, x3, x4, x5, x6) = U74_AAAAG(x1, x5, x6)
U75_AAAAG(x1, x2, x3, x4, x5, x6) = U75_AAAAG(x1, x2, x5, x6)
ADD23_IN_GGG(x1, x2, x3) = ADD23_IN_GGG(x1, x2, x3)
U61_GGG(x1, x2) = U61_GGG(x1, x2)
U62_GGG(x1, x2, x3, x4) = U62_GGG(x1, x2, x3, x4)
ADDZ196_IN_GGG(x1, x2, x3) = ADDZ196_IN_GGG(x1, x2, x3)
U34_GGG(x1, x2, x3, x4) = U34_GGG(x1, x2, x3, x4)
U35_GGG(x1, x2) = U35_GGG(x1, x2)
U36_GGG(x1, x2) = U36_GGG(x1, x2)
U37_GGG(x1, x2, x3, x4) = U37_GGG(x1, x2, x3, x4)
U38_GGG(x1, x2, x3, x4) = U38_GGG(x1, x2, x3, x4)
ADDY219_IN_GGG(x1, x2, x3) = ADDY219_IN_GGG(x1, x2, x3)
U55_GGG(x1, x2) = U55_GGG(x1, x2)
U56_GGG(x1, x2) = U56_GGG(x1, x2)
U57_GGG(x1, x2, x3, x4) = U57_GGG(x1, x2, x3, x4)
U39_GGG(x1, x2, x3, x4) = U39_GGG(x1, x2, x3, x4)
ADDC231_IN_GGG(x1, x2, x3) = ADDC231_IN_GGG(x1, x2, x3)
U52_GGG(x1, x2, x3) = U52_GGG(x1, x2, x3)
SUCCZ241_IN_GG(x1, x2) = SUCCZ241_IN_GG(x1, x2)
U42_GG(x1, x2) = U42_GG(x1, x2)
U43_GG(x1, x2, x3) = U43_GG(x1, x2, x3)
SUCC248_IN_GG(x1, x2) = SUCC248_IN_GG(x1, x2)
U40_GG(x1, x2) = U40_GG(x1, x2)
U41_GG(x1, x2, x3) = U41_GG(x1, x2, x3)
U53_GGG(x1, x2, x3) = U53_GGG(x1, x2, x3)
U54_GGG(x1, x2, x3, x4) = U54_GGG(x1, x2, x3, x4)
ADDC266_IN_GGG(x1, x2, x3) = ADDC266_IN_GGG(x1, x2, x3)
U44_GGG(x1, x2, x3, x4) = U44_GGG(x1, x2, x3, x4)
U45_GGG(x1, x2) = U45_GGG(x1, x2)
U46_GGG(x1, x2, x3) = U46_GGG(x1, x2, x3)
U47_GGG(x1, x2, x3, x4) = U47_GGG(x1, x2, x3, x4)
U48_GGG(x1, x2) = U48_GGG(x1, x2)
U49_GGG(x1, x2, x3) = U49_GGG(x1, x2, x3)
U50_GGG(x1, x2, x3, x4) = U50_GGG(x1, x2, x3, x4)
U51_GGG(x1, x2, x3, x4) = U51_GGG(x1, x2, x3, x4)
U63_GGG(x1, x2, x3, x4) = U63_GGG(x1, x2, x3, x4)
U82_AAG(x1, x2, x3, x4) = U82_AAG(x3, x4)
U83_AAG(x1, x2, x3, x4) = U83_AAG(x3, x4)
U84_AAG(x1, x2, x3, x4) = U84_AAG(x3, x4)
U85_AAG(x1, x2, x3) = U85_AAG(x2, x3)
U86_AAG(x1, x2, x3, x4) = U86_AAG(x3, x4)
U87_AAG(x1, x2, x3, x4) = U87_AAG(x3, x4)

We have to consider all (P,R,Pi)-chains

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(4) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

TIMES1_IN_AAG(zero(zero(T34)), T35, zero(zero(T33))) → U76_AAG(T34, T35, T33, times1_in_aag(T34, T35, T33))
TIMES1_IN_AAG(zero(zero(T34)), T35, zero(zero(T33))) → TIMES1_IN_AAG(T34, T35, T33)
TIMES1_IN_AAG(zero(one(T53)), T54, zero(T52)) → U77_AAG(T53, T54, T52, p20_in_aaag(T53, T54, X56, T52))
TIMES1_IN_AAG(zero(one(T53)), T54, zero(T52)) → P20_IN_AAAG(T53, T54, X56, T52)
P20_IN_AAAG(T53, T54, X56, T52) → U58_AAAG(T53, T54, X56, T52, times22_in_aaa(T53, T54, X56))
P20_IN_AAAG(T53, T54, X56, T52) → TIMES22_IN_AAA(T53, T54, X56)
TIMES22_IN_AAA(zero(T76), T77, zero(X89)) → U1_AAA(T76, T77, X89, times22_in_aaa(T76, T77, X89))
TIMES22_IN_AAA(zero(T76), T77, zero(X89)) → TIMES22_IN_AAA(T76, T77, X89)
TIMES22_IN_AAA(one(T86), T87, X108) → U2_AAA(T86, T87, X108, times22_in_aaa(T86, T87, X107))
TIMES22_IN_AAA(one(T86), T87, X108) → TIMES22_IN_AAA(T86, T87, X107)
TIMES22_IN_AAA(one(T86), T91, X108) → U3_AAA(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U3_AAA(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U4_AAA(T86, T91, X108, add37_in_aaa(T91, T90, X108))
U3_AAA(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → ADD37_IN_AAA(T91, T90, X108)
ADD37_IN_AAA(b, T102, zero(T102)) → U64_AAA(T102, binaryZ43_in_a(T102))
ADD37_IN_AAA(b, T102, zero(T102)) → BINARYZ43_IN_A(T102)
BINARYZ43_IN_A(T113) → U33_A(T113, binaryZ48_in_a(T113))
BINARYZ43_IN_A(T113) → BINARYZ48_IN_A(T113)
BINARYZ48_IN_A(zero(T120)) → U5_A(T120, binaryZ48_in_a(T120))
BINARYZ48_IN_A(zero(T120)) → BINARYZ48_IN_A(T120)
BINARYZ48_IN_A(one(T125)) → U6_A(T125, binary54_in_a(T125))
BINARYZ48_IN_A(one(T125)) → BINARY54_IN_A(T125)
BINARY54_IN_A(zero(T131)) → U7_A(T131, binaryZ48_in_a(T131))
BINARY54_IN_A(zero(T131)) → BINARYZ48_IN_A(T131)
BINARY54_IN_A(one(T136)) → U8_A(T136, binary54_in_a(T136))
BINARY54_IN_A(one(T136)) → BINARY54_IN_A(T136)
ADD37_IN_AAA(zero(T161), T162, zero(X196)) → U65_AAA(T161, T162, X196, addz73_in_aaa(T161, T162, X196))
ADD37_IN_AAA(zero(T161), T162, zero(X196)) → ADDZ73_IN_AAA(T161, T162, X196)
ADDZ73_IN_AAA(zero(T175), zero(T176), zero(X223)) → U9_AAA(T175, T176, X223, addz73_in_aaa(T175, T176, X223))
ADDZ73_IN_AAA(zero(T175), zero(T176), zero(X223)) → ADDZ73_IN_AAA(T175, T176, X223)
ADDZ73_IN_AAA(zero(one(T197)), one(b), one(one(T197))) → U10_AAA(T197, binary54_in_a(T197))
ADDZ73_IN_AAA(zero(one(T197)), one(b), one(one(T197))) → BINARY54_IN_A(T197)
ADDZ73_IN_AAA(zero(zero(T203)), one(b), one(zero(T203))) → U11_AAA(T203, binaryZ48_in_a(T203))
ADDZ73_IN_AAA(zero(zero(T203)), one(b), one(zero(T203))) → BINARYZ48_IN_A(T203)
ADDZ73_IN_AAA(zero(T215), one(T216), one(X283)) → U12_AAA(T215, T216, X283, addz73_in_aaa(T215, T216, X283))
ADDZ73_IN_AAA(zero(T215), one(T216), one(X283)) → ADDZ73_IN_AAA(T215, T216, X283)
ADDZ73_IN_AAA(one(T229), zero(T230), one(X307)) → U13_AAA(T229, T230, X307, addy96_in_aaa(T229, T230, X307))
ADDZ73_IN_AAA(one(T229), zero(T230), one(X307)) → ADDY96_IN_AAA(T229, T230, X307)
ADDY96_IN_AAA(b, one(T237), one(T237)) → U30_AAA(T237, binary54_in_a(T237))
ADDY96_IN_AAA(b, one(T237), one(T237)) → BINARY54_IN_A(T237)
ADDY96_IN_AAA(b, zero(T243), zero(T243)) → U31_AAA(T243, binaryZ48_in_a(T243))
ADDY96_IN_AAA(b, zero(T243), zero(T243)) → BINARYZ48_IN_A(T243)
ADDY96_IN_AAA(T255, T256, X340) → U32_AAA(T255, T256, X340, addz73_in_aaa(T255, T256, X340))
ADDY96_IN_AAA(T255, T256, X340) → ADDZ73_IN_AAA(T255, T256, X340)
ADDZ73_IN_AAA(one(T265), one(T266), zero(X356)) → U14_AAA(T265, T266, X356, addc108_in_aaa(T265, T266, X356))
ADDZ73_IN_AAA(one(T265), one(T266), zero(X356)) → ADDC108_IN_AAA(T265, T266, X356)
ADDC108_IN_AAA(T272, b, X374) → U27_AAA(T272, X374, succZ118_in_aa(T272, X374))
ADDC108_IN_AAA(T272, b, X374) → SUCCZ118_IN_AA(T272, X374)
SUCCZ118_IN_AA(zero(T279), one(T279)) → U17_AA(T279, binaryZ48_in_a(T279))
SUCCZ118_IN_AA(zero(T279), one(T279)) → BINARYZ48_IN_A(T279)
SUCCZ118_IN_AA(one(T284), zero(X393)) → U18_AA(T284, X393, succ125_in_aa(T284, X393))
SUCCZ118_IN_AA(one(T284), zero(X393)) → SUCC125_IN_AA(T284, X393)
SUCC125_IN_AA(zero(T290), one(T290)) → U15_AA(T290, binaryZ48_in_a(T290))
SUCC125_IN_AA(zero(T290), one(T290)) → BINARYZ48_IN_A(T290)
SUCC125_IN_AA(one(T295), zero(X411)) → U16_AA(T295, X411, succ125_in_aa(T295, X411))
SUCC125_IN_AA(one(T295), zero(X411)) → SUCC125_IN_AA(T295, X411)
ADDC108_IN_AAA(b, T301, X428) → U28_AAA(T301, X428, succZ118_in_aa(T301, X428))
ADDC108_IN_AAA(b, T301, X428) → SUCCZ118_IN_AA(T301, X428)
ADDC108_IN_AAA(T313, T314, X447) → U29_AAA(T313, T314, X447, addC143_in_aaa(T313, T314, X447))
ADDC108_IN_AAA(T313, T314, X447) → ADDC143_IN_AAA(T313, T314, X447)
ADDC143_IN_AAA(zero(T327), zero(T328), one(X471)) → U19_AAA(T327, T328, X471, addz73_in_aaa(T327, T328, X471))
ADDC143_IN_AAA(zero(T327), zero(T328), one(X471)) → ADDZ73_IN_AAA(T327, T328, X471)
ADDC143_IN_AAA(zero(zero(T349)), one(b), zero(one(T349))) → U20_AAA(T349, binaryZ48_in_a(T349))
ADDC143_IN_AAA(zero(zero(T349)), one(b), zero(one(T349))) → BINARYZ48_IN_A(T349)
ADDC143_IN_AAA(zero(one(T356)), one(b), zero(zero(X524))) → U21_AAA(T356, X524, succ125_in_aa(T356, X524))
ADDC143_IN_AAA(zero(one(T356)), one(b), zero(zero(X524))) → SUCC125_IN_AA(T356, X524)
ADDC143_IN_AAA(zero(T367), one(T368), zero(X542)) → U22_AAA(T367, T368, X542, addC143_in_aaa(T367, T368, X542))
ADDC143_IN_AAA(zero(T367), one(T368), zero(X542)) → ADDC143_IN_AAA(T367, T368, X542)
ADDC143_IN_AAA(one(b), zero(zero(T389)), zero(one(T389))) → U23_AAA(T389, binaryZ48_in_a(T389))
ADDC143_IN_AAA(one(b), zero(zero(T389)), zero(one(T389))) → BINARYZ48_IN_A(T389)
ADDC143_IN_AAA(one(b), zero(one(T396)), zero(zero(X592))) → U24_AAA(T396, X592, succ125_in_aa(T396, X592))
ADDC143_IN_AAA(one(b), zero(one(T396)), zero(zero(X592))) → SUCC125_IN_AA(T396, X592)
ADDC143_IN_AAA(one(T407), zero(T408), zero(X610)) → U25_AAA(T407, T408, X610, addC143_in_aaa(T407, T408, X610))
ADDC143_IN_AAA(one(T407), zero(T408), zero(X610)) → ADDC143_IN_AAA(T407, T408, X610)
ADDC143_IN_AAA(one(T417), one(T418), one(X626)) → U26_AAA(T417, T418, X626, addc108_in_aaa(T417, T418, X626))
ADDC143_IN_AAA(one(T417), one(T418), one(X626)) → ADDC108_IN_AAA(T417, T418, X626)
ADD37_IN_AAA(one(T430), T431, one(X652)) → U66_AAA(T430, T431, X652, addy96_in_aaa(T430, T431, X652))
ADD37_IN_AAA(one(T430), T431, one(X652)) → ADDY96_IN_AAA(T430, T431, X652)
P20_IN_AAAG(T53, T58, T57, T52) → U59_AAAG(T53, T58, T57, T52, timesc22_in_aaa(T53, T58, T57))
U59_AAAG(T53, T58, T57, T52, timesc22_out_aaa(T53, T58, T57)) → U60_AAAG(T53, T58, T57, T52, add23_in_aag(T58, T57, T52))
U59_AAAG(T53, T58, T57, T52, timesc22_out_aaa(T53, T58, T57)) → ADD23_IN_AAG(T58, T57, T52)
ADD23_IN_AAG(b, T441, zero(T441)) → U61_AAG(T441, binaryZ43_in_g(T441))
ADD23_IN_AAG(b, T441, zero(T441)) → BINARYZ43_IN_G(T441)
BINARYZ43_IN_G(T113) → U33_G(T113, binaryZ48_in_g(T113))
BINARYZ43_IN_G(T113) → BINARYZ48_IN_G(T113)
BINARYZ48_IN_G(zero(T120)) → U5_G(T120, binaryZ48_in_g(T120))
BINARYZ48_IN_G(zero(T120)) → BINARYZ48_IN_G(T120)
BINARYZ48_IN_G(one(T125)) → U6_G(T125, binary54_in_g(T125))
BINARYZ48_IN_G(one(T125)) → BINARY54_IN_G(T125)
BINARY54_IN_G(zero(T131)) → U7_G(T131, binaryZ48_in_g(T131))
BINARY54_IN_G(zero(T131)) → BINARYZ48_IN_G(T131)
BINARY54_IN_G(one(T136)) → U8_G(T136, binary54_in_g(T136))
BINARY54_IN_G(one(T136)) → BINARY54_IN_G(T136)
ADD23_IN_AAG(zero(T477), T478, zero(T476)) → U62_AAG(T477, T478, T476, addz196_in_aag(T477, T478, T476))
ADD23_IN_AAG(zero(T477), T478, zero(T476)) → ADDZ196_IN_AAG(T477, T478, T476)
ADDZ196_IN_AAG(zero(T497), zero(T498), zero(T496)) → U34_AAG(T497, T498, T496, addz196_in_aag(T497, T498, T496))
ADDZ196_IN_AAG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_AAG(T497, T498, T496)
ADDZ196_IN_AAG(zero(one(T524)), one(b), one(one(T524))) → U35_AAG(T524, binary54_in_g(T524))
ADDZ196_IN_AAG(zero(one(T524)), one(b), one(one(T524))) → BINARY54_IN_G(T524)
ADDZ196_IN_AAG(zero(zero(T529)), one(b), one(zero(T529))) → U36_AAG(T529, binaryZ48_in_g(T529))
ADDZ196_IN_AAG(zero(zero(T529)), one(b), one(zero(T529))) → BINARYZ48_IN_G(T529)
ADDZ196_IN_AAG(zero(T545), one(T546), one(T544)) → U37_AAG(T545, T546, T544, addz196_in_aag(T545, T546, T544))
ADDZ196_IN_AAG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_AAG(T545, T546, T544)
ADDZ196_IN_AAG(one(T565), zero(T566), one(T564)) → U38_AAG(T565, T566, T564, addy219_in_aag(T565, T566, T564))
ADDZ196_IN_AAG(one(T565), zero(T566), one(T564)) → ADDY219_IN_AAG(T565, T566, T564)
ADDY219_IN_AAG(b, one(T572), one(T572)) → U55_AAG(T572, binary54_in_g(T572))
ADDY219_IN_AAG(b, one(T572), one(T572)) → BINARY54_IN_G(T572)
ADDY219_IN_AAG(b, zero(T577), zero(T577)) → U56_AAG(T577, binaryZ48_in_g(T577))
ADDY219_IN_AAG(b, zero(T577), zero(T577)) → BINARYZ48_IN_G(T577)
ADDY219_IN_AAG(T593, T594, T592) → U57_AAG(T593, T594, T592, addz196_in_aag(T593, T594, T592))
ADDY219_IN_AAG(T593, T594, T592) → ADDZ196_IN_AAG(T593, T594, T592)
ADDZ196_IN_AAG(one(T607), one(T608), zero(T606)) → U39_AAG(T607, T608, T606, addc231_in_aag(T607, T608, T606))
ADDZ196_IN_AAG(one(T607), one(T608), zero(T606)) → ADDC231_IN_AAG(T607, T608, T606)
ADDC231_IN_AAG(T619, b, T618) → U52_AAG(T619, T618, succZ241_in_ag(T619, T618))
ADDC231_IN_AAG(T619, b, T618) → SUCCZ241_IN_AG(T619, T618)
SUCCZ241_IN_AG(zero(T625), one(T625)) → U42_AG(T625, binaryZ48_in_g(T625))
SUCCZ241_IN_AG(zero(T625), one(T625)) → BINARYZ48_IN_G(T625)
SUCCZ241_IN_AG(one(T633), zero(T632)) → U43_AG(T633, T632, succ248_in_ag(T633, T632))
SUCCZ241_IN_AG(one(T633), zero(T632)) → SUCC248_IN_AG(T633, T632)
SUCC248_IN_AG(zero(T638), one(T638)) → U40_AG(T638, binaryZ48_in_g(T638))
SUCC248_IN_AG(zero(T638), one(T638)) → BINARYZ48_IN_G(T638)
SUCC248_IN_AG(one(T646), zero(T645)) → U41_AG(T646, T645, succ248_in_ag(T646, T645))
SUCC248_IN_AG(one(T646), zero(T645)) → SUCC248_IN_AG(T646, T645)
ADDC231_IN_AAG(b, T657, T656) → U53_AAG(T657, T656, succZ241_in_ag(T657, T656))
ADDC231_IN_AAG(b, T657, T656) → SUCCZ241_IN_AG(T657, T656)
ADDC231_IN_AAG(T673, T674, T672) → U54_AAG(T673, T674, T672, addC266_in_aag(T673, T674, T672))
ADDC231_IN_AAG(T673, T674, T672) → ADDC266_IN_AAG(T673, T674, T672)
ADDC266_IN_AAG(zero(T693), zero(T694), one(T692)) → U44_AAG(T693, T694, T692, addz196_in_aag(T693, T694, T692))
ADDC266_IN_AAG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_AAG(T693, T694, T692)
ADDC266_IN_AAG(zero(zero(T720)), one(b), zero(one(T720))) → U45_AAG(T720, binaryZ48_in_g(T720))
ADDC266_IN_AAG(zero(zero(T720)), one(b), zero(one(T720))) → BINARYZ48_IN_G(T720)
ADDC266_IN_AAG(zero(one(T732)), one(b), zero(zero(T731))) → U46_AAG(T732, T731, succ248_in_ag(T732, T731))
ADDC266_IN_AAG(zero(one(T732)), one(b), zero(zero(T731))) → SUCC248_IN_AG(T732, T731)
ADDC266_IN_AAG(zero(T747), one(T748), zero(T746)) → U47_AAG(T747, T748, T746, addC266_in_aag(T747, T748, T746))
ADDC266_IN_AAG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_AAG(T747, T748, T746)
ADDC266_IN_AAG(one(b), zero(zero(T774)), zero(one(T774))) → U48_AAG(T774, binaryZ48_in_g(T774))
ADDC266_IN_AAG(one(b), zero(zero(T774)), zero(one(T774))) → BINARYZ48_IN_G(T774)
ADDC266_IN_AAG(one(b), zero(one(T786)), zero(zero(T785))) → U49_AAG(T786, T785, succ248_in_ag(T786, T785))
ADDC266_IN_AAG(one(b), zero(one(T786)), zero(zero(T785))) → SUCC248_IN_AG(T786, T785)
ADDC266_IN_AAG(one(T801), zero(T802), zero(T800)) → U50_AAG(T801, T802, T800, addC266_in_aag(T801, T802, T800))
ADDC266_IN_AAG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_AAG(T801, T802, T800)
ADDC266_IN_AAG(one(T815), one(T816), one(T814)) → U51_AAG(T815, T816, T814, addc231_in_aag(T815, T816, T814))
ADDC266_IN_AAG(one(T815), one(T816), one(T814)) → ADDC231_IN_AAG(T815, T816, T814)
ADD23_IN_AAG(one(T833), T834, one(T832)) → U63_AAG(T833, T834, T832, addy219_in_aag(T833, T834, T832))
ADD23_IN_AAG(one(T833), T834, one(T832)) → ADDY219_IN_AAG(T833, T834, T832)
TIMES1_IN_AAG(one(T846), T847, zero(T845)) → U78_AAG(T846, T847, T845, p20_in_aaag(T846, T847, X1078, zero(T845)))
TIMES1_IN_AAG(one(T846), T847, zero(T845)) → P20_IN_AAAG(T846, T847, X1078, zero(T845))
TIMES1_IN_AAG(one(one(b)), T863, T855) → U79_AAG(T863, T855, add23_in_aag(T863, T863, T855))
TIMES1_IN_AAG(one(one(b)), T863, T855) → ADD23_IN_AAG(T863, T863, T855)
TIMES1_IN_AAG(one(zero(T875)), T876, T855) → U80_AAG(T875, T876, T855, p320_in_aaag(T875, T876, X1121, T855))
TIMES1_IN_AAG(one(zero(T875)), T876, T855) → P320_IN_AAAG(T875, T876, X1121, T855)
P320_IN_AAAG(T875, T876, X1121, T855) → U67_AAAG(T875, T876, X1121, T855, times22_in_aaa(T875, T876, X1121))
P320_IN_AAAG(T875, T876, X1121, T855) → TIMES22_IN_AAA(T875, T876, X1121)
P320_IN_AAAG(T875, T880, T879, T855) → U68_AAAG(T875, T880, T879, T855, timesc22_in_aaa(T875, T880, T879))
U68_AAAG(T875, T880, T879, T855, timesc22_out_aaa(T875, T880, T879)) → U69_AAAG(T875, T880, T879, T855, add23_in_aag(T880, zero(T879), T855))
U68_AAAG(T875, T880, T879, T855, timesc22_out_aaa(T875, T880, T879)) → ADD23_IN_AAG(T880, zero(T879), T855)
TIMES1_IN_AAG(one(one(T896)), T897, T855) → U81_AAG(T896, T897, T855, p324_in_aaaag(T896, T897, X1143, X1144, T855))
TIMES1_IN_AAG(one(one(T896)), T897, T855) → P324_IN_AAAAG(T896, T897, X1143, X1144, T855)
P324_IN_AAAAG(T896, T897, X1143, X1144, T855) → U70_AAAAG(T896, T897, X1143, X1144, T855, times22_in_aaa(T896, T897, X1143))
P324_IN_AAAAG(T896, T897, X1143, X1144, T855) → TIMES22_IN_AAA(T896, T897, X1143)
P324_IN_AAAAG(T896, T901, T900, X1144, T855) → U71_AAAAG(T896, T901, T900, X1144, T855, timesc22_in_aaa(T896, T901, T900))
U71_AAAAG(T896, T901, T900, X1144, T855, timesc22_out_aaa(T896, T901, T900)) → U72_AAAAG(T896, T901, T900, X1144, T855, add37_in_aaa(T901, T900, X1144))
U71_AAAAG(T896, T901, T900, X1144, T855, timesc22_out_aaa(T896, T901, T900)) → ADD37_IN_AAA(T901, T900, X1144)
P324_IN_AAAAG(T896, T912, T900, T911, T855) → U73_AAAAG(T896, T912, T900, T911, T855, timesc22_in_aaa(T896, T912, T900))
U73_AAAAG(T896, T912, T900, T911, T855, timesc22_out_aaa(T896, T912, T900)) → U74_AAAAG(T896, T912, T900, T911, T855, addc37_in_aaa(T912, T900, T911))
U74_AAAAG(T896, T912, T900, T911, T855, addc37_out_aaa(T912, T900, T911)) → U75_AAAAG(T896, T912, T900, T911, T855, add23_in_ggg(T912, T911, T855))
U74_AAAAG(T896, T912, T900, T911, T855, addc37_out_aaa(T912, T900, T911)) → ADD23_IN_GGG(T912, T911, T855)
ADD23_IN_GGG(b, T441, zero(T441)) → U61_GGG(T441, binaryZ43_in_g(T441))
ADD23_IN_GGG(b, T441, zero(T441)) → BINARYZ43_IN_G(T441)
ADD23_IN_GGG(zero(T477), T478, zero(T476)) → U62_GGG(T477, T478, T476, addz196_in_ggg(T477, T478, T476))
ADD23_IN_GGG(zero(T477), T478, zero(T476)) → ADDZ196_IN_GGG(T477, T478, T476)
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → U34_GGG(T497, T498, T496, addz196_in_ggg(T497, T498, T496))
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_GGG(T497, T498, T496)
ADDZ196_IN_GGG(zero(one(T524)), one(b), one(one(T524))) → U35_GGG(T524, binary54_in_g(T524))
ADDZ196_IN_GGG(zero(one(T524)), one(b), one(one(T524))) → BINARY54_IN_G(T524)
ADDZ196_IN_GGG(zero(zero(T529)), one(b), one(zero(T529))) → U36_GGG(T529, binaryZ48_in_g(T529))
ADDZ196_IN_GGG(zero(zero(T529)), one(b), one(zero(T529))) → BINARYZ48_IN_G(T529)
ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → U37_GGG(T545, T546, T544, addz196_in_ggg(T545, T546, T544))
ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_GGG(T545, T546, T544)
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → U38_GGG(T565, T566, T564, addy219_in_ggg(T565, T566, T564))
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → ADDY219_IN_GGG(T565, T566, T564)
ADDY219_IN_GGG(b, one(T572), one(T572)) → U55_GGG(T572, binary54_in_g(T572))
ADDY219_IN_GGG(b, one(T572), one(T572)) → BINARY54_IN_G(T572)
ADDY219_IN_GGG(b, zero(T577), zero(T577)) → U56_GGG(T577, binaryZ48_in_g(T577))
ADDY219_IN_GGG(b, zero(T577), zero(T577)) → BINARYZ48_IN_G(T577)
ADDY219_IN_GGG(T593, T594, T592) → U57_GGG(T593, T594, T592, addz196_in_ggg(T593, T594, T592))
ADDY219_IN_GGG(T593, T594, T592) → ADDZ196_IN_GGG(T593, T594, T592)
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → U39_GGG(T607, T608, T606, addc231_in_ggg(T607, T608, T606))
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → ADDC231_IN_GGG(T607, T608, T606)
ADDC231_IN_GGG(T619, b, T618) → U52_GGG(T619, T618, succZ241_in_gg(T619, T618))
ADDC231_IN_GGG(T619, b, T618) → SUCCZ241_IN_GG(T619, T618)
SUCCZ241_IN_GG(zero(T625), one(T625)) → U42_GG(T625, binaryZ48_in_g(T625))
SUCCZ241_IN_GG(zero(T625), one(T625)) → BINARYZ48_IN_G(T625)
SUCCZ241_IN_GG(one(T633), zero(T632)) → U43_GG(T633, T632, succ248_in_gg(T633, T632))
SUCCZ241_IN_GG(one(T633), zero(T632)) → SUCC248_IN_GG(T633, T632)
SUCC248_IN_GG(zero(T638), one(T638)) → U40_GG(T638, binaryZ48_in_g(T638))
SUCC248_IN_GG(zero(T638), one(T638)) → BINARYZ48_IN_G(T638)
SUCC248_IN_GG(one(T646), zero(T645)) → U41_GG(T646, T645, succ248_in_gg(T646, T645))
SUCC248_IN_GG(one(T646), zero(T645)) → SUCC248_IN_GG(T646, T645)
ADDC231_IN_GGG(b, T657, T656) → U53_GGG(T657, T656, succZ241_in_gg(T657, T656))
ADDC231_IN_GGG(b, T657, T656) → SUCCZ241_IN_GG(T657, T656)
ADDC231_IN_GGG(T673, T674, T672) → U54_GGG(T673, T674, T672, addC266_in_ggg(T673, T674, T672))
ADDC231_IN_GGG(T673, T674, T672) → ADDC266_IN_GGG(T673, T674, T672)
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → U44_GGG(T693, T694, T692, addz196_in_ggg(T693, T694, T692))
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_GGG(T693, T694, T692)
ADDC266_IN_GGG(zero(zero(T720)), one(b), zero(one(T720))) → U45_GGG(T720, binaryZ48_in_g(T720))
ADDC266_IN_GGG(zero(zero(T720)), one(b), zero(one(T720))) → BINARYZ48_IN_G(T720)
ADDC266_IN_GGG(zero(one(T732)), one(b), zero(zero(T731))) → U46_GGG(T732, T731, succ248_in_gg(T732, T731))
ADDC266_IN_GGG(zero(one(T732)), one(b), zero(zero(T731))) → SUCC248_IN_GG(T732, T731)
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → U47_GGG(T747, T748, T746, addC266_in_ggg(T747, T748, T746))
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_GGG(T747, T748, T746)
ADDC266_IN_GGG(one(b), zero(zero(T774)), zero(one(T774))) → U48_GGG(T774, binaryZ48_in_g(T774))
ADDC266_IN_GGG(one(b), zero(zero(T774)), zero(one(T774))) → BINARYZ48_IN_G(T774)
ADDC266_IN_GGG(one(b), zero(one(T786)), zero(zero(T785))) → U49_GGG(T786, T785, succ248_in_gg(T786, T785))
ADDC266_IN_GGG(one(b), zero(one(T786)), zero(zero(T785))) → SUCC248_IN_GG(T786, T785)
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → U50_GGG(T801, T802, T800, addC266_in_ggg(T801, T802, T800))
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_GGG(T801, T802, T800)
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → U51_GGG(T815, T816, T814, addc231_in_ggg(T815, T816, T814))
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → ADDC231_IN_GGG(T815, T816, T814)
ADD23_IN_GGG(one(T833), T834, one(T832)) → U63_GGG(T833, T834, T832, addy219_in_ggg(T833, T834, T832))
ADD23_IN_GGG(one(T833), T834, one(T832)) → ADDY219_IN_GGG(T833, T834, T832)
TIMES1_IN_AAG(zero(zero(T950)), T951, zero(zero(T949))) → U82_AAG(T950, T951, T949, times1_in_aag(T950, T951, T949))
TIMES1_IN_AAG(zero(one(T969)), T970, zero(T968)) → U83_AAG(T969, T970, T968, p20_in_aaag(T969, T970, X1210, T968))
TIMES1_IN_AAG(one(T982), T983, zero(T981)) → U84_AAG(T982, T983, T981, p20_in_aaag(T982, T983, X1226, zero(T981)))
TIMES1_IN_AAG(one(one(b)), T999, T991) → U85_AAG(T999, T991, add23_in_aag(T999, T999, T991))
TIMES1_IN_AAG(one(zero(T1011)), T1012, T991) → U86_AAG(T1011, T1012, T991, p320_in_aaag(T1011, T1012, X1269, T991))
TIMES1_IN_AAG(one(one(T1021)), T1022, T991) → U87_AAG(T1021, T1022, T991, p324_in_aaaag(T1021, T1022, X1287, X1288, T991))

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 10 SCCs with 182 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

BINARYZ48_IN_G(one(T125)) → BINARY54_IN_G(T125)
BINARY54_IN_G(zero(T131)) → BINARYZ48_IN_G(T131)
BINARYZ48_IN_G(zero(T120)) → BINARYZ48_IN_G(T120)
BINARY54_IN_G(one(T136)) → BINARY54_IN_G(T136)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
BINARYZ48_IN_G(x1) = BINARYZ48_IN_G(x1)
BINARY54_IN_G(x1) = BINARY54_IN_G(x1)

We have to consider all (P,R,Pi)-chains

(8) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(9) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

BINARYZ48_IN_G(one(T125)) → BINARY54_IN_G(T125)
BINARY54_IN_G(zero(T131)) → BINARYZ48_IN_G(T131)
BINARYZ48_IN_G(zero(T120)) → BINARYZ48_IN_G(T120)
BINARY54_IN_G(one(T136)) → BINARY54_IN_G(T136)

R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains

(10) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(11) Obligation:

Q DP problem:
The TRS P consists of the following rules:

BINARYZ48_IN_G(one(T125)) → BINARY54_IN_G(T125)
BINARY54_IN_G(zero(T131)) → BINARYZ48_IN_G(T131)
BINARYZ48_IN_G(zero(T120)) → BINARYZ48_IN_G(T120)
BINARY54_IN_G(one(T136)) → BINARY54_IN_G(T136)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(12) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

BINARY54_IN_G(zero(T131)) → BINARYZ48_IN_G(T131)
The graph contains the following edges 1 > 1
BINARY54_IN_G(one(T136)) → BINARY54_IN_G(T136)
The graph contains the following edges 1 > 1
BINARYZ48_IN_G(zero(T120)) → BINARYZ48_IN_G(T120)
The graph contains the following edges 1 > 1
BINARYZ48_IN_G(one(T125)) → BINARY54_IN_G(T125)
The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SUCC248_IN_GG(one(T646), zero(T645)) → SUCC248_IN_GG(T646, T645)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
SUCC248_IN_GG(x1, x2) = SUCC248_IN_GG(x1, x2)

We have to consider all (P,R,Pi)-chains

(15) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(16) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SUCC248_IN_GG(one(T646), zero(T645)) → SUCC248_IN_GG(T646, T645)

R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains

(17) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(18) Obligation:

Q DP problem:
The TRS P consists of the following rules:

SUCC248_IN_GG(one(T646), zero(T645)) → SUCC248_IN_GG(T646, T645)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(19) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

SUCC248_IN_GG(one(T646), zero(T645)) → SUCC248_IN_GG(T646, T645)
The graph contains the following edges 1 > 1, 2 > 2

(20) YES

(21) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_GGG(T545, T546, T544)
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_GGG(T497, T498, T496)
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → ADDY219_IN_GGG(T565, T566, T564)
ADDY219_IN_GGG(T593, T594, T592) → ADDZ196_IN_GGG(T593, T594, T592)
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → ADDC231_IN_GGG(T607, T608, T606)
ADDC231_IN_GGG(T673, T674, T672) → ADDC266_IN_GGG(T673, T674, T672)
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_GGG(T693, T694, T692)
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_GGG(T747, T748, T746)
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_GGG(T801, T802, T800)
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → ADDC231_IN_GGG(T815, T816, T814)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
ADDZ196_IN_GGG(x1, x2, x3) = ADDZ196_IN_GGG(x1, x2, x3)
ADDY219_IN_GGG(x1, x2, x3) = ADDY219_IN_GGG(x1, x2, x3)
ADDC231_IN_GGG(x1, x2, x3) = ADDC231_IN_GGG(x1, x2, x3)
ADDC266_IN_GGG(x1, x2, x3) = ADDC266_IN_GGG(x1, x2, x3)

We have to consider all (P,R,Pi)-chains

(22) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(23) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_GGG(T545, T546, T544)
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_GGG(T497, T498, T496)
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → ADDY219_IN_GGG(T565, T566, T564)
ADDY219_IN_GGG(T593, T594, T592) → ADDZ196_IN_GGG(T593, T594, T592)
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → ADDC231_IN_GGG(T607, T608, T606)
ADDC231_IN_GGG(T673, T674, T672) → ADDC266_IN_GGG(T673, T674, T672)
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_GGG(T693, T694, T692)
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_GGG(T747, T748, T746)
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_GGG(T801, T802, T800)
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → ADDC231_IN_GGG(T815, T816, T814)

R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains

(24) PiDPToQDPProof (EQUIVALENT transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(25) Obligation:

Q DP problem:
The TRS P consists of the following rules:

ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_GGG(T545, T546, T544)
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_GGG(T497, T498, T496)
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → ADDY219_IN_GGG(T565, T566, T564)
ADDY219_IN_GGG(T593, T594, T592) → ADDZ196_IN_GGG(T593, T594, T592)
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → ADDC231_IN_GGG(T607, T608, T606)
ADDC231_IN_GGG(T673, T674, T672) → ADDC266_IN_GGG(T673, T674, T672)
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_GGG(T693, T694, T692)
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_GGG(T747, T748, T746)
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_GGG(T801, T802, T800)
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → ADDC231_IN_GGG(T815, T816, T814)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(26) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

ADDY219_IN_GGG(T593, T594, T592) → ADDZ196_IN_GGG(T593, T594, T592)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
ADDC266_IN_GGG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_GGG(T693, T694, T692)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
ADDZ196_IN_GGG(one(T565), zero(T566), one(T564)) → ADDY219_IN_GGG(T565, T566, T564)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
ADDZ196_IN_GGG(one(T607), one(T608), zero(T606)) → ADDC231_IN_GGG(T607, T608, T606)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
ADDC231_IN_GGG(T673, T674, T672) → ADDC266_IN_GGG(T673, T674, T672)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3
ADDC266_IN_GGG(one(T815), one(T816), one(T814)) → ADDC231_IN_GGG(T815, T816, T814)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
ADDZ196_IN_GGG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_GGG(T545, T546, T544)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
ADDZ196_IN_GGG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_GGG(T497, T498, T496)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
ADDC266_IN_GGG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_GGG(T747, T748, T746)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3
ADDC266_IN_GGG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_GGG(T801, T802, T800)
The graph contains the following edges 1 > 1, 2 > 2, 3 > 3

(27) YES

(28) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SUCC248_IN_AG(one(T646), zero(T645)) → SUCC248_IN_AG(T646, T645)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
SUCC248_IN_AG(x1, x2) = SUCC248_IN_AG(x2)

We have to consider all (P,R,Pi)-chains

(29) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(30) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SUCC248_IN_AG(one(T646), zero(T645)) → SUCC248_IN_AG(T646, T645)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
one(x1) = one(x1)
SUCC248_IN_AG(x1, x2) = SUCC248_IN_AG(x2)

We have to consider all (P,R,Pi)-chains

(31) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(32) Obligation:

Q DP problem:
The TRS P consists of the following rules:

SUCC248_IN_AG(zero(T645)) → SUCC248_IN_AG(T645)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(33) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

SUCC248_IN_AG(zero(T645)) → SUCC248_IN_AG(T645)
The graph contains the following edges 1 > 1

(34) YES

(35) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDZ196_IN_AAG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_AAG(T545, T546, T544)
ADDZ196_IN_AAG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_AAG(T497, T498, T496)
ADDZ196_IN_AAG(one(T565), zero(T566), one(T564)) → ADDY219_IN_AAG(T565, T566, T564)
ADDY219_IN_AAG(T593, T594, T592) → ADDZ196_IN_AAG(T593, T594, T592)
ADDZ196_IN_AAG(one(T607), one(T608), zero(T606)) → ADDC231_IN_AAG(T607, T608, T606)
ADDC231_IN_AAG(T673, T674, T672) → ADDC266_IN_AAG(T673, T674, T672)
ADDC266_IN_AAG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_AAG(T693, T694, T692)
ADDC266_IN_AAG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_AAG(T747, T748, T746)
ADDC266_IN_AAG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_AAG(T801, T802, T800)
ADDC266_IN_AAG(one(T815), one(T816), one(T814)) → ADDC231_IN_AAG(T815, T816, T814)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
ADDZ196_IN_AAG(x1, x2, x3) = ADDZ196_IN_AAG(x3)
ADDY219_IN_AAG(x1, x2, x3) = ADDY219_IN_AAG(x3)
ADDC231_IN_AAG(x1, x2, x3) = ADDC231_IN_AAG(x3)
ADDC266_IN_AAG(x1, x2, x3) = ADDC266_IN_AAG(x3)

We have to consider all (P,R,Pi)-chains

(36) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(37) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDZ196_IN_AAG(zero(T545), one(T546), one(T544)) → ADDZ196_IN_AAG(T545, T546, T544)
ADDZ196_IN_AAG(zero(T497), zero(T498), zero(T496)) → ADDZ196_IN_AAG(T497, T498, T496)
ADDZ196_IN_AAG(one(T565), zero(T566), one(T564)) → ADDY219_IN_AAG(T565, T566, T564)
ADDY219_IN_AAG(T593, T594, T592) → ADDZ196_IN_AAG(T593, T594, T592)
ADDZ196_IN_AAG(one(T607), one(T608), zero(T606)) → ADDC231_IN_AAG(T607, T608, T606)
ADDC231_IN_AAG(T673, T674, T672) → ADDC266_IN_AAG(T673, T674, T672)
ADDC266_IN_AAG(zero(T693), zero(T694), one(T692)) → ADDZ196_IN_AAG(T693, T694, T692)
ADDC266_IN_AAG(zero(T747), one(T748), zero(T746)) → ADDC266_IN_AAG(T747, T748, T746)
ADDC266_IN_AAG(one(T801), zero(T802), zero(T800)) → ADDC266_IN_AAG(T801, T802, T800)
ADDC266_IN_AAG(one(T815), one(T816), one(T814)) → ADDC231_IN_AAG(T815, T816, T814)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
one(x1) = one(x1)
ADDZ196_IN_AAG(x1, x2, x3) = ADDZ196_IN_AAG(x3)
ADDY219_IN_AAG(x1, x2, x3) = ADDY219_IN_AAG(x3)
ADDC231_IN_AAG(x1, x2, x3) = ADDC231_IN_AAG(x3)
ADDC266_IN_AAG(x1, x2, x3) = ADDC266_IN_AAG(x3)

We have to consider all (P,R,Pi)-chains

(38) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(39) Obligation:

Q DP problem:
The TRS P consists of the following rules:

ADDZ196_IN_AAG(one(T544)) → ADDZ196_IN_AAG(T544)
ADDZ196_IN_AAG(zero(T496)) → ADDZ196_IN_AAG(T496)
ADDZ196_IN_AAG(one(T564)) → ADDY219_IN_AAG(T564)
ADDY219_IN_AAG(T592) → ADDZ196_IN_AAG(T592)
ADDZ196_IN_AAG(zero(T606)) → ADDC231_IN_AAG(T606)
ADDC231_IN_AAG(T672) → ADDC266_IN_AAG(T672)
ADDC266_IN_AAG(one(T692)) → ADDZ196_IN_AAG(T692)
ADDC266_IN_AAG(zero(T746)) → ADDC266_IN_AAG(T746)
ADDC266_IN_AAG(one(T814)) → ADDC231_IN_AAG(T814)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(40) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

ADDY219_IN_AAG(T592) → ADDZ196_IN_AAG(T592)
The graph contains the following edges 1 >= 1
ADDC266_IN_AAG(one(T692)) → ADDZ196_IN_AAG(T692)
The graph contains the following edges 1 > 1
ADDZ196_IN_AAG(one(T564)) → ADDY219_IN_AAG(T564)
The graph contains the following edges 1 > 1
ADDZ196_IN_AAG(zero(T606)) → ADDC231_IN_AAG(T606)
The graph contains the following edges 1 > 1
ADDC231_IN_AAG(T672) → ADDC266_IN_AAG(T672)
The graph contains the following edges 1 >= 1
ADDC266_IN_AAG(one(T814)) → ADDC231_IN_AAG(T814)
The graph contains the following edges 1 > 1
ADDC266_IN_AAG(zero(T746)) → ADDC266_IN_AAG(T746)
The graph contains the following edges 1 > 1
ADDZ196_IN_AAG(one(T544)) → ADDZ196_IN_AAG(T544)
The graph contains the following edges 1 > 1
ADDZ196_IN_AAG(zero(T496)) → ADDZ196_IN_AAG(T496)
The graph contains the following edges 1 > 1

(41) YES

(42) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

BINARYZ48_IN_A(one(T125)) → BINARY54_IN_A(T125)
BINARY54_IN_A(zero(T131)) → BINARYZ48_IN_A(T131)
BINARYZ48_IN_A(zero(T120)) → BINARYZ48_IN_A(T120)
BINARY54_IN_A(one(T136)) → BINARY54_IN_A(T136)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
BINARYZ48_IN_A(x1) = BINARYZ48_IN_A
BINARY54_IN_A(x1) = BINARY54_IN_A

We have to consider all (P,R,Pi)-chains

(43) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(44) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

BINARYZ48_IN_A(one(T125)) → BINARY54_IN_A(T125)
BINARY54_IN_A(zero(T131)) → BINARYZ48_IN_A(T131)
BINARYZ48_IN_A(zero(T120)) → BINARYZ48_IN_A(T120)
BINARY54_IN_A(one(T136)) → BINARY54_IN_A(T136)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
one(x1) = one(x1)
BINARYZ48_IN_A(x1) = BINARYZ48_IN_A
BINARY54_IN_A(x1) = BINARY54_IN_A

We have to consider all (P,R,Pi)-chains

(45) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(46) Obligation:

Q DP problem:
The TRS P consists of the following rules:

BINARYZ48_IN_A → BINARY54_IN_A
BINARY54_IN_A → BINARYZ48_IN_A
BINARYZ48_IN_A → BINARYZ48_IN_A
BINARY54_IN_A → BINARY54_IN_A

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(47) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = BINARYZ48_IN_A evaluates to t =BINARYZ48_IN_A

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Matcher: [ ]
Semiunifier: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from BINARYZ48_IN_A to BINARYZ48_IN_A.

(48) NO

(49) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SUCC125_IN_AA(one(T295), zero(X411)) → SUCC125_IN_AA(T295, X411)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
SUCC125_IN_AA(x1, x2) = SUCC125_IN_AA

We have to consider all (P,R,Pi)-chains

(50) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(51) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

SUCC125_IN_AA(one(T295), zero(X411)) → SUCC125_IN_AA(T295, X411)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
one(x1) = one(x1)
SUCC125_IN_AA(x1, x2) = SUCC125_IN_AA

We have to consider all (P,R,Pi)-chains

(52) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(53) Obligation:

Q DP problem:
The TRS P consists of the following rules:

SUCC125_IN_AA → SUCC125_IN_AA

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(54) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = SUCC125_IN_AA evaluates to t =SUCC125_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from SUCC125_IN_AA to SUCC125_IN_AA.

(55) NO

(56) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDZ73_IN_AAA(zero(T215), one(T216), one(X283)) → ADDZ73_IN_AAA(T215, T216, X283)
ADDZ73_IN_AAA(zero(T175), zero(T176), zero(X223)) → ADDZ73_IN_AAA(T175, T176, X223)
ADDZ73_IN_AAA(one(T229), zero(T230), one(X307)) → ADDY96_IN_AAA(T229, T230, X307)
ADDY96_IN_AAA(T255, T256, X340) → ADDZ73_IN_AAA(T255, T256, X340)
ADDZ73_IN_AAA(one(T265), one(T266), zero(X356)) → ADDC108_IN_AAA(T265, T266, X356)
ADDC108_IN_AAA(T313, T314, X447) → ADDC143_IN_AAA(T313, T314, X447)
ADDC143_IN_AAA(zero(T327), zero(T328), one(X471)) → ADDZ73_IN_AAA(T327, T328, X471)
ADDC143_IN_AAA(zero(T367), one(T368), zero(X542)) → ADDC143_IN_AAA(T367, T368, X542)
ADDC143_IN_AAA(one(T407), zero(T408), zero(X610)) → ADDC143_IN_AAA(T407, T408, X610)
ADDC143_IN_AAA(one(T417), one(T418), one(X626)) → ADDC108_IN_AAA(T417, T418, X626)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
ADDZ73_IN_AAA(x1, x2, x3) = ADDZ73_IN_AAA
ADDY96_IN_AAA(x1, x2, x3) = ADDY96_IN_AAA
ADDC108_IN_AAA(x1, x2, x3) = ADDC108_IN_AAA
ADDC143_IN_AAA(x1, x2, x3) = ADDC143_IN_AAA

We have to consider all (P,R,Pi)-chains

(57) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(58) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ADDZ73_IN_AAA(zero(T215), one(T216), one(X283)) → ADDZ73_IN_AAA(T215, T216, X283)
ADDZ73_IN_AAA(zero(T175), zero(T176), zero(X223)) → ADDZ73_IN_AAA(T175, T176, X223)
ADDZ73_IN_AAA(one(T229), zero(T230), one(X307)) → ADDY96_IN_AAA(T229, T230, X307)
ADDY96_IN_AAA(T255, T256, X340) → ADDZ73_IN_AAA(T255, T256, X340)
ADDZ73_IN_AAA(one(T265), one(T266), zero(X356)) → ADDC108_IN_AAA(T265, T266, X356)
ADDC108_IN_AAA(T313, T314, X447) → ADDC143_IN_AAA(T313, T314, X447)
ADDC143_IN_AAA(zero(T327), zero(T328), one(X471)) → ADDZ73_IN_AAA(T327, T328, X471)
ADDC143_IN_AAA(zero(T367), one(T368), zero(X542)) → ADDC143_IN_AAA(T367, T368, X542)
ADDC143_IN_AAA(one(T407), zero(T408), zero(X610)) → ADDC143_IN_AAA(T407, T408, X610)
ADDC143_IN_AAA(one(T417), one(T418), one(X626)) → ADDC108_IN_AAA(T417, T418, X626)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
one(x1) = one(x1)
ADDZ73_IN_AAA(x1, x2, x3) = ADDZ73_IN_AAA
ADDY96_IN_AAA(x1, x2, x3) = ADDY96_IN_AAA
ADDC108_IN_AAA(x1, x2, x3) = ADDC108_IN_AAA
ADDC143_IN_AAA(x1, x2, x3) = ADDC143_IN_AAA

We have to consider all (P,R,Pi)-chains

(59) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(60) Obligation:

Q DP problem:
The TRS P consists of the following rules:

ADDZ73_IN_AAA → ADDZ73_IN_AAA
ADDZ73_IN_AAA → ADDY96_IN_AAA
ADDY96_IN_AAA → ADDZ73_IN_AAA
ADDZ73_IN_AAA → ADDC108_IN_AAA
ADDC108_IN_AAA → ADDC143_IN_AAA
ADDC143_IN_AAA → ADDZ73_IN_AAA
ADDC143_IN_AAA → ADDC143_IN_AAA
ADDC143_IN_AAA → ADDC108_IN_AAA

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(61) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = ADDZ73_IN_AAA evaluates to t =ADDZ73_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Semiunifier: [ ]
Matcher: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from ADDZ73_IN_AAA to ADDZ73_IN_AAA.

(62) NO

(63) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

TIMES22_IN_AAA(one(T86), T87, X108) → TIMES22_IN_AAA(T86, T87, X107)
TIMES22_IN_AAA(zero(T76), T77, zero(X89)) → TIMES22_IN_AAA(T76, T77, X89)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
TIMES22_IN_AAA(x1, x2, x3) = TIMES22_IN_AAA

We have to consider all (P,R,Pi)-chains

(64) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(65) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

TIMES22_IN_AAA(one(T86), T87, X108) → TIMES22_IN_AAA(T86, T87, X107)
TIMES22_IN_AAA(zero(T76), T77, zero(X89)) → TIMES22_IN_AAA(T76, T77, X89)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
one(x1) = one(x1)
TIMES22_IN_AAA(x1, x2, x3) = TIMES22_IN_AAA

We have to consider all (P,R,Pi)-chains

(66) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(67) Obligation:

Q DP problem:
The TRS P consists of the following rules:

TIMES22_IN_AAA → TIMES22_IN_AAA

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(68) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = TIMES22_IN_AAA evaluates to t =TIMES22_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

Matcher: [ ]
Semiunifier: [ ]

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TIMES22_IN_AAA to TIMES22_IN_AAA.

(69) NO

(70) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

TIMES1_IN_AAG(zero(zero(T34)), T35, zero(zero(T33))) → TIMES1_IN_AAG(T34, T35, T33)

The TRS R consists of the following rules:

timesc22_in_aaa(one(b), T65, T65) → timesc22_out_aaa(one(b), T65, T65)
timesc22_in_aaa(zero(T76), T77, zero(X89)) → U101_aaa(T76, T77, X89, timesc22_in_aaa(T76, T77, X89))
timesc22_in_aaa(one(T86), T91, X108) → U102_aaa(T86, T91, X108, timesc22_in_aaa(T86, T91, T90))
U102_aaa(T86, T91, X108, timesc22_out_aaa(T86, T91, T90)) → U103_aaa(T86, T91, X108, addc37_in_aaa(T91, T90, X108))
addc37_in_aaa(b, T102, zero(T102)) → U162_aaa(T102, binaryZc43_in_a(T102))
binaryZc43_in_a(T113) → U132_a(T113, binaryZc48_in_a(T113))
binaryZc48_in_a(zero(T120)) → U104_a(T120, binaryZc48_in_a(T120))
binaryZc48_in_a(one(T125)) → U105_a(T125, binaryc54_in_a(T125))
binaryc54_in_a(b) → binaryc54_out_a(b)
binaryc54_in_a(zero(T131)) → U106_a(T131, binaryZc48_in_a(T131))
U106_a(T131, binaryZc48_out_a(T131)) → binaryc54_out_a(zero(T131))
binaryc54_in_a(one(T136)) → U107_a(T136, binaryc54_in_a(T136))
U107_a(T136, binaryc54_out_a(T136)) → binaryc54_out_a(one(T136))
U105_a(T125, binaryc54_out_a(T125)) → binaryZc48_out_a(one(T125))
U104_a(T120, binaryZc48_out_a(T120)) → binaryZc48_out_a(zero(T120))
U132_a(T113, binaryZc48_out_a(T113)) → binaryZc43_out_a(T113)
U162_aaa(T102, binaryZc43_out_a(T102)) → addc37_out_aaa(b, T102, zero(T102))
addc37_in_aaa(zero(T161), T162, zero(X196)) → U163_aaa(T161, T162, X196, addzc73_in_aaa(T161, T162, X196))
addzc73_in_aaa(zero(T175), zero(T176), zero(X223)) → U108_aaa(T175, T176, X223, addzc73_in_aaa(T175, T176, X223))
addzc73_in_aaa(zero(one(T197)), one(b), one(one(T197))) → U109_aaa(T197, binaryc54_in_a(T197))
U109_aaa(T197, binaryc54_out_a(T197)) → addzc73_out_aaa(zero(one(T197)), one(b), one(one(T197)))
addzc73_in_aaa(zero(zero(T203)), one(b), one(zero(T203))) → U110_aaa(T203, binaryZc48_in_a(T203))
U110_aaa(T203, binaryZc48_out_a(T203)) → addzc73_out_aaa(zero(zero(T203)), one(b), one(zero(T203)))
addzc73_in_aaa(zero(T215), one(T216), one(X283)) → U111_aaa(T215, T216, X283, addzc73_in_aaa(T215, T216, X283))
addzc73_in_aaa(one(T229), zero(T230), one(X307)) → U112_aaa(T229, T230, X307, addyc96_in_aaa(T229, T230, X307))
addyc96_in_aaa(b, one(T237), one(T237)) → U129_aaa(T237, binaryc54_in_a(T237))
U129_aaa(T237, binaryc54_out_a(T237)) → addyc96_out_aaa(b, one(T237), one(T237))
addyc96_in_aaa(b, zero(T243), zero(T243)) → U130_aaa(T243, binaryZc48_in_a(T243))
U130_aaa(T243, binaryZc48_out_a(T243)) → addyc96_out_aaa(b, zero(T243), zero(T243))
addyc96_in_aaa(T255, T256, X340) → U131_aaa(T255, T256, X340, addzc73_in_aaa(T255, T256, X340))
addzc73_in_aaa(one(T265), one(T266), zero(X356)) → U113_aaa(T265, T266, X356, addcc108_in_aaa(T265, T266, X356))
addcc108_in_aaa(b, b, one(b)) → addcc108_out_aaa(b, b, one(b))
addcc108_in_aaa(T272, b, X374) → U126_aaa(T272, X374, succZc118_in_aa(T272, X374))
succZc118_in_aa(zero(T279), one(T279)) → U116_aa(T279, binaryZc48_in_a(T279))
U116_aa(T279, binaryZc48_out_a(T279)) → succZc118_out_aa(zero(T279), one(T279))
succZc118_in_aa(one(T284), zero(X393)) → U117_aa(T284, X393, succc125_in_aa(T284, X393))
succc125_in_aa(b, one(b)) → succc125_out_aa(b, one(b))
succc125_in_aa(zero(T290), one(T290)) → U114_aa(T290, binaryZc48_in_a(T290))
U114_aa(T290, binaryZc48_out_a(T290)) → succc125_out_aa(zero(T290), one(T290))
succc125_in_aa(one(T295), zero(X411)) → U115_aa(T295, X411, succc125_in_aa(T295, X411))
U115_aa(T295, X411, succc125_out_aa(T295, X411)) → succc125_out_aa(one(T295), zero(X411))
U117_aa(T284, X393, succc125_out_aa(T284, X393)) → succZc118_out_aa(one(T284), zero(X393))
U126_aaa(T272, X374, succZc118_out_aa(T272, X374)) → addcc108_out_aaa(T272, b, X374)
addcc108_in_aaa(b, T301, X428) → U127_aaa(T301, X428, succZc118_in_aa(T301, X428))
U127_aaa(T301, X428, succZc118_out_aa(T301, X428)) → addcc108_out_aaa(b, T301, X428)
addcc108_in_aaa(T313, T314, X447) → U128_aaa(T313, T314, X447, addCc143_in_aaa(T313, T314, X447))
addCc143_in_aaa(zero(T327), zero(T328), one(X471)) → U118_aaa(T327, T328, X471, addzc73_in_aaa(T327, T328, X471))
U118_aaa(T327, T328, X471, addzc73_out_aaa(T327, T328, X471)) → addCc143_out_aaa(zero(T327), zero(T328), one(X471))
addCc143_in_aaa(zero(zero(T349)), one(b), zero(one(T349))) → U119_aaa(T349, binaryZc48_in_a(T349))
U119_aaa(T349, binaryZc48_out_a(T349)) → addCc143_out_aaa(zero(zero(T349)), one(b), zero(one(T349)))
addCc143_in_aaa(zero(one(T356)), one(b), zero(zero(X524))) → U120_aaa(T356, X524, succc125_in_aa(T356, X524))
U120_aaa(T356, X524, succc125_out_aa(T356, X524)) → addCc143_out_aaa(zero(one(T356)), one(b), zero(zero(X524)))
addCc143_in_aaa(zero(T367), one(T368), zero(X542)) → U121_aaa(T367, T368, X542, addCc143_in_aaa(T367, T368, X542))
addCc143_in_aaa(one(b), zero(zero(T389)), zero(one(T389))) → U122_aaa(T389, binaryZc48_in_a(T389))
U122_aaa(T389, binaryZc48_out_a(T389)) → addCc143_out_aaa(one(b), zero(zero(T389)), zero(one(T389)))
addCc143_in_aaa(one(b), zero(one(T396)), zero(zero(X592))) → U123_aaa(T396, X592, succc125_in_aa(T396, X592))
U123_aaa(T396, X592, succc125_out_aa(T396, X592)) → addCc143_out_aaa(one(b), zero(one(T396)), zero(zero(X592)))
addCc143_in_aaa(one(T407), zero(T408), zero(X610)) → U124_aaa(T407, T408, X610, addCc143_in_aaa(T407, T408, X610))
addCc143_in_aaa(one(T417), one(T418), one(X626)) → U125_aaa(T417, T418, X626, addcc108_in_aaa(T417, T418, X626))
U125_aaa(T417, T418, X626, addcc108_out_aaa(T417, T418, X626)) → addCc143_out_aaa(one(T417), one(T418), one(X626))
U124_aaa(T407, T408, X610, addCc143_out_aaa(T407, T408, X610)) → addCc143_out_aaa(one(T407), zero(T408), zero(X610))
U121_aaa(T367, T368, X542, addCc143_out_aaa(T367, T368, X542)) → addCc143_out_aaa(zero(T367), one(T368), zero(X542))
U128_aaa(T313, T314, X447, addCc143_out_aaa(T313, T314, X447)) → addcc108_out_aaa(T313, T314, X447)
U113_aaa(T265, T266, X356, addcc108_out_aaa(T265, T266, X356)) → addzc73_out_aaa(one(T265), one(T266), zero(X356))
U131_aaa(T255, T256, X340, addzc73_out_aaa(T255, T256, X340)) → addyc96_out_aaa(T255, T256, X340)
U112_aaa(T229, T230, X307, addyc96_out_aaa(T229, T230, X307)) → addzc73_out_aaa(one(T229), zero(T230), one(X307))
U111_aaa(T215, T216, X283, addzc73_out_aaa(T215, T216, X283)) → addzc73_out_aaa(zero(T215), one(T216), one(X283))
U108_aaa(T175, T176, X223, addzc73_out_aaa(T175, T176, X223)) → addzc73_out_aaa(zero(T175), zero(T176), zero(X223))
U163_aaa(T161, T162, X196, addzc73_out_aaa(T161, T162, X196)) → addc37_out_aaa(zero(T161), T162, zero(X196))
addc37_in_aaa(one(T430), T431, one(X652)) → U164_aaa(T430, T431, X652, addyc96_in_aaa(T430, T431, X652))
U164_aaa(T430, T431, X652, addyc96_out_aaa(T430, T431, X652)) → addc37_out_aaa(one(T430), T431, one(X652))
U103_aaa(T86, T91, X108, addc37_out_aaa(T91, T90, X108)) → timesc22_out_aaa(one(T86), T91, X108)
U101_aaa(T76, T77, X89, timesc22_out_aaa(T76, T77, X89)) → timesc22_out_aaa(zero(T76), T77, zero(X89))

The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
timesc22_in_aaa(x1, x2, x3) = timesc22_in_aaa
timesc22_out_aaa(x1, x2, x3) = timesc22_out_aaa(x1)
U101_aaa(x1, x2, x3, x4) = U101_aaa(x4)
U102_aaa(x1, x2, x3, x4) = U102_aaa(x4)
U103_aaa(x1, x2, x3, x4) = U103_aaa(x1, x4)
addc37_in_aaa(x1, x2, x3) = addc37_in_aaa
U162_aaa(x1, x2) = U162_aaa(x2)
binaryZc43_in_a(x1) = binaryZc43_in_a
U132_a(x1, x2) = U132_a(x2)
binaryZc48_in_a(x1) = binaryZc48_in_a
U104_a(x1, x2) = U104_a(x2)
U105_a(x1, x2) = U105_a(x2)
binaryc54_in_a(x1) = binaryc54_in_a
binaryc54_out_a(x1) = binaryc54_out_a(x1)
U106_a(x1, x2) = U106_a(x2)
binaryZc48_out_a(x1) = binaryZc48_out_a(x1)
U107_a(x1, x2) = U107_a(x2)
binaryZc43_out_a(x1) = binaryZc43_out_a(x1)
addc37_out_aaa(x1, x2, x3) = addc37_out_aaa(x1, x2, x3)
U163_aaa(x1, x2, x3, x4) = U163_aaa(x4)
addzc73_in_aaa(x1, x2, x3) = addzc73_in_aaa
U108_aaa(x1, x2, x3, x4) = U108_aaa(x4)
U109_aaa(x1, x2) = U109_aaa(x2)
addzc73_out_aaa(x1, x2, x3) = addzc73_out_aaa(x1, x2, x3)
U110_aaa(x1, x2) = U110_aaa(x2)
U111_aaa(x1, x2, x3, x4) = U111_aaa(x4)
U112_aaa(x1, x2, x3, x4) = U112_aaa(x4)
addyc96_in_aaa(x1, x2, x3) = addyc96_in_aaa
U129_aaa(x1, x2) = U129_aaa(x2)
addyc96_out_aaa(x1, x2, x3) = addyc96_out_aaa(x1, x2, x3)
U130_aaa(x1, x2) = U130_aaa(x2)
U131_aaa(x1, x2, x3, x4) = U131_aaa(x4)
U113_aaa(x1, x2, x3, x4) = U113_aaa(x4)
addcc108_in_aaa(x1, x2, x3) = addcc108_in_aaa
addcc108_out_aaa(x1, x2, x3) = addcc108_out_aaa(x1, x2, x3)
U126_aaa(x1, x2, x3) = U126_aaa(x3)
succZc118_in_aa(x1, x2) = succZc118_in_aa
U116_aa(x1, x2) = U116_aa(x2)
succZc118_out_aa(x1, x2) = succZc118_out_aa(x1, x2)
U117_aa(x1, x2, x3) = U117_aa(x3)
succc125_in_aa(x1, x2) = succc125_in_aa
succc125_out_aa(x1, x2) = succc125_out_aa(x1, x2)
U114_aa(x1, x2) = U114_aa(x2)
U115_aa(x1, x2, x3) = U115_aa(x3)
U127_aaa(x1, x2, x3) = U127_aaa(x3)
U128_aaa(x1, x2, x3, x4) = U128_aaa(x4)
addCc143_in_aaa(x1, x2, x3) = addCc143_in_aaa
U118_aaa(x1, x2, x3, x4) = U118_aaa(x4)
addCc143_out_aaa(x1, x2, x3) = addCc143_out_aaa(x1, x2, x3)
U119_aaa(x1, x2) = U119_aaa(x2)
U120_aaa(x1, x2, x3) = U120_aaa(x3)
U121_aaa(x1, x2, x3, x4) = U121_aaa(x4)
U122_aaa(x1, x2) = U122_aaa(x2)
U123_aaa(x1, x2, x3) = U123_aaa(x3)
U124_aaa(x1, x2, x3, x4) = U124_aaa(x4)
U125_aaa(x1, x2, x3, x4) = U125_aaa(x4)
U164_aaa(x1, x2, x3, x4) = U164_aaa(x4)
one(x1) = one(x1)
b = b
TIMES1_IN_AAG(x1, x2, x3) = TIMES1_IN_AAG(x3)

We have to consider all (P,R,Pi)-chains

(71) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(72) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

TIMES1_IN_AAG(zero(zero(T34)), T35, zero(zero(T33))) → TIMES1_IN_AAG(T34, T35, T33)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
TIMES1_IN_AAG(x1, x2, x3) = TIMES1_IN_AAG(x3)

We have to consider all (P,R,Pi)-chains

(73) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(74) Obligation:

Q DP problem:
The TRS P consists of the following rules:

TIMES1_IN_AAG(zero(zero(T33))) → TIMES1_IN_AAG(T33)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(75) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

TIMES1_IN_AAG(zero(zero(T33))) → TIMES1_IN_AAG(T33)
The graph contains the following edges 1 > 1

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) TriplesToPiDPProof (SOUND transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (EQUIVALENT transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (EQUIVALENT transformation)

(18) Obligation:

(19) QDPSizeChangeProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) UsableRulesProof (EQUIVALENT transformation)

(23) Obligation:

(24) PiDPToQDPProof (EQUIVALENT transformation)

(25) Obligation:

(26) QDPSizeChangeProof (EQUIVALENT transformation)

(27) YES

(28) Obligation:

(29) UsableRulesProof (EQUIVALENT transformation)

(30) Obligation:

(31) PiDPToQDPProof (SOUND transformation)

(32) Obligation:

(33) QDPSizeChangeProof (EQUIVALENT transformation)

(34) YES

(35) Obligation:

(36) UsableRulesProof (EQUIVALENT transformation)

(37) Obligation:

(38) PiDPToQDPProof (SOUND transformation)

(39) Obligation:

(40) QDPSizeChangeProof (EQUIVALENT transformation)

(41) YES

(42) Obligation:

(43) UsableRulesProof (EQUIVALENT transformation)

(44) Obligation:

(45) PiDPToQDPProof (SOUND transformation)

(46) Obligation:

(47) NonTerminationProof (EQUIVALENT transformation)

(48) NO

(49) Obligation:

(50) UsableRulesProof (EQUIVALENT transformation)

(51) Obligation:

(52) PiDPToQDPProof (SOUND transformation)

(53) Obligation:

(54) NonTerminationProof (EQUIVALENT transformation)

(55) NO

(56) Obligation:

(57) UsableRulesProof (EQUIVALENT transformation)

(58) Obligation:

(59) PiDPToQDPProof (SOUND transformation)

(60) Obligation:

(61) NonTerminationProof (EQUIVALENT transformation)

(62) NO

(63) Obligation:

(64) UsableRulesProof (EQUIVALENT transformation)

(65) Obligation:

(66) PiDPToQDPProof (SOUND transformation)

(67) Obligation:

(68) NonTerminationProof (EQUIVALENT transformation)

(69) NO

(70) Obligation:

(71) UsableRulesProof (EQUIVALENT transformation)

(72) Obligation:

(73) PiDPToQDPProof (SOUND transformation)

(74) Obligation:

(75) QDPSizeChangeProof (EQUIVALENT transformation)

(76) YES