Left Termination proof of /tmp/tmpCKB1Fe/binary2.pl

Left Termination of the query pattern
add(a,a,g)
w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇒, 486 ms)

↳2 Prolog

↳3 PrologToPiTRSProof (⇒, 91 ms)

↳4 PiTRS

↳5 DependencyPairsProof (⇔, 568 ms)

↳6 PiDP

↳7 DependencyGraphProof (⇔, 0 ms)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔, 0 ms)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇔, 29 ms)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔, 0 ms)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔, 0 ms)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇒, 0 ms)

        ↳20 QDP

        ↳21 QDPSizeChangeProof (⇔, 0 ms)

        ↳22 YES

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔, 0 ms)

        ↳25 PiDP

        ↳26 PiDPToQDPProof (⇒, 0 ms)

        ↳27 QDP

        ↳28 QDPSizeChangeProof (⇔, 0 ms)

        ↳29 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)).

Query: add(a,a,g)

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph ICLP10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: add(T1, T2, T3)\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: add(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | add(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | add(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | add(T1, T2, b), SCOPE: 1, CLAUSE: 1 | add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: add(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | add(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\nadd(T1, T2, T3) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: add(T1, T2, b), SCOPE: 1, CLAUSE: 1 | add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: binaryZ(b) | add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\nX2 is free\nadd(T1, T2, b) !=? add(X2, b, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: binaryZ(b), SCOPE: 2, CLAUSE: 31 | binaryZ(b), SCOPE: 2, CLAUSE: 32 | ?_2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: binaryZ(b), SCOPE: 2, CLAUSE: 32 | ?_2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: ?_2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: add(T1, T2, b), SCOPE: 1, CLAUSE: 2 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: add(T1, T2, b), SCOPE: 1, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: binaryZ(b)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: binaryZ(b), SCOPE: 3, CLAUSE: 31 | binaryZ(b), SCOPE: 3, CLAUSE: 32\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: binaryZ(b), SCOPE: 3, CLAUSE: 32\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: addz(T21, T22, b)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: addz(T21, T22, b), SCOPE: 4, CLAUSE: 10 | addz(T21, T22, b), SCOPE: 4, CLAUSE: 11 | addz(T21, T22, b), SCOPE: 4, CLAUSE: 12 | addz(T21, T22, b), SCOPE: 4, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: addz(T21, T22, b), SCOPE: 4, CLAUSE: 11 | addz(T21, T22, b), SCOPE: 4, CLAUSE: 12 | addz(T21, T22, b), SCOPE: 4, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: addz(T21, T22, b), SCOPE: 4, CLAUSE: 12 | addz(T21, T22, b), SCOPE: 4, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: addz(T21, T22, b), SCOPE: 4, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: binaryZ(b) | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\nX2 is free\nadd(T1, T2, b) !=? add(X2, b, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\nX2 is free\nX41 is free\nadd(T1, T2, b) !=? add(X2, b, X2)\nadd(T1, T2, b) !=? add(b, X41, X41)", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: binaryZ(b), SCOPE: 5, CLAUSE: 31 | binaryZ(b), SCOPE: 5, CLAUSE: 32 | ?_5 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\nX2 is free\nadd(T1, T2, b) !=? add(X2, b, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: binaryZ(b), SCOPE: 5, CLAUSE: 32 | ?_5 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\nX2 is free\nadd(T1, T2, b) !=? add(X2, b, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ?_5 | add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\nX2 is free\nadd(T1, T2, b) !=? add(X2, b, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: add(T1, T2, b), SCOPE: 1, CLAUSE: 3\n\nX2 is free\nadd(T1, T2, b) !=? add(X2, b, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: addz(T45, T46, b)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: addz(T53, T54, b)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: addz(T53, T54, b), SCOPE: 6, CLAUSE: 10 | addz(T53, T54, b), SCOPE: 6, CLAUSE: 11 | addz(T53, T54, b), SCOPE: 6, CLAUSE: 12 | addz(T53, T54, b), SCOPE: 6, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: addz(T53, T54, b), SCOPE: 6, CLAUSE: 11 | addz(T53, T54, b), SCOPE: 6, CLAUSE: 12 | addz(T53, T54, b), SCOPE: 6, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: addz(T53, T54, b), SCOPE: 6, CLAUSE: 12 | addz(T53, T54, b), SCOPE: 6, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: addz(T53, T54, b), SCOPE: 6, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: binaryZ(T64) | add(T1, T2, T64), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 3\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: add(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\nX78 is free\nadd(T1, T2, T3) !=? add(b, b, b)\nadd(T1, T2, T3) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: binaryZ(T64), SCOPE: 7, CLAUSE: 31 | binaryZ(T64), SCOPE: 7, CLAUSE: 32 | ?_7 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 3\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: binaryZ(T64), SCOPE: 7, CLAUSE: 31\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: binaryZ(T64), SCOPE: 7, CLAUSE: 32 | ?_7 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 3\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: binaryZ(T69)\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: binaryZ(T69), SCOPE: 8, CLAUSE: 31 | binaryZ(T69), SCOPE: 8, CLAUSE: 32\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: binaryZ(T69), SCOPE: 8, CLAUSE: 31\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: binaryZ(T69), SCOPE: 8, CLAUSE: 32\n\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: binaryZ(T75)\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: binary(T79)\n\nT79 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: binary(T79), SCOPE: 9, CLAUSE: 28 | binary(T79), SCOPE: 9, CLAUSE: 29 | binary(T79), SCOPE: 9, CLAUSE: 30\n\nT79 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: binary(T79), SCOPE: 9, CLAUSE: 28\n\nT79 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: binary(T79), SCOPE: 9, CLAUSE: 29 | binary(T79), SCOPE: 9, CLAUSE: 30\n\nT79 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: binary(T79), SCOPE: 9, CLAUSE: 29\n\nT79 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: binary(T79), SCOPE: 9, CLAUSE: 30\n\nT79 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: binaryZ(T84)\n\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: binary(T88)\n\nT88 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: binaryZ(T64), SCOPE: 7, CLAUSE: 32\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ?_7 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 3\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: binary(T93)\n\nT93 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: add(T1, T2, T64), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T64), SCOPE: 1, CLAUSE: 3\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: add(T1, T2, T64), SCOPE: 1, CLAUSE: 2\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: add(T1, T2, T64), SCOPE: 1, CLAUSE: 3\n\nT64 is ground\nadd(T1, T2, T64) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: binaryZ(T98)\n\nT98 is ground\nadd(T1, T2, T98) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: addz(T114, T115, T113)\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: addz(T114, T115, T113), SCOPE: 10, CLAUSE: 10 | addz(T114, T115, T113), SCOPE: 10, CLAUSE: 11 | addz(T114, T115, T113), SCOPE: 10, CLAUSE: 12 | addz(T114, T115, T113), SCOPE: 10, CLAUSE: 13\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: addz(T114, T115, T113), SCOPE: 10, CLAUSE: 10\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: addz(T114, T115, T113), SCOPE: 10, CLAUSE: 11 | addz(T114, T115, T113), SCOPE: 10, CLAUSE: 12 | addz(T114, T115, T113), SCOPE: 10, CLAUSE: 13\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: addz(T134, T135, T133)\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: addz(T134, T135, T133), SCOPE: 11, CLAUSE: 10 | addz(T134, T135, T133), SCOPE: 11, CLAUSE: 11 | addz(T134, T135, T133), SCOPE: 11, CLAUSE: 12 | addz(T134, T135, T133), SCOPE: 11, CLAUSE: 13\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: addz(T134, T135, T133), SCOPE: 11, CLAUSE: 10\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: addz(T134, T135, T133), SCOPE: 11, CLAUSE: 11 | addz(T134, T135, T133), SCOPE: 11, CLAUSE: 12 | addz(T134, T135, T133), SCOPE: 11, CLAUSE: 13\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: addz(T154, T155, T153)\n\nT153 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: addz(T134, T135, T133), SCOPE: 11, CLAUSE: 11\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: addz(T134, T135, T133), SCOPE: 11, CLAUSE: 12 | addz(T134, T135, T133), SCOPE: 11, CLAUSE: 13\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: addx(T174, T175, T173)\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: addx(T174, T175, T173), SCOPE: 12, CLAUSE: 4 | addx(T174, T175, T173), SCOPE: 12, CLAUSE: 5 | addx(T174, T175, T173), SCOPE: 12, CLAUSE: 6\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: addx(T174, T175, T173), SCOPE: 12, CLAUSE: 4\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: addx(T174, T175, T173), SCOPE: 12, CLAUSE: 5 | addx(T174, T175, T173), SCOPE: 12, CLAUSE: 6\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: binary(T181)\n\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: addx(T174, T175, T173), SCOPE: 12, CLAUSE: 5\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: addx(T174, T175, T173), SCOPE: 12, CLAUSE: 6\n\nT173 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: binaryZ(T186)\n\nT186 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: addz(T202, T203, T201)\n\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: addz(T134, T135, T133), SCOPE: 11, CLAUSE: 12\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: addz(T134, T135, T133), SCOPE: 11, CLAUSE: 13\n\nT133 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: addy(T222, T223, T221)\n\nT221 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: addy(T222, T223, T221), SCOPE: 13, CLAUSE: 7 | addy(T222, T223, T221), SCOPE: 13, CLAUSE: 8 | addy(T222, T223, T221), SCOPE: 13, CLAUSE: 9\n\nT221 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: addy(T222, T223, T221), SCOPE: 13, CLAUSE: 7\n\nT221 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: addy(T222, T223, T221), SCOPE: 13, CLAUSE: 8 | addy(T222, T223, T221), SCOPE: 13, CLAUSE: 9\n\nT221 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: binary(T229)\n\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: addy(T222, T223, T221), SCOPE: 13, CLAUSE: 8\n\nT221 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: addy(T222, T223, T221), SCOPE: 13, CLAUSE: 9\n\nT221 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: binaryZ(T234)\n\nT234 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: addz(T250, T251, T249)\n\nT249 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: addc(T264, T265, T263)\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: addc(T264, T265, T263), SCOPE: 14, CLAUSE: 14 | addc(T264, T265, T263), SCOPE: 14, CLAUSE: 15 | addc(T264, T265, T263), SCOPE: 14, CLAUSE: 16 | addc(T264, T265, T263), SCOPE: 14, CLAUSE: 17\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: addc(T264, T265, T263), SCOPE: 14, CLAUSE: 14\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: addc(T264, T265, T263), SCOPE: 14, CLAUSE: 15 | addc(T264, T265, T263), SCOPE: 14, CLAUSE: 16 | addc(T264, T265, T263), SCOPE: 14, CLAUSE: 17\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: addc(T264, T265, T263), SCOPE: 14, CLAUSE: 15\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: addc(T264, T265, T263), SCOPE: 14, CLAUSE: 16 | addc(T264, T265, T263), SCOPE: 14, CLAUSE: 17\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: succZ(T276, T275)\n\nT275 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: succZ(T276, T275), SCOPE: 15, CLAUSE: 36 | succZ(T276, T275), SCOPE: 15, CLAUSE: 37\n\nT275 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: succZ(T276, T275), SCOPE: 15, CLAUSE: 36\n\nT275 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: succZ(T276, T275), SCOPE: 15, CLAUSE: 37\n\nT275 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: binaryZ(T282)\n\nT282 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: succ(T290, T289)\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: succ(T290, T289), SCOPE: 16, CLAUSE: 33 | succ(T290, T289), SCOPE: 16, CLAUSE: 34 | succ(T290, T289), SCOPE: 16, CLAUSE: 35\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: succ(T290, T289), SCOPE: 16, CLAUSE: 33\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: succ(T290, T289), SCOPE: 16, CLAUSE: 34 | succ(T290, T289), SCOPE: 16, CLAUSE: 35\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: succ(T290, T289), SCOPE: 16, CLAUSE: 34\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: succ(T290, T289), SCOPE: 16, CLAUSE: 35\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: binaryZ(T295)\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: succ(T303, T302)\n\nT302 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: addc(T264, T265, T263), SCOPE: 14, CLAUSE: 16\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: addc(T264, T265, T263), SCOPE: 14, CLAUSE: 17\n\nT263 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: succZ(T314, T313)\n\nT313 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: addC(T330, T331, T329)\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: addC(T330, T331, T329), SCOPE: 17, CLAUSE: 24 | addC(T330, T331, T329), SCOPE: 17, CLAUSE: 25 | addC(T330, T331, T329), SCOPE: 17, CLAUSE: 26 | addC(T330, T331, T329), SCOPE: 17, CLAUSE: 27\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: addC(T330, T331, T329), SCOPE: 17, CLAUSE: 24\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: addC(T330, T331, T329), SCOPE: 17, CLAUSE: 25 | addC(T330, T331, T329), SCOPE: 17, CLAUSE: 26 | addC(T330, T331, T329), SCOPE: 17, CLAUSE: 27\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: addz(T350, T351, T349)\n\nT349 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: addC(T330, T331, T329), SCOPE: 17, CLAUSE: 25\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: addC(T330, T331, T329), SCOPE: 17, CLAUSE: 26 | addC(T330, T331, T329), SCOPE: 17, CLAUSE: 27\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: addX(T370, T371, T369)\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: addX(T370, T371, T369), SCOPE: 18, CLAUSE: 18 | addX(T370, T371, T369), SCOPE: 18, CLAUSE: 19 | addX(T370, T371, T369), SCOPE: 18, CLAUSE: 20\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: addX(T370, T371, T369), SCOPE: 18, CLAUSE: 18\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: addX(T370, T371, T369), SCOPE: 18, CLAUSE: 19 | addX(T370, T371, T369), SCOPE: 18, CLAUSE: 20\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: binaryZ(T377)\n\nT377 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: addX(T370, T371, T369), SCOPE: 18, CLAUSE: 19\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: addX(T370, T371, T369), SCOPE: 18, CLAUSE: 20\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: succ(T389, T388)\n\nT388 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: addC(T404, T405, T403)\n\nT403 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: addC(T330, T331, T329), SCOPE: 17, CLAUSE: 26\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: addC(T330, T331, T329), SCOPE: 17, CLAUSE: 27\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: addY(T424, T425, T423)\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: addY(T424, T425, T423), SCOPE: 19, CLAUSE: 21 | addY(T424, T425, T423), SCOPE: 19, CLAUSE: 22 | addY(T424, T425, T423), SCOPE: 19, CLAUSE: 23\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: addY(T424, T425, T423), SCOPE: 19, CLAUSE: 21\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: addY(T424, T425, T423), SCOPE: 19, CLAUSE: 22 | addY(T424, T425, T423), SCOPE: 19, CLAUSE: 23\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: binaryZ(T431)\n\nT431 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: addY(T424, T425, T423), SCOPE: 19, CLAUSE: 22\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: addY(T424, T425, T423), SCOPE: 19, CLAUSE: 23\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: succ(T443, T442)\n\nT442 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: addC(T458, T459, T457)\n\nT457 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: addc(T472, T473, T471)\n\nT471 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: addz(T114, T115, T113), SCOPE: 10, CLAUSE: 11\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: addz(T114, T115, T113), SCOPE: 10, CLAUSE: 12 | addz(T114, T115, T113), SCOPE: 10, CLAUSE: 13\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: addx(T489, T490, T488)\n\nT488 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: addz(T114, T115, T113), SCOPE: 10, CLAUSE: 12\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: addz(T114, T115, T113), SCOPE: 10, CLAUSE: 13\n\nT113 is ground\nadd(T1, T2, T113) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: addy(T507, T508, T506)\n\nT506 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: addc(T519, T520, T518)\n\nT518 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: binaryZ(T522) | add(T1, T2, T522), SCOPE: 1, CLAUSE: 3\n\nT522 is ground\nX78 is free\nadd(T1, T2, T522) !=? add(b, b, b)\nadd(T1, T2, T522) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: add(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T3) !=? add(b, b, b)\nadd(T1, T2, T3) !=? add(X78, b, X78)\nadd(T1, T2, T3) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: binaryZ(T522), SCOPE: 20, CLAUSE: 31 | binaryZ(T522), SCOPE: 20, CLAUSE: 32 | ?_20 | add(T1, T2, T522), SCOPE: 1, CLAUSE: 3\n\nT522 is ground\nX78 is free\nadd(T1, T2, T522) !=? add(b, b, b)\nadd(T1, T2, T522) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: binaryZ(T522), SCOPE: 20, CLAUSE: 31\n\nT522 is ground\nX78 is free\nadd(T1, T2, T522) !=? add(b, b, b)\nadd(T1, T2, T522) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: binaryZ(T522), SCOPE: 20, CLAUSE: 32 | ?_20 | add(T1, T2, T522), SCOPE: 1, CLAUSE: 3\n\nT522 is ground\nX78 is free\nadd(T1, T2, T522) !=? add(b, b, b)\nadd(T1, T2, T522) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: binaryZ(T527)\n\nT527 is ground\nX78 is free\nadd(T1, T2, zero(T527)) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: binaryZ(T522), SCOPE: 20, CLAUSE: 32\n\nT522 is ground\nX78 is free\nadd(T1, T2, T522) !=? add(b, b, b)\nadd(T1, T2, T522) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ?_20 | add(T1, T2, T522), SCOPE: 1, CLAUSE: 3\n\nT522 is ground\nX78 is free\nadd(T1, T2, T522) !=? add(b, b, b)\nadd(T1, T2, T522) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: binary(T533)\n\nT533 is ground\nX78 is free\nadd(T1, T2, one(T533)) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: add(T1, T2, T522), SCOPE: 1, CLAUSE: 3\n\nT522 is ground\nX78 is free\nadd(T1, T2, T522) !=? add(b, b, b)\nadd(T1, T2, T522) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: addz(T548, T549, T547)\n\nT547 is ground\nX78 is free\nadd(T1, T2, T547) !=? add(b, b, b)\nadd(T1, T2, T547) !=? add(X78, b, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: addz(T559, T560, T558)\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: addz(T559, T560, T558), SCOPE: 21, CLAUSE: 10 | addz(T559, T560, T558), SCOPE: 21, CLAUSE: 11 | addz(T559, T560, T558), SCOPE: 21, CLAUSE: 12 | addz(T559, T560, T558), SCOPE: 21, CLAUSE: 13\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: addz(T559, T560, T558), SCOPE: 21, CLAUSE: 10\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: addz(T559, T560, T558), SCOPE: 21, CLAUSE: 11 | addz(T559, T560, T558), SCOPE: 21, CLAUSE: 12 | addz(T559, T560, T558), SCOPE: 21, CLAUSE: 13\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: addz(T576, T577, T575)\n\nT575 is ground\nX78 is free\nX482 is free\nadd(T1, T2, zero(T575)) !=? add(X78, b, X78)\nadd(T1, T2, zero(T575)) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: addz(T559, T560, T558), SCOPE: 21, CLAUSE: 11\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: addz(T559, T560, T558), SCOPE: 21, CLAUSE: 12 | addz(T559, T560, T558), SCOPE: 21, CLAUSE: 13\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: addx(T596, T597, T595)\n\nT595 is ground\nX78 is free\nX482 is free\nadd(T1, T2, one(T595)) !=? add(X78, b, X78)\nadd(T1, T2, one(T595)) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: addz(T559, T560, T558), SCOPE: 21, CLAUSE: 12\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: addz(T559, T560, T558), SCOPE: 21, CLAUSE: 13\n\nT558 is ground\nX78 is free\nX482 is free\nadd(T1, T2, T558) !=? add(b, b, b)\nadd(T1, T2, T558) !=? add(X78, b, X78)\nadd(T1, T2, T558) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: addy(T614, T615, T613)\n\nT613 is ground\nX78 is free\nX482 is free\nadd(T1, T2, one(T613)) !=? add(X78, b, X78)\nadd(T1, T2, one(T613)) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: addc(T626, T627, T625)\n\nT625 is ground\nX78 is free\nX482 is free\nadd(T1, T2, zero(T625)) !=? add(X78, b, X78)\nadd(T1, T2, zero(T625)) !=? add(b, X482, X482)", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 222 [arrowhead = none ];
222 -> 2;

223 [label="EVAL with clause\nadd(b, b, b).\nand substitutionT1 -> b,\nT2 -> b,\nT3 -> b", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 223 [arrowhead = none ];
223 -> 3;

224 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 224 [arrowhead = none ];
224 -> 4;

225 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 225 [arrowhead = none ];
225 -> 5;

226 [label="EVAL with clause\nadd(X78, b, X78) :- binaryZ(X78).\nand substitutionT1 -> T64,\nX78 -> T64,\nT2 -> b,\nT3 -> T64", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 226 [arrowhead = none ];
226 -> 38;

227 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 227 [arrowhead = none ];
227 -> 39;

228 [label="EVAL with clause\nadd(X2, b, X2) :- binaryZ(X2).\nand substitutionT1 -> b,\nX2 -> b,\nT2 -> b,\nT5 -> b", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 228 [arrowhead = none ];
228 -> 6;

229 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 229 [arrowhead = none ];
229 -> 7;

230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
6 -> 230 [arrowhead = none ];
230 -> 8;

231 [label="EVAL with clause\nadd(b, X41, X41) :- binaryZ(X41).\nand substitutionT1 -> b,\nT2 -> b,\nX41 -> b,\nT34 -> b", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 231 [arrowhead = none ];
231 -> 25;

232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 232 [arrowhead = none ];
232 -> 26;

233 [label="BACKTRACK\nfor clause: binaryZ(zero(X)) :- binaryZ(X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 233 [arrowhead = none ];
233 -> 9;

234 [label="BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 234 [arrowhead = none ];
234 -> 10;

235 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 235 [arrowhead = none ];
235 -> 11;

236 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 236 [arrowhead = none ];
236 -> 12;

237 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 237 [arrowhead = none ];
237 -> 13;

238 [label="EVAL with clause\nadd(b, X9, X9) :- binaryZ(X9).\nand substitutionT1 -> b,\nT2 -> b,\nX9 -> b,\nT10 -> b", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 238 [arrowhead = none ];
238 -> 14;

239 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 239 [arrowhead = none ];
239 -> 15;

240 [label="ONLY EVAL with clause\nadd(X22, X23, X24) :- addz(X22, X23, X24).\nand substitutionT1 -> T21,\nX22 -> T21,\nT2 -> T22,\nX23 -> T22,\nX24 -> b,\nT19 -> T21,\nT20 -> T22", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 240 [arrowhead = none ];
240 -> 19;

241 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 241 [arrowhead = none ];
241 -> 16;

242 [label="BACKTRACK\nfor clause: binaryZ(zero(X)) :- binaryZ(X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 242 [arrowhead = none ];
242 -> 17;

243 [label="BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 243 [arrowhead = none ];
243 -> 18;

244 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 244 [arrowhead = none ];
244 -> 20;

245 [label="BACKTRACK\nfor clause: addz(zero(X), zero(Y), zero(Z)) :- addz(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 245 [arrowhead = none ];
245 -> 21;

246 [label="BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 246 [arrowhead = none ];
246 -> 22;

247 [label="BACKTRACK\nfor clause: addz(one(X), zero(Y), one(Z)) :- addy(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 247 [arrowhead = none ];
247 -> 23;

248 [label="BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 248 [arrowhead = none ];
248 -> 24;

249 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 249 [arrowhead = none ];
249 -> 27;

250 [label="ONLY EVAL with clause\nadd(X62, X63, X64) :- addz(X62, X63, X64).\nand substitutionT1 -> T53,\nX62 -> T53,\nT2 -> T54,\nX63 -> T54,\nX64 -> b,\nT51 -> T53,\nT52 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
26 -> 250 [arrowhead = none ];
250 -> 32;

251 [label="BACKTRACK\nfor clause: binaryZ(zero(X)) :- binaryZ(X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 251 [arrowhead = none ];
251 -> 28;

252 [label="BACKTRACK\nfor clause: binaryZ(one(X)) :- binary(X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 252 [arrowhead = none ];
252 -> 29;

253 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 253 [arrowhead = none ];
253 -> 30;

254 [label="ONLY EVAL with clause\nadd(X53, X54, X55) :- addz(X53, X54, X55).\nand substitutionT1 -> T45,\nX53 -> T45,\nT2 -> T46,\nX54 -> T46,\nX55 -> b,\nT43 -> T45,\nT44 -> T46", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 254 [arrowhead = none ];
254 -> 31;

255 [label="INSTANCE with matching:\nT21 -> T45\nT22 -> T46", fontsize=14, style = filled, fillcolor = lightgrey];
31 -> 255 [arrowhead = none , style=dashed];
255 -> 19[style=dashed];

256 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
32 -> 256 [arrowhead = none ];
256 -> 33;

257 [label="BACKTRACK\nfor clause: addz(zero(X), zero(Y), zero(Z)) :- addz(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 257 [arrowhead = none ];
257 -> 34;

258 [label="BACKTRACK\nfor clause: addz(zero(X), one(Y), one(Z)) :- addx(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 258 [arrowhead = none ];
258 -> 35;

259 [label="BACKTRACK\nfor clause: addz(one(X), zero(Y), one(Z)) :- addy(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 259 [arrowhead = none ];
259 -> 36;

260 [label="BACKTRACK\nfor clause: addz(one(X), one(Y), zero(Z)) :- addc(X, Y, Z)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 260 [arrowhead = none ];
260 -> 37;

261 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
38 -> 261 [arrowhead = none ];
261 -> 40;

262 [label="EVAL with clause\nadd(b, X482, X482) :- binaryZ(X482).\nand substitutionT1 -> b,\nT2 -> T522,\nX482 -> T522,\nT3 -> T522", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 262 [arrowhead = none ];
262 -> 193;

263 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 263 [arrowhead = none ];
263 -> 194;

264 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 264 [arrowhead = none ];
264 -> 41;

265 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
40 -> 265 [arrowhead = none ];
265 -> 42;

266 [label="EVAL with clause\nbinaryZ(zero(X83)) :- binaryZ(X83).\nand substitutionX83 -> T69,\nT64 -> zero(T69)", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 266 [arrowhead = none ];
266 -> 43;

267 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 267 [arrowhead = none ];
267 -> 44;

268 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
42 -> 268 [arrowhead = none ];
268 -> 64;

269 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
42 -> 269 [arrowhead = none ];
269 -> 65;

270 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
43 -> 270 [arrowhead = none ];
270 -> 45;

271 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 271 [arrowhead = none ];
271 -> 46;

272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 272 [arrowhead = none ];
272 -> 47;

273 [label="EVAL with clause\nbinaryZ(zero(X89)) :- binaryZ(X89).\nand substitutionX89 -> T75,\nT69 -> zero(T75)", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 273 [arrowhead = none ];
273 -> 48;

274 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 274 [arrowhead = none ];
274 -> 49;

275 [label="EVAL with clause\nbinaryZ(one(X93)) :- binary(X93).\nand substitutionX93 -> T79,\nT69 -> one(T79)", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 275 [arrowhead = none ];
275 -> 50;

276 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 276 [arrowhead = none ];
276 -> 51;

277 [label="INSTANCE with matching:\nT69 -> T75", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 277 [arrowhead = none , style=dashed];
277 -> 43[style=dashed];

278 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
50 -> 278 [arrowhead = none ];
278 -> 52;

279 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
52 -> 279 [arrowhead = none ];
279 -> 53;

280 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
52 -> 280 [arrowhead = none ];
280 -> 54;

281 [label="EVAL with clause\nbinary(b).\nand substitutionT79 -> b", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 281 [arrowhead = none ];
281 -> 55;

282 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
53 -> 282 [arrowhead = none ];
282 -> 56;

283 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 283 [arrowhead = none ];
283 -> 58;

284 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 284 [arrowhead = none ];
284 -> 59;

285 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 285 [arrowhead = none ];
285 -> 57;

286 [label="EVAL with clause\nbinary(zero(X98)) :- binaryZ(X98).\nand substitutionX98 -> T84,\nT79 -> zero(T84)", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 286 [arrowhead = none ];
286 -> 60;

287 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 287 [arrowhead = none ];
287 -> 61;

288 [label="EVAL with clause\nbinary(one(X102)) :- binary(X102).\nand substitutionX102 -> T88,\nT79 -> one(T88)", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 288 [arrowhead = none ];
288 -> 62;

289 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 289 [arrowhead = none ];
289 -> 63;

290 [label="INSTANCE with matching:\nT69 -> T84", fontsize=14, style = filled, fillcolor = lightgrey];
60 -> 290 [arrowhead = none , style=dashed];
290 -> 43[style=dashed];

291 [label="INSTANCE with matching:\nT79 -> T88", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 291 [arrowhead = none , style=dashed];
291 -> 50[style=dashed];

292 [label="EVAL with clause\nbinaryZ(one(X107)) :- binary(X107).\nand substitutionX107 -> T93,\nT64 -> one(T93)", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 292 [arrowhead = none ];
292 -> 66;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
64 -> 293 [arrowhead = none ];
293 -> 67;

294 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 294 [arrowhead = none ];
294 -> 68;

295 [label="INSTANCE with matching:\nT79 -> T93", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 295 [arrowhead = none , style=dashed];
295 -> 50[style=dashed];

296 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 296 [arrowhead = none ];
296 -> 69;

297 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 297 [arrowhead = none ];
297 -> 70;

298 [label="EVAL with clause\nadd(b, X112, X112) :- binaryZ(X112).\nand substitutionT1 -> b,\nT2 -> T98,\nX112 -> T98,\nT64 -> T98", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 298 [arrowhead = none ];
298 -> 71;

299 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 299 [arrowhead = none ];
299 -> 72;

300 [label="ONLY EVAL with clause\nadd(X123, X124, X125) :- addz(X123, X124, X125).\nand substitutionT1 -> T114,\nX123 -> T114,\nT2 -> T115,\nX124 -> T115,\nT64 -> T113,\nX125 -> T113,\nT111 -> T114,\nT112 -> T115", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 300 [arrowhead = none ];
300 -> 73;

301 [label="INSTANCE with matching:\nT69 -> T98", fontsize=14, style = filled, fillcolor = lightgrey];
71 -> 301 [arrowhead = none , style=dashed];
301 -> 43[style=dashed];

302 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
73 -> 302 [arrowhead = none ];
302 -> 74;

303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 303 [arrowhead = none ];
303 -> 75;

304 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 304 [arrowhead = none ];
304 -> 76;

305 [label="EVAL with clause\naddz(zero(X141), zero(X142), zero(X143)) :- addz(X141, X142, X143).\nand substitutionX141 -> T134,\nT114 -> zero(T134),\nX142 -> T135,\nT115 -> zero(T135),\nX143 -> T133,\nT113 -> zero(T133),\nT131 -> T134,\nT132 -> T135", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 305 [arrowhead = none ];
305 -> 77;

306 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
75 -> 306 [arrowhead = none ];
306 -> 78;

307 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 307 [arrowhead = none ];
307 -> 183;

308 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 308 [arrowhead = none ];
308 -> 184;

309 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
77 -> 309 [arrowhead = none ];
309 -> 79;

310 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 310 [arrowhead = none ];
310 -> 80;

311 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 311 [arrowhead = none ];
311 -> 81;

312 [label="EVAL with clause\naddz(zero(X159), zero(X160), zero(X161)) :- addz(X159, X160, X161).\nand substitutionX159 -> T154,\nT134 -> zero(T154),\nX160 -> T155,\nT135 -> zero(T155),\nX161 -> T153,\nT133 -> zero(T153),\nT151 -> T154,\nT152 -> T155", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 312 [arrowhead = none ];
312 -> 82;

313 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 313 [arrowhead = none ];
313 -> 83;

314 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 314 [arrowhead = none ];
314 -> 84;

315 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 315 [arrowhead = none ];
315 -> 85;

316 [label="INSTANCE with matching:\nT134 -> T154\nT135 -> T155\nT133 -> T153", fontsize=14, style = filled, fillcolor = lightgrey];
82 -> 316 [arrowhead = none , style=dashed];
316 -> 77[style=dashed];

317 [label="EVAL with clause\naddz(zero(X177), one(X178), one(X179)) :- addx(X177, X178, X179).\nand substitutionX177 -> T174,\nT134 -> zero(T174),\nX178 -> T175,\nT135 -> one(T175),\nX179 -> T173,\nT133 -> one(T173),\nT171 -> T174,\nT172 -> T175", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 317 [arrowhead = none ];
317 -> 86;

318 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
84 -> 318 [arrowhead = none ];
318 -> 87;

319 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
85 -> 319 [arrowhead = none ];
319 -> 98;

320 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
85 -> 320 [arrowhead = none ];
320 -> 99;

321 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
86 -> 321 [arrowhead = none ];
321 -> 88;

322 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 322 [arrowhead = none ];
322 -> 89;

323 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 323 [arrowhead = none ];
323 -> 90;

324 [label="EVAL with clause\naddx(one(X185), b, one(X185)) :- binary(X185).\nand substitutionX185 -> T181,\nT174 -> one(T181),\nT175 -> b,\nT173 -> one(T181)", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 324 [arrowhead = none ];
324 -> 91;

325 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 325 [arrowhead = none ];
325 -> 92;

326 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 326 [arrowhead = none ];
326 -> 93;

327 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
90 -> 327 [arrowhead = none ];
327 -> 94;

328 [label="INSTANCE with matching:\nT79 -> T181", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 328 [arrowhead = none , style=dashed];
328 -> 50[style=dashed];

329 [label="EVAL with clause\naddx(zero(X190), b, zero(X190)) :- binaryZ(X190).\nand substitutionX190 -> T186,\nT174 -> zero(T186),\nT175 -> b,\nT173 -> zero(T186)", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 329 [arrowhead = none ];
329 -> 95;

330 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
93 -> 330 [arrowhead = none ];
330 -> 96;

331 [label="ONLY EVAL with clause\naddx(X201, X202, X203) :- addz(X201, X202, X203).\nand substitutionT174 -> T202,\nX201 -> T202,\nT175 -> T203,\nX202 -> T203,\nT173 -> T201,\nX203 -> T201,\nT199 -> T202,\nT200 -> T203", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 331 [arrowhead = none ];
331 -> 97;

332 [label="INSTANCE with matching:\nT69 -> T186", fontsize=14, style = filled, fillcolor = lightgrey];
95 -> 332 [arrowhead = none , style=dashed];
332 -> 43[style=dashed];

333 [label="INSTANCE with matching:\nT134 -> T202\nT135 -> T203\nT133 -> T201", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 333 [arrowhead = none , style=dashed];
333 -> 77[style=dashed];

334 [label="EVAL with clause\naddz(one(X219), zero(X220), one(X221)) :- addy(X219, X220, X221).\nand substitutionX219 -> T222,\nT134 -> one(T222),\nX220 -> T223,\nT135 -> zero(T223),\nX221 -> T221,\nT133 -> one(T221),\nT219 -> T222,\nT220 -> T223", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 334 [arrowhead = none ];
334 -> 100;

335 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 335 [arrowhead = none ];
335 -> 101;

336 [label="EVAL with clause\naddz(one(X255), one(X256), zero(X257)) :- addc(X255, X256, X257).\nand substitutionX255 -> T264,\nT134 -> one(T264),\nX256 -> T265,\nT135 -> one(T265),\nX257 -> T263,\nT133 -> zero(T263),\nT261 -> T264,\nT262 -> T265", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 336 [arrowhead = none ];
336 -> 112;

337 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 337 [arrowhead = none ];
337 -> 113;

338 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
100 -> 338 [arrowhead = none ];
338 -> 102;

339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 339 [arrowhead = none ];
339 -> 103;

340 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 340 [arrowhead = none ];
340 -> 104;

341 [label="EVAL with clause\naddy(b, one(X227), one(X227)) :- binary(X227).\nand substitutionT222 -> b,\nX227 -> T229,\nT223 -> one(T229),\nT221 -> one(T229)", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 341 [arrowhead = none ];
341 -> 105;

342 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
103 -> 342 [arrowhead = none ];
342 -> 106;

343 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 343 [arrowhead = none ];
343 -> 107;

344 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 344 [arrowhead = none ];
344 -> 108;

345 [label="INSTANCE with matching:\nT79 -> T229", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 345 [arrowhead = none , style=dashed];
345 -> 50[style=dashed];

346 [label="EVAL with clause\naddy(b, zero(X232), zero(X232)) :- binaryZ(X232).\nand substitutionT222 -> b,\nX232 -> T234,\nT223 -> zero(T234),\nT221 -> zero(T234)", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 346 [arrowhead = none ];
346 -> 109;

347 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
107 -> 347 [arrowhead = none ];
347 -> 110;

348 [label="ONLY EVAL with clause\naddy(X243, X244, X245) :- addz(X243, X244, X245).\nand substitutionT222 -> T250,\nX243 -> T250,\nT223 -> T251,\nX244 -> T251,\nT221 -> T249,\nX245 -> T249,\nT247 -> T250,\nT248 -> T251", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 348 [arrowhead = none ];
348 -> 111;

349 [label="INSTANCE with matching:\nT69 -> T234", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 349 [arrowhead = none , style=dashed];
349 -> 43[style=dashed];

350 [label="INSTANCE with matching:\nT134 -> T250\nT135 -> T251\nT133 -> T249", fontsize=14, style = filled, fillcolor = lightgrey];
111 -> 350 [arrowhead = none , style=dashed];
350 -> 77[style=dashed];

351 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
112 -> 351 [arrowhead = none ];
351 -> 114;

352 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
114 -> 352 [arrowhead = none ];
352 -> 115;

353 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
114 -> 353 [arrowhead = none ];
353 -> 116;

354 [label="EVAL with clause\naddc(b, b, one(b)).\nand substitutionT264 -> b,\nT265 -> b,\nT263 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 354 [arrowhead = none ];
354 -> 117;

355 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
115 -> 355 [arrowhead = none ];
355 -> 118;

356 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 356 [arrowhead = none ];
356 -> 120;

357 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 357 [arrowhead = none ];
357 -> 121;

358 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 358 [arrowhead = none ];
358 -> 119;

359 [label="EVAL with clause\naddc(X266, b, X267) :- succZ(X266, X267).\nand substitutionT264 -> T276,\nX266 -> T276,\nT265 -> b,\nT263 -> T275,\nX267 -> T275,\nT274 -> T276", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 359 [arrowhead = none ];
359 -> 122;

360 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 360 [arrowhead = none ];
360 -> 123;

361 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 361 [arrowhead = none ];
361 -> 143;

362 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 362 [arrowhead = none ];
362 -> 144;

363 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
122 -> 363 [arrowhead = none ];
363 -> 124;

364 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 364 [arrowhead = none ];
364 -> 125;

365 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 365 [arrowhead = none ];
365 -> 126;

366 [label="EVAL with clause\nsuccZ(zero(X273), one(X273)) :- binaryZ(X273).\nand substitutionX273 -> T282,\nT276 -> zero(T282),\nT275 -> one(T282)", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 366 [arrowhead = none ];
366 -> 127;

367 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 367 [arrowhead = none ];
367 -> 128;

368 [label="EVAL with clause\nsuccZ(one(X279), zero(X280)) :- succ(X279, X280).\nand substitutionX279 -> T290,\nT276 -> one(T290),\nX280 -> T289,\nT275 -> zero(T289),\nT288 -> T290", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 368 [arrowhead = none ];
368 -> 129;

369 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
126 -> 369 [arrowhead = none ];
369 -> 130;

370 [label="INSTANCE with matching:\nT69 -> T282", fontsize=14, style = filled, fillcolor = lightgrey];
127 -> 370 [arrowhead = none , style=dashed];
370 -> 43[style=dashed];

371 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
129 -> 371 [arrowhead = none ];
371 -> 131;

372 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 372 [arrowhead = none ];
372 -> 132;

373 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 373 [arrowhead = none ];
373 -> 133;

374 [label="EVAL with clause\nsucc(b, one(b)).\nand substitutionT290 -> b,\nT289 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 374 [arrowhead = none ];
374 -> 134;

375 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
132 -> 375 [arrowhead = none ];
375 -> 135;

376 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
133 -> 376 [arrowhead = none ];
376 -> 137;

377 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
133 -> 377 [arrowhead = none ];
377 -> 138;

378 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 378 [arrowhead = none ];
378 -> 136;

379 [label="EVAL with clause\nsucc(zero(X285), one(X285)) :- binaryZ(X285).\nand substitutionX285 -> T295,\nT290 -> zero(T295),\nT289 -> one(T295)", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 379 [arrowhead = none ];
379 -> 139;

380 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 380 [arrowhead = none ];
380 -> 140;

381 [label="EVAL with clause\nsucc(one(X291), zero(X292)) :- succ(X291, X292).\nand substitutionX291 -> T303,\nT290 -> one(T303),\nX292 -> T302,\nT289 -> zero(T302),\nT301 -> T303", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 381 [arrowhead = none ];
381 -> 141;

382 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 382 [arrowhead = none ];
382 -> 142;

383 [label="INSTANCE with matching:\nT69 -> T295", fontsize=14, style = filled, fillcolor = lightgrey];
139 -> 383 [arrowhead = none , style=dashed];
383 -> 43[style=dashed];

384 [label="INSTANCE with matching:\nT290 -> T303\nT289 -> T302", fontsize=14, style = filled, fillcolor = lightgrey];
141 -> 384 [arrowhead = none , style=dashed];
384 -> 129[style=dashed];

385 [label="EVAL with clause\naddc(b, X301, X302) :- succZ(X301, X302).\nand substitutionT264 -> b,\nT265 -> T314,\nX301 -> T314,\nT263 -> T313,\nX302 -> T313,\nT312 -> T314", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 385 [arrowhead = none ];
385 -> 145;

386 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 386 [arrowhead = none ];
386 -> 146;

387 [label="ONLY EVAL with clause\naddc(X313, X314, X315) :- addC(X313, X314, X315).\nand substitutionT264 -> T330,\nX313 -> T330,\nT265 -> T331,\nX314 -> T331,\nT263 -> T329,\nX315 -> T329,\nT327 -> T330,\nT328 -> T331", fontsize=14, style = filled, fillcolor = lightblue];
144 -> 387 [arrowhead = none ];
387 -> 147;

388 [label="INSTANCE with matching:\nT276 -> T314\nT275 -> T313", fontsize=14, style = filled, fillcolor = lightgrey];
145 -> 388 [arrowhead = none , style=dashed];
388 -> 122[style=dashed];

389 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
147 -> 389 [arrowhead = none ];
389 -> 148;

390 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
148 -> 390 [arrowhead = none ];
390 -> 149;

391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
148 -> 391 [arrowhead = none ];
391 -> 150;

392 [label="EVAL with clause\naddC(zero(X331), zero(X332), one(X333)) :- addz(X331, X332, X333).\nand substitutionX331 -> T350,\nT330 -> zero(T350),\nX332 -> T351,\nT331 -> zero(T351),\nX333 -> T349,\nT329 -> one(T349),\nT347 -> T350,\nT348 -> T351", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 392 [arrowhead = none ];
392 -> 151;

393 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
149 -> 393 [arrowhead = none ];
393 -> 152;

394 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 394 [arrowhead = none ];
394 -> 153;

395 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 395 [arrowhead = none ];
395 -> 154;

396 [label="INSTANCE with matching:\nT134 -> T350\nT135 -> T351\nT133 -> T349", fontsize=14, style = filled, fillcolor = lightgrey];
151 -> 396 [arrowhead = none , style=dashed];
396 -> 77[style=dashed];

397 [label="EVAL with clause\naddC(zero(X349), one(X350), zero(X351)) :- addX(X349, X350, X351).\nand substitutionX349 -> T370,\nT330 -> zero(T370),\nX350 -> T371,\nT331 -> one(T371),\nX351 -> T369,\nT329 -> zero(T369),\nT367 -> T370,\nT368 -> T371", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 397 [arrowhead = none ];
397 -> 155;

398 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 398 [arrowhead = none ];
398 -> 156;

399 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 399 [arrowhead = none ];
399 -> 167;

400 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 400 [arrowhead = none ];
400 -> 168;

401 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
155 -> 401 [arrowhead = none ];
401 -> 157;

402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 402 [arrowhead = none ];
402 -> 158;

403 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 403 [arrowhead = none ];
403 -> 159;

404 [label="EVAL with clause\naddX(zero(X357), b, one(X357)) :- binaryZ(X357).\nand substitutionX357 -> T377,\nT370 -> zero(T377),\nT371 -> b,\nT369 -> one(T377)", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 404 [arrowhead = none ];
404 -> 160;

405 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 405 [arrowhead = none ];
405 -> 161;

406 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
159 -> 406 [arrowhead = none ];
406 -> 162;

407 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
159 -> 407 [arrowhead = none ];
407 -> 163;

408 [label="INSTANCE with matching:\nT69 -> T377", fontsize=14, style = filled, fillcolor = lightgrey];
160 -> 408 [arrowhead = none , style=dashed];
408 -> 43[style=dashed];

409 [label="EVAL with clause\naddX(one(X367), b, zero(X368)) :- succ(X367, X368).\nand substitutionX367 -> T389,\nT370 -> one(T389),\nT371 -> b,\nX368 -> T388,\nT369 -> zero(T388),\nT387 -> T389", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 409 [arrowhead = none ];
409 -> 164;

410 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
162 -> 410 [arrowhead = none ];
410 -> 165;

411 [label="ONLY EVAL with clause\naddX(X378, X379, X380) :- addC(X378, X379, X380).\nand substitutionT370 -> T404,\nX378 -> T404,\nT371 -> T405,\nX379 -> T405,\nT369 -> T403,\nX380 -> T403,\nT401 -> T404,\nT402 -> T405", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 411 [arrowhead = none ];
411 -> 166;

412 [label="INSTANCE with matching:\nT290 -> T389\nT289 -> T388", fontsize=14, style = filled, fillcolor = lightgrey];
164 -> 412 [arrowhead = none , style=dashed];
412 -> 129[style=dashed];

413 [label="INSTANCE with matching:\nT330 -> T404\nT331 -> T405\nT329 -> T403", fontsize=14, style = filled, fillcolor = lightgrey];
166 -> 413 [arrowhead = none , style=dashed];
413 -> 147[style=dashed];

414 [label="EVAL with clause\naddC(one(X396), zero(X397), zero(X398)) :- addY(X396, X397, X398).\nand substitutionX396 -> T424,\nT330 -> one(T424),\nX397 -> T425,\nT331 -> zero(T425),\nX398 -> T423,\nT329 -> zero(T423),\nT421 -> T424,\nT422 -> T425", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 414 [arrowhead = none ];
414 -> 169;

415 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 415 [arrowhead = none ];
415 -> 170;

416 [label="EVAL with clause\naddC(one(X437), one(X438), one(X439)) :- addc(X437, X438, X439).\nand substitutionX437 -> T472,\nT330 -> one(T472),\nX438 -> T473,\nT331 -> one(T473),\nX439 -> T471,\nT329 -> one(T471),\nT469 -> T472,\nT470 -> T473", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 416 [arrowhead = none ];
416 -> 181;

417 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 417 [arrowhead = none ];
417 -> 182;

418 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
169 -> 418 [arrowhead = none ];
418 -> 171;

419 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
171 -> 419 [arrowhead = none ];
419 -> 172;

420 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
171 -> 420 [arrowhead = none ];
420 -> 173;

421 [label="EVAL with clause\naddY(b, zero(X404), one(X404)) :- binaryZ(X404).\nand substitutionT424 -> b,\nX404 -> T431,\nT425 -> zero(T431),\nT423 -> one(T431)", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 421 [arrowhead = none ];
421 -> 174;

422 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
172 -> 422 [arrowhead = none ];
422 -> 175;

423 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
173 -> 423 [arrowhead = none ];
423 -> 176;

424 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
173 -> 424 [arrowhead = none ];
424 -> 177;

425 [label="INSTANCE with matching:\nT69 -> T431", fontsize=14, style = filled, fillcolor = lightgrey];
174 -> 425 [arrowhead = none , style=dashed];
425 -> 43[style=dashed];

426 [label="EVAL with clause\naddY(b, one(X414), zero(X415)) :- succ(X414, X415).\nand substitutionT424 -> b,\nX414 -> T443,\nT425 -> one(T443),\nX415 -> T442,\nT423 -> zero(T442),\nT441 -> T443", fontsize=14, style = filled, fillcolor = lightblue];
176 -> 426 [arrowhead = none ];
426 -> 178;

427 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
176 -> 427 [arrowhead = none ];
427 -> 179;

428 [label="ONLY EVAL with clause\naddY(X425, X426, X427) :- addC(X425, X426, X427).\nand substitutionT424 -> T458,\nX425 -> T458,\nT425 -> T459,\nX426 -> T459,\nT423 -> T457,\nX427 -> T457,\nT455 -> T458,\nT456 -> T459", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 428 [arrowhead = none ];
428 -> 180;

429 [label="INSTANCE with matching:\nT290 -> T443\nT289 -> T442", fontsize=14, style = filled, fillcolor = lightgrey];
178 -> 429 [arrowhead = none , style=dashed];
429 -> 129[style=dashed];

430 [label="INSTANCE with matching:\nT330 -> T458\nT331 -> T459\nT329 -> T457", fontsize=14, style = filled, fillcolor = lightgrey];
180 -> 430 [arrowhead = none , style=dashed];
430 -> 147[style=dashed];

431 [label="INSTANCE with matching:\nT264 -> T472\nT265 -> T473\nT263 -> T471", fontsize=14, style = filled, fillcolor = lightgrey];
181 -> 431 [arrowhead = none , style=dashed];
431 -> 112[style=dashed];

432 [label="EVAL with clause\naddz(zero(X452), one(X453), one(X454)) :- addx(X452, X453, X454).\nand substitutionX452 -> T489,\nT114 -> zero(T489),\nX453 -> T490,\nT115 -> one(T490),\nX454 -> T488,\nT113 -> one(T488),\nT486 -> T489,\nT487 -> T490", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 432 [arrowhead = none ];
432 -> 185;

433 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 433 [arrowhead = none ];
433 -> 186;

434 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 434 [arrowhead = none ];
434 -> 187;

435 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 435 [arrowhead = none ];
435 -> 188;

436 [label="INSTANCE with matching:\nT174 -> T489\nT175 -> T490\nT173 -> T488", fontsize=14, style = filled, fillcolor = lightgrey];
185 -> 436 [arrowhead = none , style=dashed];
436 -> 86[style=dashed];

437 [label="EVAL with clause\naddz(one(X468), zero(X469), one(X470)) :- addy(X468, X469, X470).\nand substitutionX468 -> T507,\nT114 -> one(T507),\nX469 -> T508,\nT115 -> zero(T508),\nX470 -> T506,\nT113 -> one(T506),\nT504 -> T507,\nT505 -> T508", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 437 [arrowhead = none ];
437 -> 189;

438 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 438 [arrowhead = none ];
438 -> 190;

439 [label="EVAL with clause\naddz(one(X478), one(X479), zero(X480)) :- addc(X478, X479, X480).\nand substitutionX478 -> T519,\nT114 -> one(T519),\nX479 -> T520,\nT115 -> one(T520),\nX480 -> T518,\nT113 -> zero(T518),\nT516 -> T519,\nT517 -> T520", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 439 [arrowhead = none ];
439 -> 191;

440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
188 -> 440 [arrowhead = none ];
440 -> 192;

441 [label="INSTANCE with matching:\nT222 -> T507\nT223 -> T508\nT221 -> T506", fontsize=14, style = filled, fillcolor = lightgrey];
189 -> 441 [arrowhead = none , style=dashed];
441 -> 100[style=dashed];

442 [label="INSTANCE with matching:\nT264 -> T519\nT265 -> T520\nT263 -> T518", fontsize=14, style = filled, fillcolor = lightgrey];
191 -> 442 [arrowhead = none , style=dashed];
442 -> 112[style=dashed];

443 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
193 -> 443 [arrowhead = none ];
443 -> 195;

444 [label="ONLY EVAL with clause\nadd(X512, X513, X514) :- addz(X512, X513, X514).\nand substitutionT1 -> T559,\nX512 -> T559,\nT2 -> T560,\nX513 -> T560,\nT3 -> T558,\nX514 -> T558,\nT556 -> T559,\nT557 -> T560", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 444 [arrowhead = none ];
444 -> 206;

445 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
195 -> 445 [arrowhead = none ];
445 -> 196;

446 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
195 -> 446 [arrowhead = none ];
446 -> 197;

447 [label="EVAL with clause\nbinaryZ(zero(X487)) :- binaryZ(X487).\nand substitutionX487 -> T527,\nT522 -> zero(T527)", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 447 [arrowhead = none ];
447 -> 198;

448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 448 [arrowhead = none ];
448 -> 199;

449 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 449 [arrowhead = none ];
449 -> 200;

450 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
197 -> 450 [arrowhead = none ];
450 -> 201;

451 [label="INSTANCE with matching:\nT69 -> T527", fontsize=14, style = filled, fillcolor = lightgrey];
198 -> 451 [arrowhead = none , style=dashed];
451 -> 43[style=dashed];

452 [label="EVAL with clause\nbinaryZ(one(X493)) :- binary(X493).\nand substitutionX493 -> T533,\nT522 -> one(T533)", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 452 [arrowhead = none ];
452 -> 202;

453 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 453 [arrowhead = none ];
453 -> 203;

454 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
201 -> 454 [arrowhead = none ];
454 -> 204;

455 [label="INSTANCE with matching:\nT79 -> T533", fontsize=14, style = filled, fillcolor = lightgrey];
202 -> 455 [arrowhead = none , style=dashed];
455 -> 50[style=dashed];

456 [label="ONLY EVAL with clause\nadd(X503, X504, X505) :- addz(X503, X504, X505).\nand substitutionT1 -> T548,\nX503 -> T548,\nT2 -> T549,\nX504 -> T549,\nT522 -> T547,\nX505 -> T547,\nT545 -> T548,\nT546 -> T549", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 456 [arrowhead = none ];
456 -> 205;

457 [label="INSTANCE with matching:\nT114 -> T548\nT115 -> T549\nT113 -> T547", fontsize=14, style = filled, fillcolor = lightgrey];
205 -> 457 [arrowhead = none , style=dashed];
457 -> 73[style=dashed];

458 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
206 -> 458 [arrowhead = none ];
458 -> 207;

459 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
207 -> 459 [arrowhead = none ];
459 -> 208;

460 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
207 -> 460 [arrowhead = none ];
460 -> 209;

461 [label="EVAL with clause\naddz(zero(X527), zero(X528), zero(X529)) :- addz(X527, X528, X529).\nand substitutionX527 -> T576,\nT559 -> zero(T576),\nX528 -> T577,\nT560 -> zero(T577),\nX529 -> T575,\nT558 -> zero(T575),\nT573 -> T576,\nT574 -> T577", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 461 [arrowhead = none ];
461 -> 210;

462 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 462 [arrowhead = none ];
462 -> 211;

463 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
209 -> 463 [arrowhead = none ];
463 -> 212;

464 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
209 -> 464 [arrowhead = none ];
464 -> 213;

465 [label="INSTANCE with matching:\nT134 -> T576\nT135 -> T577\nT133 -> T575", fontsize=14, style = filled, fillcolor = lightgrey];
210 -> 465 [arrowhead = none , style=dashed];
465 -> 77[style=dashed];

466 [label="EVAL with clause\naddz(zero(X545), one(X546), one(X547)) :- addx(X545, X546, X547).\nand substitutionX545 -> T596,\nT559 -> zero(T596),\nX546 -> T597,\nT560 -> one(T597),\nX547 -> T595,\nT558 -> one(T595),\nT593 -> T596,\nT594 -> T597", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 466 [arrowhead = none ];
466 -> 214;

467 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
212 -> 467 [arrowhead = none ];
467 -> 215;

468 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
213 -> 468 [arrowhead = none ];
468 -> 216;

469 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
213 -> 469 [arrowhead = none ];
469 -> 217;

470 [label="INSTANCE with matching:\nT174 -> T596\nT175 -> T597\nT173 -> T595", fontsize=14, style = filled, fillcolor = lightgrey];
214 -> 470 [arrowhead = none , style=dashed];
470 -> 86[style=dashed];

471 [label="EVAL with clause\naddz(one(X561), zero(X562), one(X563)) :- addy(X561, X562, X563).\nand substitutionX561 -> T614,\nT559 -> one(T614),\nX562 -> T615,\nT560 -> zero(T615),\nX563 -> T613,\nT558 -> one(T613),\nT611 -> T614,\nT612 -> T615", fontsize=14, style = filled, fillcolor = lightblue];
216 -> 471 [arrowhead = none ];
471 -> 218;

472 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
216 -> 472 [arrowhead = none ];
472 -> 219;

473 [label="EVAL with clause\naddz(one(X571), one(X572), zero(X573)) :- addc(X571, X572, X573).\nand substitutionX571 -> T626,\nT559 -> one(T626),\nX572 -> T627,\nT560 -> one(T627),\nX573 -> T625,\nT558 -> zero(T625),\nT623 -> T626,\nT624 -> T627", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 473 [arrowhead = none ];
473 -> 220;

474 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
217 -> 474 [arrowhead = none ];
474 -> 221;

475 [label="INSTANCE with matching:\nT222 -> T614\nT223 -> T615\nT221 -> T613", fontsize=14, style = filled, fillcolor = lightgrey];
218 -> 475 [arrowhead = none , style=dashed];
475 -> 100[style=dashed];

476 [label="INSTANCE with matching:\nT264 -> T626\nT265 -> T627\nT263 -> T625", fontsize=14, style = filled, fillcolor = lightgrey];
220 -> 476 [arrowhead = none , style=dashed];
476 -> 112[style=dashed];

}

(2) Obligation:

Clauses:

binaryZA(zero(T75)) :- binaryZA(T75).
binaryZA(one(T79)) :- binaryB(T79).
binaryB(b).
binaryB(zero(T84)) :- binaryZA(T84).
binaryB(one(T88)) :- binaryB(T88).
addzC(zero(T154), zero(T155), zero(T153)) :- addzC(T154, T155, T153).
addzC(zero(T174), one(T175), one(T173)) :- addxD(T174, T175, T173).
addzC(one(T222), zero(T223), one(T221)) :- addyE(T222, T223, T221).
addzC(one(T264), one(T265), zero(T263)) :- addcF(T264, T265, T263).
succG(b, one(b)).
succG(zero(T295), one(T295)) :- binaryZA(T295).
succG(one(T303), zero(T302)) :- succG(T303, T302).
succZH(zero(T282), one(T282)) :- binaryZA(T282).
succZH(one(T290), zero(T289)) :- succG(T290, T289).
addCI(zero(T350), zero(T351), one(T349)) :- addzC(T350, T351, T349).
addCI(zero(zero(T377)), one(b), zero(one(T377))) :- binaryZA(T377).
addCI(zero(one(T389)), one(b), zero(zero(T388))) :- succG(T389, T388).
addCI(zero(T404), one(T405), zero(T403)) :- addCI(T404, T405, T403).
addCI(one(b), zero(zero(T431)), zero(one(T431))) :- binaryZA(T431).
addCI(one(b), zero(one(T443)), zero(zero(T442))) :- succG(T443, T442).
addCI(one(T458), zero(T459), zero(T457)) :- addCI(T458, T459, T457).
addCI(one(T472), one(T473), one(T471)) :- addcF(T472, T473, T471).
addcF(b, b, one(b)).
addcF(T276, b, T275) :- succZH(T276, T275).
addcF(b, T314, T313) :- succZH(T314, T313).
addcF(T330, T331, T329) :- addCI(T330, T331, T329).
addxD(one(T181), b, one(T181)) :- binaryB(T181).
addxD(zero(T186), b, zero(T186)) :- binaryZA(T186).
addxD(T202, T203, T201) :- addzC(T202, T203, T201).
addyE(b, one(T229), one(T229)) :- binaryB(T229).
addyE(b, zero(T234), zero(T234)) :- binaryZA(T234).
addyE(T250, T251, T249) :- addzC(T250, T251, T249).
addzJ(zero(T134), zero(T135), zero(T133)) :- addzC(T134, T135, T133).
addzJ(zero(T489), one(T490), one(T488)) :- addxD(T489, T490, T488).
addzJ(one(T507), zero(T508), one(T506)) :- addyE(T507, T508, T506).
addzJ(one(T519), one(T520), zero(T518)) :- addcF(T519, T520, T518).
addK(b, b, b).
addK(zero(T69), b, zero(T69)) :- binaryZA(T69).
addK(one(T93), b, one(T93)) :- binaryB(T93).
addK(b, T98, T98) :- binaryZA(T98).
addK(T114, T115, T113) :- addzJ(T114, T115, T113).
addK(b, zero(T527), zero(T527)) :- binaryZA(T527).
addK(b, one(T533), one(T533)) :- binaryB(T533).
addK(T548, T549, T547) :- addzJ(T548, T549, T547).
addK(zero(T576), zero(T577), zero(T575)) :- addzC(T576, T577, T575).
addK(zero(T596), one(T597), one(T595)) :- addxD(T596, T597, T595).
addK(one(T614), zero(T615), one(T613)) :- addyE(T614, T615, T613).
addK(one(T626), one(T627), zero(T625)) :- addcF(T626, T627, T625).

Query: addK(a,a,g)

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
addK_in: (f,f,b)
binaryZA_in: (b)
binaryB_in: (b)
addzJ_in: (f,f,b)
addzC_in: (f,f,b)
addxD_in: (f,f,b)
addyE_in: (f,f,b)
addcF_in: (f,f,b)
succZH_in: (f,b)
succG_in: (f,b)
addCI_in: (f,f,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

addK_in_aag(b, b, b) → addK_out_aag(b, b, b)
addK_in_aag(zero(T69), b, zero(T69)) → U34_aag(T69, binaryZA_in_g(T69))
binaryZA_in_g(zero(T75)) → U1_g(T75, binaryZA_in_g(T75))
binaryZA_in_g(one(T79)) → U2_g(T79, binaryB_in_g(T79))
binaryB_in_g(b) → binaryB_out_g(b)
binaryB_in_g(zero(T84)) → U3_g(T84, binaryZA_in_g(T84))
U3_g(T84, binaryZA_out_g(T84)) → binaryB_out_g(zero(T84))
binaryB_in_g(one(T88)) → U4_g(T88, binaryB_in_g(T88))
U4_g(T88, binaryB_out_g(T88)) → binaryB_out_g(one(T88))
U2_g(T79, binaryB_out_g(T79)) → binaryZA_out_g(one(T79))
U1_g(T75, binaryZA_out_g(T75)) → binaryZA_out_g(zero(T75))
U34_aag(T69, binaryZA_out_g(T69)) → addK_out_aag(zero(T69), b, zero(T69))
addK_in_aag(one(T93), b, one(T93)) → U35_aag(T93, binaryB_in_g(T93))
U35_aag(T93, binaryB_out_g(T93)) → addK_out_aag(one(T93), b, one(T93))
addK_in_aag(b, T98, T98) → U36_aag(T98, binaryZA_in_g(T98))
U36_aag(T98, binaryZA_out_g(T98)) → addK_out_aag(b, T98, T98)
addK_in_aag(T114, T115, T113) → U37_aag(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
addzJ_in_aag(zero(T134), zero(T135), zero(T133)) → U30_aag(T134, T135, T133, addzC_in_aag(T134, T135, T133))
addzC_in_aag(zero(T154), zero(T155), zero(T153)) → U5_aag(T154, T155, T153, addzC_in_aag(T154, T155, T153))
addzC_in_aag(zero(T174), one(T175), one(T173)) → U6_aag(T174, T175, T173, addxD_in_aag(T174, T175, T173))
addxD_in_aag(one(T181), b, one(T181)) → U24_aag(T181, binaryB_in_g(T181))
U24_aag(T181, binaryB_out_g(T181)) → addxD_out_aag(one(T181), b, one(T181))
addxD_in_aag(zero(T186), b, zero(T186)) → U25_aag(T186, binaryZA_in_g(T186))
U25_aag(T186, binaryZA_out_g(T186)) → addxD_out_aag(zero(T186), b, zero(T186))
addxD_in_aag(T202, T203, T201) → U26_aag(T202, T203, T201, addzC_in_aag(T202, T203, T201))
addzC_in_aag(one(T222), zero(T223), one(T221)) → U7_aag(T222, T223, T221, addyE_in_aag(T222, T223, T221))
addyE_in_aag(b, one(T229), one(T229)) → U27_aag(T229, binaryB_in_g(T229))
U27_aag(T229, binaryB_out_g(T229)) → addyE_out_aag(b, one(T229), one(T229))
addyE_in_aag(b, zero(T234), zero(T234)) → U28_aag(T234, binaryZA_in_g(T234))
U28_aag(T234, binaryZA_out_g(T234)) → addyE_out_aag(b, zero(T234), zero(T234))
addyE_in_aag(T250, T251, T249) → U29_aag(T250, T251, T249, addzC_in_aag(T250, T251, T249))
addzC_in_aag(one(T264), one(T265), zero(T263)) → U8_aag(T264, T265, T263, addcF_in_aag(T264, T265, T263))
addcF_in_aag(b, b, one(b)) → addcF_out_aag(b, b, one(b))
addcF_in_aag(T276, b, T275) → U21_aag(T276, T275, succZH_in_ag(T276, T275))
succZH_in_ag(zero(T282), one(T282)) → U11_ag(T282, binaryZA_in_g(T282))
U11_ag(T282, binaryZA_out_g(T282)) → succZH_out_ag(zero(T282), one(T282))
succZH_in_ag(one(T290), zero(T289)) → U12_ag(T290, T289, succG_in_ag(T290, T289))
succG_in_ag(b, one(b)) → succG_out_ag(b, one(b))
succG_in_ag(zero(T295), one(T295)) → U9_ag(T295, binaryZA_in_g(T295))
U9_ag(T295, binaryZA_out_g(T295)) → succG_out_ag(zero(T295), one(T295))
succG_in_ag(one(T303), zero(T302)) → U10_ag(T303, T302, succG_in_ag(T303, T302))
U10_ag(T303, T302, succG_out_ag(T303, T302)) → succG_out_ag(one(T303), zero(T302))
U12_ag(T290, T289, succG_out_ag(T290, T289)) → succZH_out_ag(one(T290), zero(T289))
U21_aag(T276, T275, succZH_out_ag(T276, T275)) → addcF_out_aag(T276, b, T275)
addcF_in_aag(b, T314, T313) → U22_aag(T314, T313, succZH_in_ag(T314, T313))
U22_aag(T314, T313, succZH_out_ag(T314, T313)) → addcF_out_aag(b, T314, T313)
addcF_in_aag(T330, T331, T329) → U23_aag(T330, T331, T329, addCI_in_aag(T330, T331, T329))
addCI_in_aag(zero(T350), zero(T351), one(T349)) → U13_aag(T350, T351, T349, addzC_in_aag(T350, T351, T349))
U13_aag(T350, T351, T349, addzC_out_aag(T350, T351, T349)) → addCI_out_aag(zero(T350), zero(T351), one(T349))
addCI_in_aag(zero(zero(T377)), one(b), zero(one(T377))) → U14_aag(T377, binaryZA_in_g(T377))
U14_aag(T377, binaryZA_out_g(T377)) → addCI_out_aag(zero(zero(T377)), one(b), zero(one(T377)))
addCI_in_aag(zero(one(T389)), one(b), zero(zero(T388))) → U15_aag(T389, T388, succG_in_ag(T389, T388))
U15_aag(T389, T388, succG_out_ag(T389, T388)) → addCI_out_aag(zero(one(T389)), one(b), zero(zero(T388)))
addCI_in_aag(zero(T404), one(T405), zero(T403)) → U16_aag(T404, T405, T403, addCI_in_aag(T404, T405, T403))
addCI_in_aag(one(b), zero(zero(T431)), zero(one(T431))) → U17_aag(T431, binaryZA_in_g(T431))
U17_aag(T431, binaryZA_out_g(T431)) → addCI_out_aag(one(b), zero(zero(T431)), zero(one(T431)))
addCI_in_aag(one(b), zero(one(T443)), zero(zero(T442))) → U18_aag(T443, T442, succG_in_ag(T443, T442))
U18_aag(T443, T442, succG_out_ag(T443, T442)) → addCI_out_aag(one(b), zero(one(T443)), zero(zero(T442)))
addCI_in_aag(one(T458), zero(T459), zero(T457)) → U19_aag(T458, T459, T457, addCI_in_aag(T458, T459, T457))
addCI_in_aag(one(T472), one(T473), one(T471)) → U20_aag(T472, T473, T471, addcF_in_aag(T472, T473, T471))
U20_aag(T472, T473, T471, addcF_out_aag(T472, T473, T471)) → addCI_out_aag(one(T472), one(T473), one(T471))
U19_aag(T458, T459, T457, addCI_out_aag(T458, T459, T457)) → addCI_out_aag(one(T458), zero(T459), zero(T457))
U16_aag(T404, T405, T403, addCI_out_aag(T404, T405, T403)) → addCI_out_aag(zero(T404), one(T405), zero(T403))
U23_aag(T330, T331, T329, addCI_out_aag(T330, T331, T329)) → addcF_out_aag(T330, T331, T329)
U8_aag(T264, T265, T263, addcF_out_aag(T264, T265, T263)) → addzC_out_aag(one(T264), one(T265), zero(T263))
U29_aag(T250, T251, T249, addzC_out_aag(T250, T251, T249)) → addyE_out_aag(T250, T251, T249)
U7_aag(T222, T223, T221, addyE_out_aag(T222, T223, T221)) → addzC_out_aag(one(T222), zero(T223), one(T221))
U26_aag(T202, T203, T201, addzC_out_aag(T202, T203, T201)) → addxD_out_aag(T202, T203, T201)
U6_aag(T174, T175, T173, addxD_out_aag(T174, T175, T173)) → addzC_out_aag(zero(T174), one(T175), one(T173))
U5_aag(T154, T155, T153, addzC_out_aag(T154, T155, T153)) → addzC_out_aag(zero(T154), zero(T155), zero(T153))
U30_aag(T134, T135, T133, addzC_out_aag(T134, T135, T133)) → addzJ_out_aag(zero(T134), zero(T135), zero(T133))
addzJ_in_aag(zero(T489), one(T490), one(T488)) → U31_aag(T489, T490, T488, addxD_in_aag(T489, T490, T488))
U31_aag(T489, T490, T488, addxD_out_aag(T489, T490, T488)) → addzJ_out_aag(zero(T489), one(T490), one(T488))
addzJ_in_aag(one(T507), zero(T508), one(T506)) → U32_aag(T507, T508, T506, addyE_in_aag(T507, T508, T506))
U32_aag(T507, T508, T506, addyE_out_aag(T507, T508, T506)) → addzJ_out_aag(one(T507), zero(T508), one(T506))
addzJ_in_aag(one(T519), one(T520), zero(T518)) → U33_aag(T519, T520, T518, addcF_in_aag(T519, T520, T518))
U33_aag(T519, T520, T518, addcF_out_aag(T519, T520, T518)) → addzJ_out_aag(one(T519), one(T520), zero(T518))
U37_aag(T114, T115, T113, addzJ_out_aag(T114, T115, T113)) → addK_out_aag(T114, T115, T113)
addK_in_aag(b, zero(T527), zero(T527)) → U38_aag(T527, binaryZA_in_g(T527))
U38_aag(T527, binaryZA_out_g(T527)) → addK_out_aag(b, zero(T527), zero(T527))
addK_in_aag(b, one(T533), one(T533)) → U39_aag(T533, binaryB_in_g(T533))
U39_aag(T533, binaryB_out_g(T533)) → addK_out_aag(b, one(T533), one(T533))
addK_in_aag(T548, T549, T547) → U40_aag(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
U40_aag(T548, T549, T547, addzJ_out_aag(T548, T549, T547)) → addK_out_aag(T548, T549, T547)
addK_in_aag(zero(T576), zero(T577), zero(T575)) → U41_aag(T576, T577, T575, addzC_in_aag(T576, T577, T575))
U41_aag(T576, T577, T575, addzC_out_aag(T576, T577, T575)) → addK_out_aag(zero(T576), zero(T577), zero(T575))
addK_in_aag(zero(T596), one(T597), one(T595)) → U42_aag(T596, T597, T595, addxD_in_aag(T596, T597, T595))
U42_aag(T596, T597, T595, addxD_out_aag(T596, T597, T595)) → addK_out_aag(zero(T596), one(T597), one(T595))
addK_in_aag(one(T614), zero(T615), one(T613)) → U43_aag(T614, T615, T613, addyE_in_aag(T614, T615, T613))
U43_aag(T614, T615, T613, addyE_out_aag(T614, T615, T613)) → addK_out_aag(one(T614), zero(T615), one(T613))
addK_in_aag(one(T626), one(T627), zero(T625)) → U44_aag(T626, T627, T625, addcF_in_aag(T626, T627, T625))
U44_aag(T626, T627, T625, addcF_out_aag(T626, T627, T625)) → addK_out_aag(one(T626), one(T627), zero(T625))

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

addK_in_aag(b, b, b) → addK_out_aag(b, b, b)
addK_in_aag(zero(T69), b, zero(T69)) → U34_aag(T69, binaryZA_in_g(T69))
binaryZA_in_g(zero(T75)) → U1_g(T75, binaryZA_in_g(T75))
binaryZA_in_g(one(T79)) → U2_g(T79, binaryB_in_g(T79))
binaryB_in_g(b) → binaryB_out_g(b)
binaryB_in_g(zero(T84)) → U3_g(T84, binaryZA_in_g(T84))
U3_g(T84, binaryZA_out_g(T84)) → binaryB_out_g(zero(T84))
binaryB_in_g(one(T88)) → U4_g(T88, binaryB_in_g(T88))
U4_g(T88, binaryB_out_g(T88)) → binaryB_out_g(one(T88))
U2_g(T79, binaryB_out_g(T79)) → binaryZA_out_g(one(T79))
U1_g(T75, binaryZA_out_g(T75)) → binaryZA_out_g(zero(T75))
U34_aag(T69, binaryZA_out_g(T69)) → addK_out_aag(zero(T69), b, zero(T69))
addK_in_aag(one(T93), b, one(T93)) → U35_aag(T93, binaryB_in_g(T93))
U35_aag(T93, binaryB_out_g(T93)) → addK_out_aag(one(T93), b, one(T93))
addK_in_aag(b, T98, T98) → U36_aag(T98, binaryZA_in_g(T98))
U36_aag(T98, binaryZA_out_g(T98)) → addK_out_aag(b, T98, T98)
addK_in_aag(T114, T115, T113) → U37_aag(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
addzJ_in_aag(zero(T134), zero(T135), zero(T133)) → U30_aag(T134, T135, T133, addzC_in_aag(T134, T135, T133))
addzC_in_aag(zero(T154), zero(T155), zero(T153)) → U5_aag(T154, T155, T153, addzC_in_aag(T154, T155, T153))
addzC_in_aag(zero(T174), one(T175), one(T173)) → U6_aag(T174, T175, T173, addxD_in_aag(T174, T175, T173))
addxD_in_aag(one(T181), b, one(T181)) → U24_aag(T181, binaryB_in_g(T181))
U24_aag(T181, binaryB_out_g(T181)) → addxD_out_aag(one(T181), b, one(T181))
addxD_in_aag(zero(T186), b, zero(T186)) → U25_aag(T186, binaryZA_in_g(T186))
U25_aag(T186, binaryZA_out_g(T186)) → addxD_out_aag(zero(T186), b, zero(T186))
addxD_in_aag(T202, T203, T201) → U26_aag(T202, T203, T201, addzC_in_aag(T202, T203, T201))
addzC_in_aag(one(T222), zero(T223), one(T221)) → U7_aag(T222, T223, T221, addyE_in_aag(T222, T223, T221))
addyE_in_aag(b, one(T229), one(T229)) → U27_aag(T229, binaryB_in_g(T229))
U27_aag(T229, binaryB_out_g(T229)) → addyE_out_aag(b, one(T229), one(T229))
addyE_in_aag(b, zero(T234), zero(T234)) → U28_aag(T234, binaryZA_in_g(T234))
U28_aag(T234, binaryZA_out_g(T234)) → addyE_out_aag(b, zero(T234), zero(T234))
addyE_in_aag(T250, T251, T249) → U29_aag(T250, T251, T249, addzC_in_aag(T250, T251, T249))
addzC_in_aag(one(T264), one(T265), zero(T263)) → U8_aag(T264, T265, T263, addcF_in_aag(T264, T265, T263))
addcF_in_aag(b, b, one(b)) → addcF_out_aag(b, b, one(b))
addcF_in_aag(T276, b, T275) → U21_aag(T276, T275, succZH_in_ag(T276, T275))
succZH_in_ag(zero(T282), one(T282)) → U11_ag(T282, binaryZA_in_g(T282))
U11_ag(T282, binaryZA_out_g(T282)) → succZH_out_ag(zero(T282), one(T282))
succZH_in_ag(one(T290), zero(T289)) → U12_ag(T290, T289, succG_in_ag(T290, T289))
succG_in_ag(b, one(b)) → succG_out_ag(b, one(b))
succG_in_ag(zero(T295), one(T295)) → U9_ag(T295, binaryZA_in_g(T295))
U9_ag(T295, binaryZA_out_g(T295)) → succG_out_ag(zero(T295), one(T295))
succG_in_ag(one(T303), zero(T302)) → U10_ag(T303, T302, succG_in_ag(T303, T302))
U10_ag(T303, T302, succG_out_ag(T303, T302)) → succG_out_ag(one(T303), zero(T302))
U12_ag(T290, T289, succG_out_ag(T290, T289)) → succZH_out_ag(one(T290), zero(T289))
U21_aag(T276, T275, succZH_out_ag(T276, T275)) → addcF_out_aag(T276, b, T275)
addcF_in_aag(b, T314, T313) → U22_aag(T314, T313, succZH_in_ag(T314, T313))
U22_aag(T314, T313, succZH_out_ag(T314, T313)) → addcF_out_aag(b, T314, T313)
addcF_in_aag(T330, T331, T329) → U23_aag(T330, T331, T329, addCI_in_aag(T330, T331, T329))
addCI_in_aag(zero(T350), zero(T351), one(T349)) → U13_aag(T350, T351, T349, addzC_in_aag(T350, T351, T349))
U13_aag(T350, T351, T349, addzC_out_aag(T350, T351, T349)) → addCI_out_aag(zero(T350), zero(T351), one(T349))
addCI_in_aag(zero(zero(T377)), one(b), zero(one(T377))) → U14_aag(T377, binaryZA_in_g(T377))
U14_aag(T377, binaryZA_out_g(T377)) → addCI_out_aag(zero(zero(T377)), one(b), zero(one(T377)))
addCI_in_aag(zero(one(T389)), one(b), zero(zero(T388))) → U15_aag(T389, T388, succG_in_ag(T389, T388))
U15_aag(T389, T388, succG_out_ag(T389, T388)) → addCI_out_aag(zero(one(T389)), one(b), zero(zero(T388)))
addCI_in_aag(zero(T404), one(T405), zero(T403)) → U16_aag(T404, T405, T403, addCI_in_aag(T404, T405, T403))
addCI_in_aag(one(b), zero(zero(T431)), zero(one(T431))) → U17_aag(T431, binaryZA_in_g(T431))
U17_aag(T431, binaryZA_out_g(T431)) → addCI_out_aag(one(b), zero(zero(T431)), zero(one(T431)))
addCI_in_aag(one(b), zero(one(T443)), zero(zero(T442))) → U18_aag(T443, T442, succG_in_ag(T443, T442))
U18_aag(T443, T442, succG_out_ag(T443, T442)) → addCI_out_aag(one(b), zero(one(T443)), zero(zero(T442)))
addCI_in_aag(one(T458), zero(T459), zero(T457)) → U19_aag(T458, T459, T457, addCI_in_aag(T458, T459, T457))
addCI_in_aag(one(T472), one(T473), one(T471)) → U20_aag(T472, T473, T471, addcF_in_aag(T472, T473, T471))
U20_aag(T472, T473, T471, addcF_out_aag(T472, T473, T471)) → addCI_out_aag(one(T472), one(T473), one(T471))
U19_aag(T458, T459, T457, addCI_out_aag(T458, T459, T457)) → addCI_out_aag(one(T458), zero(T459), zero(T457))
U16_aag(T404, T405, T403, addCI_out_aag(T404, T405, T403)) → addCI_out_aag(zero(T404), one(T405), zero(T403))
U23_aag(T330, T331, T329, addCI_out_aag(T330, T331, T329)) → addcF_out_aag(T330, T331, T329)
U8_aag(T264, T265, T263, addcF_out_aag(T264, T265, T263)) → addzC_out_aag(one(T264), one(T265), zero(T263))
U29_aag(T250, T251, T249, addzC_out_aag(T250, T251, T249)) → addyE_out_aag(T250, T251, T249)
U7_aag(T222, T223, T221, addyE_out_aag(T222, T223, T221)) → addzC_out_aag(one(T222), zero(T223), one(T221))
U26_aag(T202, T203, T201, addzC_out_aag(T202, T203, T201)) → addxD_out_aag(T202, T203, T201)
U6_aag(T174, T175, T173, addxD_out_aag(T174, T175, T173)) → addzC_out_aag(zero(T174), one(T175), one(T173))
U5_aag(T154, T155, T153, addzC_out_aag(T154, T155, T153)) → addzC_out_aag(zero(T154), zero(T155), zero(T153))
U30_aag(T134, T135, T133, addzC_out_aag(T134, T135, T133)) → addzJ_out_aag(zero(T134), zero(T135), zero(T133))
addzJ_in_aag(zero(T489), one(T490), one(T488)) → U31_aag(T489, T490, T488, addxD_in_aag(T489, T490, T488))
U31_aag(T489, T490, T488, addxD_out_aag(T489, T490, T488)) → addzJ_out_aag(zero(T489), one(T490), one(T488))
addzJ_in_aag(one(T507), zero(T508), one(T506)) → U32_aag(T507, T508, T506, addyE_in_aag(T507, T508, T506))
U32_aag(T507, T508, T506, addyE_out_aag(T507, T508, T506)) → addzJ_out_aag(one(T507), zero(T508), one(T506))
addzJ_in_aag(one(T519), one(T520), zero(T518)) → U33_aag(T519, T520, T518, addcF_in_aag(T519, T520, T518))
U33_aag(T519, T520, T518, addcF_out_aag(T519, T520, T518)) → addzJ_out_aag(one(T519), one(T520), zero(T518))
U37_aag(T114, T115, T113, addzJ_out_aag(T114, T115, T113)) → addK_out_aag(T114, T115, T113)
addK_in_aag(b, zero(T527), zero(T527)) → U38_aag(T527, binaryZA_in_g(T527))
U38_aag(T527, binaryZA_out_g(T527)) → addK_out_aag(b, zero(T527), zero(T527))
addK_in_aag(b, one(T533), one(T533)) → U39_aag(T533, binaryB_in_g(T533))
U39_aag(T533, binaryB_out_g(T533)) → addK_out_aag(b, one(T533), one(T533))
addK_in_aag(T548, T549, T547) → U40_aag(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
U40_aag(T548, T549, T547, addzJ_out_aag(T548, T549, T547)) → addK_out_aag(T548, T549, T547)
addK_in_aag(zero(T576), zero(T577), zero(T575)) → U41_aag(T576, T577, T575, addzC_in_aag(T576, T577, T575))
U41_aag(T576, T577, T575, addzC_out_aag(T576, T577, T575)) → addK_out_aag(zero(T576), zero(T577), zero(T575))
addK_in_aag(zero(T596), one(T597), one(T595)) → U42_aag(T596, T597, T595, addxD_in_aag(T596, T597, T595))
U42_aag(T596, T597, T595, addxD_out_aag(T596, T597, T595)) → addK_out_aag(zero(T596), one(T597), one(T595))
addK_in_aag(one(T614), zero(T615), one(T613)) → U43_aag(T614, T615, T613, addyE_in_aag(T614, T615, T613))
U43_aag(T614, T615, T613, addyE_out_aag(T614, T615, T613)) → addK_out_aag(one(T614), zero(T615), one(T613))
addK_in_aag(one(T626), one(T627), zero(T625)) → U44_aag(T626, T627, T625, addcF_in_aag(T626, T627, T625))
U44_aag(T626, T627, T625, addcF_out_aag(T626, T627, T625)) → addK_out_aag(one(T626), one(T627), zero(T625))

(5) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

ADDK_IN_AAG(zero(T69), b, zero(T69)) → U34_AAG(T69, binaryZA_in_g(T69))
ADDK_IN_AAG(zero(T69), b, zero(T69)) → BINARYZA_IN_G(T69)
BINARYZA_IN_G(zero(T75)) → U1_G(T75, binaryZA_in_g(T75))
BINARYZA_IN_G(zero(T75)) → BINARYZA_IN_G(T75)
BINARYZA_IN_G(one(T79)) → U2_G(T79, binaryB_in_g(T79))
BINARYZA_IN_G(one(T79)) → BINARYB_IN_G(T79)
BINARYB_IN_G(zero(T84)) → U3_G(T84, binaryZA_in_g(T84))
BINARYB_IN_G(zero(T84)) → BINARYZA_IN_G(T84)
BINARYB_IN_G(one(T88)) → U4_G(T88, binaryB_in_g(T88))
BINARYB_IN_G(one(T88)) → BINARYB_IN_G(T88)
ADDK_IN_AAG(one(T93), b, one(T93)) → U35_AAG(T93, binaryB_in_g(T93))
ADDK_IN_AAG(one(T93), b, one(T93)) → BINARYB_IN_G(T93)
ADDK_IN_AAG(b, T98, T98) → U36_AAG(T98, binaryZA_in_g(T98))
ADDK_IN_AAG(b, T98, T98) → BINARYZA_IN_G(T98)
ADDK_IN_AAG(T114, T115, T113) → U37_AAG(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
ADDK_IN_AAG(T114, T115, T113) → ADDZJ_IN_AAG(T114, T115, T113)
ADDZJ_IN_AAG(zero(T134), zero(T135), zero(T133)) → U30_AAG(T134, T135, T133, addzC_in_aag(T134, T135, T133))
ADDZJ_IN_AAG(zero(T134), zero(T135), zero(T133)) → ADDZC_IN_AAG(T134, T135, T133)
ADDZC_IN_AAG(zero(T154), zero(T155), zero(T153)) → U5_AAG(T154, T155, T153, addzC_in_aag(T154, T155, T153))
ADDZC_IN_AAG(zero(T154), zero(T155), zero(T153)) → ADDZC_IN_AAG(T154, T155, T153)
ADDZC_IN_AAG(zero(T174), one(T175), one(T173)) → U6_AAG(T174, T175, T173, addxD_in_aag(T174, T175, T173))
ADDZC_IN_AAG(zero(T174), one(T175), one(T173)) → ADDXD_IN_AAG(T174, T175, T173)
ADDXD_IN_AAG(one(T181), b, one(T181)) → U24_AAG(T181, binaryB_in_g(T181))
ADDXD_IN_AAG(one(T181), b, one(T181)) → BINARYB_IN_G(T181)
ADDXD_IN_AAG(zero(T186), b, zero(T186)) → U25_AAG(T186, binaryZA_in_g(T186))
ADDXD_IN_AAG(zero(T186), b, zero(T186)) → BINARYZA_IN_G(T186)
ADDXD_IN_AAG(T202, T203, T201) → U26_AAG(T202, T203, T201, addzC_in_aag(T202, T203, T201))
ADDXD_IN_AAG(T202, T203, T201) → ADDZC_IN_AAG(T202, T203, T201)
ADDZC_IN_AAG(one(T222), zero(T223), one(T221)) → U7_AAG(T222, T223, T221, addyE_in_aag(T222, T223, T221))
ADDZC_IN_AAG(one(T222), zero(T223), one(T221)) → ADDYE_IN_AAG(T222, T223, T221)
ADDYE_IN_AAG(b, one(T229), one(T229)) → U27_AAG(T229, binaryB_in_g(T229))
ADDYE_IN_AAG(b, one(T229), one(T229)) → BINARYB_IN_G(T229)
ADDYE_IN_AAG(b, zero(T234), zero(T234)) → U28_AAG(T234, binaryZA_in_g(T234))
ADDYE_IN_AAG(b, zero(T234), zero(T234)) → BINARYZA_IN_G(T234)
ADDYE_IN_AAG(T250, T251, T249) → U29_AAG(T250, T251, T249, addzC_in_aag(T250, T251, T249))
ADDYE_IN_AAG(T250, T251, T249) → ADDZC_IN_AAG(T250, T251, T249)
ADDZC_IN_AAG(one(T264), one(T265), zero(T263)) → U8_AAG(T264, T265, T263, addcF_in_aag(T264, T265, T263))
ADDZC_IN_AAG(one(T264), one(T265), zero(T263)) → ADDCF_IN_AAG(T264, T265, T263)
ADDCF_IN_AAG(T276, b, T275) → U21_AAG(T276, T275, succZH_in_ag(T276, T275))
ADDCF_IN_AAG(T276, b, T275) → SUCCZH_IN_AG(T276, T275)
SUCCZH_IN_AG(zero(T282), one(T282)) → U11_AG(T282, binaryZA_in_g(T282))
SUCCZH_IN_AG(zero(T282), one(T282)) → BINARYZA_IN_G(T282)
SUCCZH_IN_AG(one(T290), zero(T289)) → U12_AG(T290, T289, succG_in_ag(T290, T289))
SUCCZH_IN_AG(one(T290), zero(T289)) → SUCCG_IN_AG(T290, T289)
SUCCG_IN_AG(zero(T295), one(T295)) → U9_AG(T295, binaryZA_in_g(T295))
SUCCG_IN_AG(zero(T295), one(T295)) → BINARYZA_IN_G(T295)
SUCCG_IN_AG(one(T303), zero(T302)) → U10_AG(T303, T302, succG_in_ag(T303, T302))
SUCCG_IN_AG(one(T303), zero(T302)) → SUCCG_IN_AG(T303, T302)
ADDCF_IN_AAG(b, T314, T313) → U22_AAG(T314, T313, succZH_in_ag(T314, T313))
ADDCF_IN_AAG(b, T314, T313) → SUCCZH_IN_AG(T314, T313)
ADDCF_IN_AAG(T330, T331, T329) → U23_AAG(T330, T331, T329, addCI_in_aag(T330, T331, T329))
ADDCF_IN_AAG(T330, T331, T329) → ADDCI_IN_AAG(T330, T331, T329)
ADDCI_IN_AAG(zero(T350), zero(T351), one(T349)) → U13_AAG(T350, T351, T349, addzC_in_aag(T350, T351, T349))
ADDCI_IN_AAG(zero(T350), zero(T351), one(T349)) → ADDZC_IN_AAG(T350, T351, T349)
ADDCI_IN_AAG(zero(zero(T377)), one(b), zero(one(T377))) → U14_AAG(T377, binaryZA_in_g(T377))
ADDCI_IN_AAG(zero(zero(T377)), one(b), zero(one(T377))) → BINARYZA_IN_G(T377)
ADDCI_IN_AAG(zero(one(T389)), one(b), zero(zero(T388))) → U15_AAG(T389, T388, succG_in_ag(T389, T388))
ADDCI_IN_AAG(zero(one(T389)), one(b), zero(zero(T388))) → SUCCG_IN_AG(T389, T388)
ADDCI_IN_AAG(zero(T404), one(T405), zero(T403)) → U16_AAG(T404, T405, T403, addCI_in_aag(T404, T405, T403))
ADDCI_IN_AAG(zero(T404), one(T405), zero(T403)) → ADDCI_IN_AAG(T404, T405, T403)
ADDCI_IN_AAG(one(b), zero(zero(T431)), zero(one(T431))) → U17_AAG(T431, binaryZA_in_g(T431))
ADDCI_IN_AAG(one(b), zero(zero(T431)), zero(one(T431))) → BINARYZA_IN_G(T431)
ADDCI_IN_AAG(one(b), zero(one(T443)), zero(zero(T442))) → U18_AAG(T443, T442, succG_in_ag(T443, T442))
ADDCI_IN_AAG(one(b), zero(one(T443)), zero(zero(T442))) → SUCCG_IN_AG(T443, T442)
ADDCI_IN_AAG(one(T458), zero(T459), zero(T457)) → U19_AAG(T458, T459, T457, addCI_in_aag(T458, T459, T457))
ADDCI_IN_AAG(one(T458), zero(T459), zero(T457)) → ADDCI_IN_AAG(T458, T459, T457)
ADDCI_IN_AAG(one(T472), one(T473), one(T471)) → U20_AAG(T472, T473, T471, addcF_in_aag(T472, T473, T471))
ADDCI_IN_AAG(one(T472), one(T473), one(T471)) → ADDCF_IN_AAG(T472, T473, T471)
ADDZJ_IN_AAG(zero(T489), one(T490), one(T488)) → U31_AAG(T489, T490, T488, addxD_in_aag(T489, T490, T488))
ADDZJ_IN_AAG(zero(T489), one(T490), one(T488)) → ADDXD_IN_AAG(T489, T490, T488)
ADDZJ_IN_AAG(one(T507), zero(T508), one(T506)) → U32_AAG(T507, T508, T506, addyE_in_aag(T507, T508, T506))
ADDZJ_IN_AAG(one(T507), zero(T508), one(T506)) → ADDYE_IN_AAG(T507, T508, T506)
ADDZJ_IN_AAG(one(T519), one(T520), zero(T518)) → U33_AAG(T519, T520, T518, addcF_in_aag(T519, T520, T518))
ADDZJ_IN_AAG(one(T519), one(T520), zero(T518)) → ADDCF_IN_AAG(T519, T520, T518)
ADDK_IN_AAG(b, zero(T527), zero(T527)) → U38_AAG(T527, binaryZA_in_g(T527))
ADDK_IN_AAG(b, zero(T527), zero(T527)) → BINARYZA_IN_G(T527)
ADDK_IN_AAG(b, one(T533), one(T533)) → U39_AAG(T533, binaryB_in_g(T533))
ADDK_IN_AAG(b, one(T533), one(T533)) → BINARYB_IN_G(T533)
ADDK_IN_AAG(T548, T549, T547) → U40_AAG(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
ADDK_IN_AAG(zero(T576), zero(T577), zero(T575)) → U41_AAG(T576, T577, T575, addzC_in_aag(T576, T577, T575))
ADDK_IN_AAG(zero(T576), zero(T577), zero(T575)) → ADDZC_IN_AAG(T576, T577, T575)
ADDK_IN_AAG(zero(T596), one(T597), one(T595)) → U42_AAG(T596, T597, T595, addxD_in_aag(T596, T597, T595))
ADDK_IN_AAG(zero(T596), one(T597), one(T595)) → ADDXD_IN_AAG(T596, T597, T595)
ADDK_IN_AAG(one(T614), zero(T615), one(T613)) → U43_AAG(T614, T615, T613, addyE_in_aag(T614, T615, T613))
ADDK_IN_AAG(one(T614), zero(T615), one(T613)) → ADDYE_IN_AAG(T614, T615, T613)
ADDK_IN_AAG(one(T626), one(T627), zero(T625)) → U44_AAG(T626, T627, T625, addcF_in_aag(T626, T627, T625))
ADDK_IN_AAG(one(T626), one(T627), zero(T625)) → ADDCF_IN_AAG(T626, T627, T625)

The TRS R consists of the following rules:

addK_in_aag(b, b, b) → addK_out_aag(b, b, b)
addK_in_aag(zero(T69), b, zero(T69)) → U34_aag(T69, binaryZA_in_g(T69))
binaryZA_in_g(zero(T75)) → U1_g(T75, binaryZA_in_g(T75))
binaryZA_in_g(one(T79)) → U2_g(T79, binaryB_in_g(T79))
binaryB_in_g(b) → binaryB_out_g(b)
binaryB_in_g(zero(T84)) → U3_g(T84, binaryZA_in_g(T84))
U3_g(T84, binaryZA_out_g(T84)) → binaryB_out_g(zero(T84))
binaryB_in_g(one(T88)) → U4_g(T88, binaryB_in_g(T88))
U4_g(T88, binaryB_out_g(T88)) → binaryB_out_g(one(T88))
U2_g(T79, binaryB_out_g(T79)) → binaryZA_out_g(one(T79))
U1_g(T75, binaryZA_out_g(T75)) → binaryZA_out_g(zero(T75))
U34_aag(T69, binaryZA_out_g(T69)) → addK_out_aag(zero(T69), b, zero(T69))
addK_in_aag(one(T93), b, one(T93)) → U35_aag(T93, binaryB_in_g(T93))
U35_aag(T93, binaryB_out_g(T93)) → addK_out_aag(one(T93), b, one(T93))
addK_in_aag(b, T98, T98) → U36_aag(T98, binaryZA_in_g(T98))
U36_aag(T98, binaryZA_out_g(T98)) → addK_out_aag(b, T98, T98)
addK_in_aag(T114, T115, T113) → U37_aag(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
addzJ_in_aag(zero(T134), zero(T135), zero(T133)) → U30_aag(T134, T135, T133, addzC_in_aag(T134, T135, T133))
addzC_in_aag(zero(T154), zero(T155), zero(T153)) → U5_aag(T154, T155, T153, addzC_in_aag(T154, T155, T153))
addzC_in_aag(zero(T174), one(T175), one(T173)) → U6_aag(T174, T175, T173, addxD_in_aag(T174, T175, T173))
addxD_in_aag(one(T181), b, one(T181)) → U24_aag(T181, binaryB_in_g(T181))
U24_aag(T181, binaryB_out_g(T181)) → addxD_out_aag(one(T181), b, one(T181))
addxD_in_aag(zero(T186), b, zero(T186)) → U25_aag(T186, binaryZA_in_g(T186))
U25_aag(T186, binaryZA_out_g(T186)) → addxD_out_aag(zero(T186), b, zero(T186))
addxD_in_aag(T202, T203, T201) → U26_aag(T202, T203, T201, addzC_in_aag(T202, T203, T201))
addzC_in_aag(one(T222), zero(T223), one(T221)) → U7_aag(T222, T223, T221, addyE_in_aag(T222, T223, T221))
addyE_in_aag(b, one(T229), one(T229)) → U27_aag(T229, binaryB_in_g(T229))
U27_aag(T229, binaryB_out_g(T229)) → addyE_out_aag(b, one(T229), one(T229))
addyE_in_aag(b, zero(T234), zero(T234)) → U28_aag(T234, binaryZA_in_g(T234))
U28_aag(T234, binaryZA_out_g(T234)) → addyE_out_aag(b, zero(T234), zero(T234))
addyE_in_aag(T250, T251, T249) → U29_aag(T250, T251, T249, addzC_in_aag(T250, T251, T249))
addzC_in_aag(one(T264), one(T265), zero(T263)) → U8_aag(T264, T265, T263, addcF_in_aag(T264, T265, T263))
addcF_in_aag(b, b, one(b)) → addcF_out_aag(b, b, one(b))
addcF_in_aag(T276, b, T275) → U21_aag(T276, T275, succZH_in_ag(T276, T275))
succZH_in_ag(zero(T282), one(T282)) → U11_ag(T282, binaryZA_in_g(T282))
U11_ag(T282, binaryZA_out_g(T282)) → succZH_out_ag(zero(T282), one(T282))
succZH_in_ag(one(T290), zero(T289)) → U12_ag(T290, T289, succG_in_ag(T290, T289))
succG_in_ag(b, one(b)) → succG_out_ag(b, one(b))
succG_in_ag(zero(T295), one(T295)) → U9_ag(T295, binaryZA_in_g(T295))
U9_ag(T295, binaryZA_out_g(T295)) → succG_out_ag(zero(T295), one(T295))
succG_in_ag(one(T303), zero(T302)) → U10_ag(T303, T302, succG_in_ag(T303, T302))
U10_ag(T303, T302, succG_out_ag(T303, T302)) → succG_out_ag(one(T303), zero(T302))
U12_ag(T290, T289, succG_out_ag(T290, T289)) → succZH_out_ag(one(T290), zero(T289))
U21_aag(T276, T275, succZH_out_ag(T276, T275)) → addcF_out_aag(T276, b, T275)
addcF_in_aag(b, T314, T313) → U22_aag(T314, T313, succZH_in_ag(T314, T313))
U22_aag(T314, T313, succZH_out_ag(T314, T313)) → addcF_out_aag(b, T314, T313)
addcF_in_aag(T330, T331, T329) → U23_aag(T330, T331, T329, addCI_in_aag(T330, T331, T329))
addCI_in_aag(zero(T350), zero(T351), one(T349)) → U13_aag(T350, T351, T349, addzC_in_aag(T350, T351, T349))
U13_aag(T350, T351, T349, addzC_out_aag(T350, T351, T349)) → addCI_out_aag(zero(T350), zero(T351), one(T349))
addCI_in_aag(zero(zero(T377)), one(b), zero(one(T377))) → U14_aag(T377, binaryZA_in_g(T377))
U14_aag(T377, binaryZA_out_g(T377)) → addCI_out_aag(zero(zero(T377)), one(b), zero(one(T377)))
addCI_in_aag(zero(one(T389)), one(b), zero(zero(T388))) → U15_aag(T389, T388, succG_in_ag(T389, T388))
U15_aag(T389, T388, succG_out_ag(T389, T388)) → addCI_out_aag(zero(one(T389)), one(b), zero(zero(T388)))
addCI_in_aag(zero(T404), one(T405), zero(T403)) → U16_aag(T404, T405, T403, addCI_in_aag(T404, T405, T403))
addCI_in_aag(one(b), zero(zero(T431)), zero(one(T431))) → U17_aag(T431, binaryZA_in_g(T431))
U17_aag(T431, binaryZA_out_g(T431)) → addCI_out_aag(one(b), zero(zero(T431)), zero(one(T431)))
addCI_in_aag(one(b), zero(one(T443)), zero(zero(T442))) → U18_aag(T443, T442, succG_in_ag(T443, T442))
U18_aag(T443, T442, succG_out_ag(T443, T442)) → addCI_out_aag(one(b), zero(one(T443)), zero(zero(T442)))
addCI_in_aag(one(T458), zero(T459), zero(T457)) → U19_aag(T458, T459, T457, addCI_in_aag(T458, T459, T457))
addCI_in_aag(one(T472), one(T473), one(T471)) → U20_aag(T472, T473, T471, addcF_in_aag(T472, T473, T471))
U20_aag(T472, T473, T471, addcF_out_aag(T472, T473, T471)) → addCI_out_aag(one(T472), one(T473), one(T471))
U19_aag(T458, T459, T457, addCI_out_aag(T458, T459, T457)) → addCI_out_aag(one(T458), zero(T459), zero(T457))
U16_aag(T404, T405, T403, addCI_out_aag(T404, T405, T403)) → addCI_out_aag(zero(T404), one(T405), zero(T403))
U23_aag(T330, T331, T329, addCI_out_aag(T330, T331, T329)) → addcF_out_aag(T330, T331, T329)
U8_aag(T264, T265, T263, addcF_out_aag(T264, T265, T263)) → addzC_out_aag(one(T264), one(T265), zero(T263))
U29_aag(T250, T251, T249, addzC_out_aag(T250, T251, T249)) → addyE_out_aag(T250, T251, T249)
U7_aag(T222, T223, T221, addyE_out_aag(T222, T223, T221)) → addzC_out_aag(one(T222), zero(T223), one(T221))
U26_aag(T202, T203, T201, addzC_out_aag(T202, T203, T201)) → addxD_out_aag(T202, T203, T201)
U6_aag(T174, T175, T173, addxD_out_aag(T174, T175, T173)) → addzC_out_aag(zero(T174), one(T175), one(T173))
U5_aag(T154, T155, T153, addzC_out_aag(T154, T155, T153)) → addzC_out_aag(zero(T154), zero(T155), zero(T153))
U30_aag(T134, T135, T133, addzC_out_aag(T134, T135, T133)) → addzJ_out_aag(zero(T134), zero(T135), zero(T133))
addzJ_in_aag(zero(T489), one(T490), one(T488)) → U31_aag(T489, T490, T488, addxD_in_aag(T489, T490, T488))
U31_aag(T489, T490, T488, addxD_out_aag(T489, T490, T488)) → addzJ_out_aag(zero(T489), one(T490), one(T488))
addzJ_in_aag(one(T507), zero(T508), one(T506)) → U32_aag(T507, T508, T506, addyE_in_aag(T507, T508, T506))
U32_aag(T507, T508, T506, addyE_out_aag(T507, T508, T506)) → addzJ_out_aag(one(T507), zero(T508), one(T506))
addzJ_in_aag(one(T519), one(T520), zero(T518)) → U33_aag(T519, T520, T518, addcF_in_aag(T519, T520, T518))
U33_aag(T519, T520, T518, addcF_out_aag(T519, T520, T518)) → addzJ_out_aag(one(T519), one(T520), zero(T518))
U37_aag(T114, T115, T113, addzJ_out_aag(T114, T115, T113)) → addK_out_aag(T114, T115, T113)
addK_in_aag(b, zero(T527), zero(T527)) → U38_aag(T527, binaryZA_in_g(T527))
U38_aag(T527, binaryZA_out_g(T527)) → addK_out_aag(b, zero(T527), zero(T527))
addK_in_aag(b, one(T533), one(T533)) → U39_aag(T533, binaryB_in_g(T533))
U39_aag(T533, binaryB_out_g(T533)) → addK_out_aag(b, one(T533), one(T533))
addK_in_aag(T548, T549, T547) → U40_aag(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
U40_aag(T548, T549, T547, addzJ_out_aag(T548, T549, T547)) → addK_out_aag(T548, T549, T547)
addK_in_aag(zero(T576), zero(T577), zero(T575)) → U41_aag(T576, T577, T575, addzC_in_aag(T576, T577, T575))
U41_aag(T576, T577, T575, addzC_out_aag(T576, T577, T575)) → addK_out_aag(zero(T576), zero(T577), zero(T575))
addK_in_aag(zero(T596), one(T597), one(T595)) → U42_aag(T596, T597, T595, addxD_in_aag(T596, T597, T595))
U42_aag(T596, T597, T595, addxD_out_aag(T596, T597, T595)) → addK_out_aag(zero(T596), one(T597), one(T595))
addK_in_aag(one(T614), zero(T615), one(T613)) → U43_aag(T614, T615, T613, addyE_in_aag(T614, T615, T613))
U43_aag(T614, T615, T613, addyE_out_aag(T614, T615, T613)) → addK_out_aag(one(T614), zero(T615), one(T613))
addK_in_aag(one(T626), one(T627), zero(T625)) → U44_aag(T626, T627, T625, addcF_in_aag(T626, T627, T625))
U44_aag(T626, T627, T625, addcF_out_aag(T626, T627, T625)) → addK_out_aag(one(T626), one(T627), zero(T625))

The argument filtering Pi contains the following mapping:
addK_in_aag(x1, x2, x3) = addK_in_aag(x3)
b = b
addK_out_aag(x1, x2, x3) = addK_out_aag(x1, x2)
zero(x1) = zero(x1)
U34_aag(x1, x2) = U34_aag(x1, x2)
binaryZA_in_g(x1) = binaryZA_in_g(x1)
U1_g(x1, x2) = U1_g(x2)
one(x1) = one(x1)
U2_g(x1, x2) = U2_g(x2)
binaryB_in_g(x1) = binaryB_in_g(x1)
binaryB_out_g(x1) = binaryB_out_g
U3_g(x1, x2) = U3_g(x2)
binaryZA_out_g(x1) = binaryZA_out_g
U4_g(x1, x2) = U4_g(x2)
U35_aag(x1, x2) = U35_aag(x1, x2)
U36_aag(x1, x2) = U36_aag(x1, x2)
U37_aag(x1, x2, x3, x4) = U37_aag(x4)
addzJ_in_aag(x1, x2, x3) = addzJ_in_aag(x3)
U30_aag(x1, x2, x3, x4) = U30_aag(x4)
addzC_in_aag(x1, x2, x3) = addzC_in_aag(x3)
U5_aag(x1, x2, x3, x4) = U5_aag(x4)
U6_aag(x1, x2, x3, x4) = U6_aag(x4)
addxD_in_aag(x1, x2, x3) = addxD_in_aag(x3)
U24_aag(x1, x2) = U24_aag(x1, x2)
addxD_out_aag(x1, x2, x3) = addxD_out_aag(x1, x2)
U25_aag(x1, x2) = U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4) = U26_aag(x4)
U7_aag(x1, x2, x3, x4) = U7_aag(x4)
addyE_in_aag(x1, x2, x3) = addyE_in_aag(x3)
U27_aag(x1, x2) = U27_aag(x1, x2)
addyE_out_aag(x1, x2, x3) = addyE_out_aag(x1, x2)
U28_aag(x1, x2) = U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4) = U29_aag(x4)
U8_aag(x1, x2, x3, x4) = U8_aag(x4)
addcF_in_aag(x1, x2, x3) = addcF_in_aag(x3)
addcF_out_aag(x1, x2, x3) = addcF_out_aag(x1, x2)
U21_aag(x1, x2, x3) = U21_aag(x3)
succZH_in_ag(x1, x2) = succZH_in_ag(x2)
U11_ag(x1, x2) = U11_ag(x1, x2)
succZH_out_ag(x1, x2) = succZH_out_ag(x1)
U12_ag(x1, x2, x3) = U12_ag(x3)
succG_in_ag(x1, x2) = succG_in_ag(x2)
succG_out_ag(x1, x2) = succG_out_ag(x1)
U9_ag(x1, x2) = U9_ag(x1, x2)
U10_ag(x1, x2, x3) = U10_ag(x3)
U22_aag(x1, x2, x3) = U22_aag(x3)
U23_aag(x1, x2, x3, x4) = U23_aag(x4)
addCI_in_aag(x1, x2, x3) = addCI_in_aag(x3)
U13_aag(x1, x2, x3, x4) = U13_aag(x4)
addzC_out_aag(x1, x2, x3) = addzC_out_aag(x1, x2)
addCI_out_aag(x1, x2, x3) = addCI_out_aag(x1, x2)
U14_aag(x1, x2) = U14_aag(x1, x2)
U15_aag(x1, x2, x3) = U15_aag(x3)
U16_aag(x1, x2, x3, x4) = U16_aag(x4)
U17_aag(x1, x2) = U17_aag(x1, x2)
U18_aag(x1, x2, x3) = U18_aag(x3)
U19_aag(x1, x2, x3, x4) = U19_aag(x4)
U20_aag(x1, x2, x3, x4) = U20_aag(x4)
addzJ_out_aag(x1, x2, x3) = addzJ_out_aag(x1, x2)
U31_aag(x1, x2, x3, x4) = U31_aag(x4)
U32_aag(x1, x2, x3, x4) = U32_aag(x4)
U33_aag(x1, x2, x3, x4) = U33_aag(x4)
U38_aag(x1, x2) = U38_aag(x1, x2)
U39_aag(x1, x2) = U39_aag(x1, x2)
U40_aag(x1, x2, x3, x4) = U40_aag(x4)
U41_aag(x1, x2, x3, x4) = U41_aag(x4)
U42_aag(x1, x2, x3, x4) = U42_aag(x4)
U43_aag(x1, x2, x3, x4) = U43_aag(x4)
U44_aag(x1, x2, x3, x4) = U44_aag(x4)
ADDK_IN_AAG(x1, x2, x3) = ADDK_IN_AAG(x3)
U34_AAG(x1, x2) = U34_AAG(x1, x2)
BINARYZA_IN_G(x1) = BINARYZA_IN_G(x1)
U1_G(x1, x2) = U1_G(x2)
U2_G(x1, x2) = U2_G(x2)
BINARYB_IN_G(x1) = BINARYB_IN_G(x1)
U3_G(x1, x2) = U3_G(x2)
U4_G(x1, x2) = U4_G(x2)
U35_AAG(x1, x2) = U35_AAG(x1, x2)
U36_AAG(x1, x2) = U36_AAG(x1, x2)
U37_AAG(x1, x2, x3, x4) = U37_AAG(x4)
ADDZJ_IN_AAG(x1, x2, x3) = ADDZJ_IN_AAG(x3)
U30_AAG(x1, x2, x3, x4) = U30_AAG(x4)
ADDZC_IN_AAG(x1, x2, x3) = ADDZC_IN_AAG(x3)
U5_AAG(x1, x2, x3, x4) = U5_AAG(x4)
U6_AAG(x1, x2, x3, x4) = U6_AAG(x4)
ADDXD_IN_AAG(x1, x2, x3) = ADDXD_IN_AAG(x3)
U24_AAG(x1, x2) = U24_AAG(x1, x2)
U25_AAG(x1, x2) = U25_AAG(x1, x2)
U26_AAG(x1, x2, x3, x4) = U26_AAG(x4)
U7_AAG(x1, x2, x3, x4) = U7_AAG(x4)
ADDYE_IN_AAG(x1, x2, x3) = ADDYE_IN_AAG(x3)
U27_AAG(x1, x2) = U27_AAG(x1, x2)
U28_AAG(x1, x2) = U28_AAG(x1, x2)
U29_AAG(x1, x2, x3, x4) = U29_AAG(x4)
U8_AAG(x1, x2, x3, x4) = U8_AAG(x4)
ADDCF_IN_AAG(x1, x2, x3) = ADDCF_IN_AAG(x3)
U21_AAG(x1, x2, x3) = U21_AAG(x3)
SUCCZH_IN_AG(x1, x2) = SUCCZH_IN_AG(x2)
U11_AG(x1, x2) = U11_AG(x1, x2)
U12_AG(x1, x2, x3) = U12_AG(x3)
SUCCG_IN_AG(x1, x2) = SUCCG_IN_AG(x2)
U9_AG(x1, x2) = U9_AG(x1, x2)
U10_AG(x1, x2, x3) = U10_AG(x3)
U22_AAG(x1, x2, x3) = U22_AAG(x3)
U23_AAG(x1, x2, x3, x4) = U23_AAG(x4)
ADDCI_IN_AAG(x1, x2, x3) = ADDCI_IN_AAG(x3)
U13_AAG(x1, x2, x3, x4) = U13_AAG(x4)
U14_AAG(x1, x2) = U14_AAG(x1, x2)
U15_AAG(x1, x2, x3) = U15_AAG(x3)
U16_AAG(x1, x2, x3, x4) = U16_AAG(x4)
U17_AAG(x1, x2) = U17_AAG(x1, x2)
U18_AAG(x1, x2, x3) = U18_AAG(x3)
U19_AAG(x1, x2, x3, x4) = U19_AAG(x4)
U20_AAG(x1, x2, x3, x4) = U20_AAG(x4)
U31_AAG(x1, x2, x3, x4) = U31_AAG(x4)
U32_AAG(x1, x2, x3, x4) = U32_AAG(x4)
U33_AAG(x1, x2, x3, x4) = U33_AAG(x4)
U38_AAG(x1, x2) = U38_AAG(x1, x2)
U39_AAG(x1, x2) = U39_AAG(x1, x2)
U40_AAG(x1, x2, x3, x4) = U40_AAG(x4)
U41_AAG(x1, x2, x3, x4) = U41_AAG(x4)
U42_AAG(x1, x2, x3, x4) = U42_AAG(x4)
U43_AAG(x1, x2, x3, x4) = U43_AAG(x4)
U44_AAG(x1, x2, x3, x4) = U44_AAG(x4)

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

(6) Obligation:

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

ADDK_IN_AAG(zero(T69), b, zero(T69)) → U34_AAG(T69, binaryZA_in_g(T69))
ADDK_IN_AAG(zero(T69), b, zero(T69)) → BINARYZA_IN_G(T69)
BINARYZA_IN_G(zero(T75)) → U1_G(T75, binaryZA_in_g(T75))
BINARYZA_IN_G(zero(T75)) → BINARYZA_IN_G(T75)
BINARYZA_IN_G(one(T79)) → U2_G(T79, binaryB_in_g(T79))
BINARYZA_IN_G(one(T79)) → BINARYB_IN_G(T79)
BINARYB_IN_G(zero(T84)) → U3_G(T84, binaryZA_in_g(T84))
BINARYB_IN_G(zero(T84)) → BINARYZA_IN_G(T84)
BINARYB_IN_G(one(T88)) → U4_G(T88, binaryB_in_g(T88))
BINARYB_IN_G(one(T88)) → BINARYB_IN_G(T88)
ADDK_IN_AAG(one(T93), b, one(T93)) → U35_AAG(T93, binaryB_in_g(T93))
ADDK_IN_AAG(one(T93), b, one(T93)) → BINARYB_IN_G(T93)
ADDK_IN_AAG(b, T98, T98) → U36_AAG(T98, binaryZA_in_g(T98))
ADDK_IN_AAG(b, T98, T98) → BINARYZA_IN_G(T98)
ADDK_IN_AAG(T114, T115, T113) → U37_AAG(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
ADDK_IN_AAG(T114, T115, T113) → ADDZJ_IN_AAG(T114, T115, T113)
ADDZJ_IN_AAG(zero(T134), zero(T135), zero(T133)) → U30_AAG(T134, T135, T133, addzC_in_aag(T134, T135, T133))
ADDZJ_IN_AAG(zero(T134), zero(T135), zero(T133)) → ADDZC_IN_AAG(T134, T135, T133)
ADDZC_IN_AAG(zero(T154), zero(T155), zero(T153)) → U5_AAG(T154, T155, T153, addzC_in_aag(T154, T155, T153))
ADDZC_IN_AAG(zero(T154), zero(T155), zero(T153)) → ADDZC_IN_AAG(T154, T155, T153)
ADDZC_IN_AAG(zero(T174), one(T175), one(T173)) → U6_AAG(T174, T175, T173, addxD_in_aag(T174, T175, T173))
ADDZC_IN_AAG(zero(T174), one(T175), one(T173)) → ADDXD_IN_AAG(T174, T175, T173)
ADDXD_IN_AAG(one(T181), b, one(T181)) → U24_AAG(T181, binaryB_in_g(T181))
ADDXD_IN_AAG(one(T181), b, one(T181)) → BINARYB_IN_G(T181)
ADDXD_IN_AAG(zero(T186), b, zero(T186)) → U25_AAG(T186, binaryZA_in_g(T186))
ADDXD_IN_AAG(zero(T186), b, zero(T186)) → BINARYZA_IN_G(T186)
ADDXD_IN_AAG(T202, T203, T201) → U26_AAG(T202, T203, T201, addzC_in_aag(T202, T203, T201))
ADDXD_IN_AAG(T202, T203, T201) → ADDZC_IN_AAG(T202, T203, T201)
ADDZC_IN_AAG(one(T222), zero(T223), one(T221)) → U7_AAG(T222, T223, T221, addyE_in_aag(T222, T223, T221))
ADDZC_IN_AAG(one(T222), zero(T223), one(T221)) → ADDYE_IN_AAG(T222, T223, T221)
ADDYE_IN_AAG(b, one(T229), one(T229)) → U27_AAG(T229, binaryB_in_g(T229))
ADDYE_IN_AAG(b, one(T229), one(T229)) → BINARYB_IN_G(T229)
ADDYE_IN_AAG(b, zero(T234), zero(T234)) → U28_AAG(T234, binaryZA_in_g(T234))
ADDYE_IN_AAG(b, zero(T234), zero(T234)) → BINARYZA_IN_G(T234)
ADDYE_IN_AAG(T250, T251, T249) → U29_AAG(T250, T251, T249, addzC_in_aag(T250, T251, T249))
ADDYE_IN_AAG(T250, T251, T249) → ADDZC_IN_AAG(T250, T251, T249)
ADDZC_IN_AAG(one(T264), one(T265), zero(T263)) → U8_AAG(T264, T265, T263, addcF_in_aag(T264, T265, T263))
ADDZC_IN_AAG(one(T264), one(T265), zero(T263)) → ADDCF_IN_AAG(T264, T265, T263)
ADDCF_IN_AAG(T276, b, T275) → U21_AAG(T276, T275, succZH_in_ag(T276, T275))
ADDCF_IN_AAG(T276, b, T275) → SUCCZH_IN_AG(T276, T275)
SUCCZH_IN_AG(zero(T282), one(T282)) → U11_AG(T282, binaryZA_in_g(T282))
SUCCZH_IN_AG(zero(T282), one(T282)) → BINARYZA_IN_G(T282)
SUCCZH_IN_AG(one(T290), zero(T289)) → U12_AG(T290, T289, succG_in_ag(T290, T289))
SUCCZH_IN_AG(one(T290), zero(T289)) → SUCCG_IN_AG(T290, T289)
SUCCG_IN_AG(zero(T295), one(T295)) → U9_AG(T295, binaryZA_in_g(T295))
SUCCG_IN_AG(zero(T295), one(T295)) → BINARYZA_IN_G(T295)
SUCCG_IN_AG(one(T303), zero(T302)) → U10_AG(T303, T302, succG_in_ag(T303, T302))
SUCCG_IN_AG(one(T303), zero(T302)) → SUCCG_IN_AG(T303, T302)
ADDCF_IN_AAG(b, T314, T313) → U22_AAG(T314, T313, succZH_in_ag(T314, T313))
ADDCF_IN_AAG(b, T314, T313) → SUCCZH_IN_AG(T314, T313)
ADDCF_IN_AAG(T330, T331, T329) → U23_AAG(T330, T331, T329, addCI_in_aag(T330, T331, T329))
ADDCF_IN_AAG(T330, T331, T329) → ADDCI_IN_AAG(T330, T331, T329)
ADDCI_IN_AAG(zero(T350), zero(T351), one(T349)) → U13_AAG(T350, T351, T349, addzC_in_aag(T350, T351, T349))
ADDCI_IN_AAG(zero(T350), zero(T351), one(T349)) → ADDZC_IN_AAG(T350, T351, T349)
ADDCI_IN_AAG(zero(zero(T377)), one(b), zero(one(T377))) → U14_AAG(T377, binaryZA_in_g(T377))
ADDCI_IN_AAG(zero(zero(T377)), one(b), zero(one(T377))) → BINARYZA_IN_G(T377)
ADDCI_IN_AAG(zero(one(T389)), one(b), zero(zero(T388))) → U15_AAG(T389, T388, succG_in_ag(T389, T388))
ADDCI_IN_AAG(zero(one(T389)), one(b), zero(zero(T388))) → SUCCG_IN_AG(T389, T388)
ADDCI_IN_AAG(zero(T404), one(T405), zero(T403)) → U16_AAG(T404, T405, T403, addCI_in_aag(T404, T405, T403))
ADDCI_IN_AAG(zero(T404), one(T405), zero(T403)) → ADDCI_IN_AAG(T404, T405, T403)
ADDCI_IN_AAG(one(b), zero(zero(T431)), zero(one(T431))) → U17_AAG(T431, binaryZA_in_g(T431))
ADDCI_IN_AAG(one(b), zero(zero(T431)), zero(one(T431))) → BINARYZA_IN_G(T431)
ADDCI_IN_AAG(one(b), zero(one(T443)), zero(zero(T442))) → U18_AAG(T443, T442, succG_in_ag(T443, T442))
ADDCI_IN_AAG(one(b), zero(one(T443)), zero(zero(T442))) → SUCCG_IN_AG(T443, T442)
ADDCI_IN_AAG(one(T458), zero(T459), zero(T457)) → U19_AAG(T458, T459, T457, addCI_in_aag(T458, T459, T457))
ADDCI_IN_AAG(one(T458), zero(T459), zero(T457)) → ADDCI_IN_AAG(T458, T459, T457)
ADDCI_IN_AAG(one(T472), one(T473), one(T471)) → U20_AAG(T472, T473, T471, addcF_in_aag(T472, T473, T471))
ADDCI_IN_AAG(one(T472), one(T473), one(T471)) → ADDCF_IN_AAG(T472, T473, T471)
ADDZJ_IN_AAG(zero(T489), one(T490), one(T488)) → U31_AAG(T489, T490, T488, addxD_in_aag(T489, T490, T488))
ADDZJ_IN_AAG(zero(T489), one(T490), one(T488)) → ADDXD_IN_AAG(T489, T490, T488)
ADDZJ_IN_AAG(one(T507), zero(T508), one(T506)) → U32_AAG(T507, T508, T506, addyE_in_aag(T507, T508, T506))
ADDZJ_IN_AAG(one(T507), zero(T508), one(T506)) → ADDYE_IN_AAG(T507, T508, T506)
ADDZJ_IN_AAG(one(T519), one(T520), zero(T518)) → U33_AAG(T519, T520, T518, addcF_in_aag(T519, T520, T518))
ADDZJ_IN_AAG(one(T519), one(T520), zero(T518)) → ADDCF_IN_AAG(T519, T520, T518)
ADDK_IN_AAG(b, zero(T527), zero(T527)) → U38_AAG(T527, binaryZA_in_g(T527))
ADDK_IN_AAG(b, zero(T527), zero(T527)) → BINARYZA_IN_G(T527)
ADDK_IN_AAG(b, one(T533), one(T533)) → U39_AAG(T533, binaryB_in_g(T533))
ADDK_IN_AAG(b, one(T533), one(T533)) → BINARYB_IN_G(T533)
ADDK_IN_AAG(T548, T549, T547) → U40_AAG(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
ADDK_IN_AAG(zero(T576), zero(T577), zero(T575)) → U41_AAG(T576, T577, T575, addzC_in_aag(T576, T577, T575))
ADDK_IN_AAG(zero(T576), zero(T577), zero(T575)) → ADDZC_IN_AAG(T576, T577, T575)
ADDK_IN_AAG(zero(T596), one(T597), one(T595)) → U42_AAG(T596, T597, T595, addxD_in_aag(T596, T597, T595))
ADDK_IN_AAG(zero(T596), one(T597), one(T595)) → ADDXD_IN_AAG(T596, T597, T595)
ADDK_IN_AAG(one(T614), zero(T615), one(T613)) → U43_AAG(T614, T615, T613, addyE_in_aag(T614, T615, T613))
ADDK_IN_AAG(one(T614), zero(T615), one(T613)) → ADDYE_IN_AAG(T614, T615, T613)
ADDK_IN_AAG(one(T626), one(T627), zero(T625)) → U44_AAG(T626, T627, T625, addcF_in_aag(T626, T627, T625))
ADDK_IN_AAG(one(T626), one(T627), zero(T625)) → ADDCF_IN_AAG(T626, T627, T625)

The TRS R consists of the following rules:

addK_in_aag(b, b, b) → addK_out_aag(b, b, b)
addK_in_aag(zero(T69), b, zero(T69)) → U34_aag(T69, binaryZA_in_g(T69))
binaryZA_in_g(zero(T75)) → U1_g(T75, binaryZA_in_g(T75))
binaryZA_in_g(one(T79)) → U2_g(T79, binaryB_in_g(T79))
binaryB_in_g(b) → binaryB_out_g(b)
binaryB_in_g(zero(T84)) → U3_g(T84, binaryZA_in_g(T84))
U3_g(T84, binaryZA_out_g(T84)) → binaryB_out_g(zero(T84))
binaryB_in_g(one(T88)) → U4_g(T88, binaryB_in_g(T88))
U4_g(T88, binaryB_out_g(T88)) → binaryB_out_g(one(T88))
U2_g(T79, binaryB_out_g(T79)) → binaryZA_out_g(one(T79))
U1_g(T75, binaryZA_out_g(T75)) → binaryZA_out_g(zero(T75))
U34_aag(T69, binaryZA_out_g(T69)) → addK_out_aag(zero(T69), b, zero(T69))
addK_in_aag(one(T93), b, one(T93)) → U35_aag(T93, binaryB_in_g(T93))
U35_aag(T93, binaryB_out_g(T93)) → addK_out_aag(one(T93), b, one(T93))
addK_in_aag(b, T98, T98) → U36_aag(T98, binaryZA_in_g(T98))
U36_aag(T98, binaryZA_out_g(T98)) → addK_out_aag(b, T98, T98)
addK_in_aag(T114, T115, T113) → U37_aag(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
addzJ_in_aag(zero(T134), zero(T135), zero(T133)) → U30_aag(T134, T135, T133, addzC_in_aag(T134, T135, T133))
addzC_in_aag(zero(T154), zero(T155), zero(T153)) → U5_aag(T154, T155, T153, addzC_in_aag(T154, T155, T153))
addzC_in_aag(zero(T174), one(T175), one(T173)) → U6_aag(T174, T175, T173, addxD_in_aag(T174, T175, T173))
addxD_in_aag(one(T181), b, one(T181)) → U24_aag(T181, binaryB_in_g(T181))
U24_aag(T181, binaryB_out_g(T181)) → addxD_out_aag(one(T181), b, one(T181))
addxD_in_aag(zero(T186), b, zero(T186)) → U25_aag(T186, binaryZA_in_g(T186))
U25_aag(T186, binaryZA_out_g(T186)) → addxD_out_aag(zero(T186), b, zero(T186))
addxD_in_aag(T202, T203, T201) → U26_aag(T202, T203, T201, addzC_in_aag(T202, T203, T201))
addzC_in_aag(one(T222), zero(T223), one(T221)) → U7_aag(T222, T223, T221, addyE_in_aag(T222, T223, T221))
addyE_in_aag(b, one(T229), one(T229)) → U27_aag(T229, binaryB_in_g(T229))
U27_aag(T229, binaryB_out_g(T229)) → addyE_out_aag(b, one(T229), one(T229))
addyE_in_aag(b, zero(T234), zero(T234)) → U28_aag(T234, binaryZA_in_g(T234))
U28_aag(T234, binaryZA_out_g(T234)) → addyE_out_aag(b, zero(T234), zero(T234))
addyE_in_aag(T250, T251, T249) → U29_aag(T250, T251, T249, addzC_in_aag(T250, T251, T249))
addzC_in_aag(one(T264), one(T265), zero(T263)) → U8_aag(T264, T265, T263, addcF_in_aag(T264, T265, T263))
addcF_in_aag(b, b, one(b)) → addcF_out_aag(b, b, one(b))
addcF_in_aag(T276, b, T275) → U21_aag(T276, T275, succZH_in_ag(T276, T275))
succZH_in_ag(zero(T282), one(T282)) → U11_ag(T282, binaryZA_in_g(T282))
U11_ag(T282, binaryZA_out_g(T282)) → succZH_out_ag(zero(T282), one(T282))
succZH_in_ag(one(T290), zero(T289)) → U12_ag(T290, T289, succG_in_ag(T290, T289))
succG_in_ag(b, one(b)) → succG_out_ag(b, one(b))
succG_in_ag(zero(T295), one(T295)) → U9_ag(T295, binaryZA_in_g(T295))
U9_ag(T295, binaryZA_out_g(T295)) → succG_out_ag(zero(T295), one(T295))
succG_in_ag(one(T303), zero(T302)) → U10_ag(T303, T302, succG_in_ag(T303, T302))
U10_ag(T303, T302, succG_out_ag(T303, T302)) → succG_out_ag(one(T303), zero(T302))
U12_ag(T290, T289, succG_out_ag(T290, T289)) → succZH_out_ag(one(T290), zero(T289))
U21_aag(T276, T275, succZH_out_ag(T276, T275)) → addcF_out_aag(T276, b, T275)
addcF_in_aag(b, T314, T313) → U22_aag(T314, T313, succZH_in_ag(T314, T313))
U22_aag(T314, T313, succZH_out_ag(T314, T313)) → addcF_out_aag(b, T314, T313)
addcF_in_aag(T330, T331, T329) → U23_aag(T330, T331, T329, addCI_in_aag(T330, T331, T329))
addCI_in_aag(zero(T350), zero(T351), one(T349)) → U13_aag(T350, T351, T349, addzC_in_aag(T350, T351, T349))
U13_aag(T350, T351, T349, addzC_out_aag(T350, T351, T349)) → addCI_out_aag(zero(T350), zero(T351), one(T349))
addCI_in_aag(zero(zero(T377)), one(b), zero(one(T377))) → U14_aag(T377, binaryZA_in_g(T377))
U14_aag(T377, binaryZA_out_g(T377)) → addCI_out_aag(zero(zero(T377)), one(b), zero(one(T377)))
addCI_in_aag(zero(one(T389)), one(b), zero(zero(T388))) → U15_aag(T389, T388, succG_in_ag(T389, T388))
U15_aag(T389, T388, succG_out_ag(T389, T388)) → addCI_out_aag(zero(one(T389)), one(b), zero(zero(T388)))
addCI_in_aag(zero(T404), one(T405), zero(T403)) → U16_aag(T404, T405, T403, addCI_in_aag(T404, T405, T403))
addCI_in_aag(one(b), zero(zero(T431)), zero(one(T431))) → U17_aag(T431, binaryZA_in_g(T431))
U17_aag(T431, binaryZA_out_g(T431)) → addCI_out_aag(one(b), zero(zero(T431)), zero(one(T431)))
addCI_in_aag(one(b), zero(one(T443)), zero(zero(T442))) → U18_aag(T443, T442, succG_in_ag(T443, T442))
U18_aag(T443, T442, succG_out_ag(T443, T442)) → addCI_out_aag(one(b), zero(one(T443)), zero(zero(T442)))
addCI_in_aag(one(T458), zero(T459), zero(T457)) → U19_aag(T458, T459, T457, addCI_in_aag(T458, T459, T457))
addCI_in_aag(one(T472), one(T473), one(T471)) → U20_aag(T472, T473, T471, addcF_in_aag(T472, T473, T471))
U20_aag(T472, T473, T471, addcF_out_aag(T472, T473, T471)) → addCI_out_aag(one(T472), one(T473), one(T471))
U19_aag(T458, T459, T457, addCI_out_aag(T458, T459, T457)) → addCI_out_aag(one(T458), zero(T459), zero(T457))
U16_aag(T404, T405, T403, addCI_out_aag(T404, T405, T403)) → addCI_out_aag(zero(T404), one(T405), zero(T403))
U23_aag(T330, T331, T329, addCI_out_aag(T330, T331, T329)) → addcF_out_aag(T330, T331, T329)
U8_aag(T264, T265, T263, addcF_out_aag(T264, T265, T263)) → addzC_out_aag(one(T264), one(T265), zero(T263))
U29_aag(T250, T251, T249, addzC_out_aag(T250, T251, T249)) → addyE_out_aag(T250, T251, T249)
U7_aag(T222, T223, T221, addyE_out_aag(T222, T223, T221)) → addzC_out_aag(one(T222), zero(T223), one(T221))
U26_aag(T202, T203, T201, addzC_out_aag(T202, T203, T201)) → addxD_out_aag(T202, T203, T201)
U6_aag(T174, T175, T173, addxD_out_aag(T174, T175, T173)) → addzC_out_aag(zero(T174), one(T175), one(T173))
U5_aag(T154, T155, T153, addzC_out_aag(T154, T155, T153)) → addzC_out_aag(zero(T154), zero(T155), zero(T153))
U30_aag(T134, T135, T133, addzC_out_aag(T134, T135, T133)) → addzJ_out_aag(zero(T134), zero(T135), zero(T133))
addzJ_in_aag(zero(T489), one(T490), one(T488)) → U31_aag(T489, T490, T488, addxD_in_aag(T489, T490, T488))
U31_aag(T489, T490, T488, addxD_out_aag(T489, T490, T488)) → addzJ_out_aag(zero(T489), one(T490), one(T488))
addzJ_in_aag(one(T507), zero(T508), one(T506)) → U32_aag(T507, T508, T506, addyE_in_aag(T507, T508, T506))
U32_aag(T507, T508, T506, addyE_out_aag(T507, T508, T506)) → addzJ_out_aag(one(T507), zero(T508), one(T506))
addzJ_in_aag(one(T519), one(T520), zero(T518)) → U33_aag(T519, T520, T518, addcF_in_aag(T519, T520, T518))
U33_aag(T519, T520, T518, addcF_out_aag(T519, T520, T518)) → addzJ_out_aag(one(T519), one(T520), zero(T518))
U37_aag(T114, T115, T113, addzJ_out_aag(T114, T115, T113)) → addK_out_aag(T114, T115, T113)
addK_in_aag(b, zero(T527), zero(T527)) → U38_aag(T527, binaryZA_in_g(T527))
U38_aag(T527, binaryZA_out_g(T527)) → addK_out_aag(b, zero(T527), zero(T527))
addK_in_aag(b, one(T533), one(T533)) → U39_aag(T533, binaryB_in_g(T533))
U39_aag(T533, binaryB_out_g(T533)) → addK_out_aag(b, one(T533), one(T533))
addK_in_aag(T548, T549, T547) → U40_aag(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
U40_aag(T548, T549, T547, addzJ_out_aag(T548, T549, T547)) → addK_out_aag(T548, T549, T547)
addK_in_aag(zero(T576), zero(T577), zero(T575)) → U41_aag(T576, T577, T575, addzC_in_aag(T576, T577, T575))
U41_aag(T576, T577, T575, addzC_out_aag(T576, T577, T575)) → addK_out_aag(zero(T576), zero(T577), zero(T575))
addK_in_aag(zero(T596), one(T597), one(T595)) → U42_aag(T596, T597, T595, addxD_in_aag(T596, T597, T595))
U42_aag(T596, T597, T595, addxD_out_aag(T596, T597, T595)) → addK_out_aag(zero(T596), one(T597), one(T595))
addK_in_aag(one(T614), zero(T615), one(T613)) → U43_aag(T614, T615, T613, addyE_in_aag(T614, T615, T613))
U43_aag(T614, T615, T613, addyE_out_aag(T614, T615, T613)) → addK_out_aag(one(T614), zero(T615), one(T613))
addK_in_aag(one(T626), one(T627), zero(T625)) → U44_aag(T626, T627, T625, addcF_in_aag(T626, T627, T625))
U44_aag(T626, T627, T625, addcF_out_aag(T626, T627, T625)) → addK_out_aag(one(T626), one(T627), zero(T625))

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 71 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

BINARYZA_IN_G(one(T79)) → BINARYB_IN_G(T79)
BINARYB_IN_G(zero(T84)) → BINARYZA_IN_G(T84)
BINARYZA_IN_G(zero(T75)) → BINARYZA_IN_G(T75)
BINARYB_IN_G(one(T88)) → BINARYB_IN_G(T88)

The TRS R consists of the following rules:

addK_in_aag(b, b, b) → addK_out_aag(b, b, b)
addK_in_aag(zero(T69), b, zero(T69)) → U34_aag(T69, binaryZA_in_g(T69))
binaryZA_in_g(zero(T75)) → U1_g(T75, binaryZA_in_g(T75))
binaryZA_in_g(one(T79)) → U2_g(T79, binaryB_in_g(T79))
binaryB_in_g(b) → binaryB_out_g(b)
binaryB_in_g(zero(T84)) → U3_g(T84, binaryZA_in_g(T84))
U3_g(T84, binaryZA_out_g(T84)) → binaryB_out_g(zero(T84))
binaryB_in_g(one(T88)) → U4_g(T88, binaryB_in_g(T88))
U4_g(T88, binaryB_out_g(T88)) → binaryB_out_g(one(T88))
U2_g(T79, binaryB_out_g(T79)) → binaryZA_out_g(one(T79))
U1_g(T75, binaryZA_out_g(T75)) → binaryZA_out_g(zero(T75))
U34_aag(T69, binaryZA_out_g(T69)) → addK_out_aag(zero(T69), b, zero(T69))
addK_in_aag(one(T93), b, one(T93)) → U35_aag(T93, binaryB_in_g(T93))
U35_aag(T93, binaryB_out_g(T93)) → addK_out_aag(one(T93), b, one(T93))
addK_in_aag(b, T98, T98) → U36_aag(T98, binaryZA_in_g(T98))
U36_aag(T98, binaryZA_out_g(T98)) → addK_out_aag(b, T98, T98)
addK_in_aag(T114, T115, T113) → U37_aag(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
addzJ_in_aag(zero(T134), zero(T135), zero(T133)) → U30_aag(T134, T135, T133, addzC_in_aag(T134, T135, T133))
addzC_in_aag(zero(T154), zero(T155), zero(T153)) → U5_aag(T154, T155, T153, addzC_in_aag(T154, T155, T153))
addzC_in_aag(zero(T174), one(T175), one(T173)) → U6_aag(T174, T175, T173, addxD_in_aag(T174, T175, T173))
addxD_in_aag(one(T181), b, one(T181)) → U24_aag(T181, binaryB_in_g(T181))
U24_aag(T181, binaryB_out_g(T181)) → addxD_out_aag(one(T181), b, one(T181))
addxD_in_aag(zero(T186), b, zero(T186)) → U25_aag(T186, binaryZA_in_g(T186))
U25_aag(T186, binaryZA_out_g(T186)) → addxD_out_aag(zero(T186), b, zero(T186))
addxD_in_aag(T202, T203, T201) → U26_aag(T202, T203, T201, addzC_in_aag(T202, T203, T201))
addzC_in_aag(one(T222), zero(T223), one(T221)) → U7_aag(T222, T223, T221, addyE_in_aag(T222, T223, T221))
addyE_in_aag(b, one(T229), one(T229)) → U27_aag(T229, binaryB_in_g(T229))
U27_aag(T229, binaryB_out_g(T229)) → addyE_out_aag(b, one(T229), one(T229))
addyE_in_aag(b, zero(T234), zero(T234)) → U28_aag(T234, binaryZA_in_g(T234))
U28_aag(T234, binaryZA_out_g(T234)) → addyE_out_aag(b, zero(T234), zero(T234))
addyE_in_aag(T250, T251, T249) → U29_aag(T250, T251, T249, addzC_in_aag(T250, T251, T249))
addzC_in_aag(one(T264), one(T265), zero(T263)) → U8_aag(T264, T265, T263, addcF_in_aag(T264, T265, T263))
addcF_in_aag(b, b, one(b)) → addcF_out_aag(b, b, one(b))
addcF_in_aag(T276, b, T275) → U21_aag(T276, T275, succZH_in_ag(T276, T275))
succZH_in_ag(zero(T282), one(T282)) → U11_ag(T282, binaryZA_in_g(T282))
U11_ag(T282, binaryZA_out_g(T282)) → succZH_out_ag(zero(T282), one(T282))
succZH_in_ag(one(T290), zero(T289)) → U12_ag(T290, T289, succG_in_ag(T290, T289))
succG_in_ag(b, one(b)) → succG_out_ag(b, one(b))
succG_in_ag(zero(T295), one(T295)) → U9_ag(T295, binaryZA_in_g(T295))
U9_ag(T295, binaryZA_out_g(T295)) → succG_out_ag(zero(T295), one(T295))
succG_in_ag(one(T303), zero(T302)) → U10_ag(T303, T302, succG_in_ag(T303, T302))
U10_ag(T303, T302, succG_out_ag(T303, T302)) → succG_out_ag(one(T303), zero(T302))
U12_ag(T290, T289, succG_out_ag(T290, T289)) → succZH_out_ag(one(T290), zero(T289))
U21_aag(T276, T275, succZH_out_ag(T276, T275)) → addcF_out_aag(T276, b, T275)
addcF_in_aag(b, T314, T313) → U22_aag(T314, T313, succZH_in_ag(T314, T313))
U22_aag(T314, T313, succZH_out_ag(T314, T313)) → addcF_out_aag(b, T314, T313)
addcF_in_aag(T330, T331, T329) → U23_aag(T330, T331, T329, addCI_in_aag(T330, T331, T329))
addCI_in_aag(zero(T350), zero(T351), one(T349)) → U13_aag(T350, T351, T349, addzC_in_aag(T350, T351, T349))
U13_aag(T350, T351, T349, addzC_out_aag(T350, T351, T349)) → addCI_out_aag(zero(T350), zero(T351), one(T349))
addCI_in_aag(zero(zero(T377)), one(b), zero(one(T377))) → U14_aag(T377, binaryZA_in_g(T377))
U14_aag(T377, binaryZA_out_g(T377)) → addCI_out_aag(zero(zero(T377)), one(b), zero(one(T377)))
addCI_in_aag(zero(one(T389)), one(b), zero(zero(T388))) → U15_aag(T389, T388, succG_in_ag(T389, T388))
U15_aag(T389, T388, succG_out_ag(T389, T388)) → addCI_out_aag(zero(one(T389)), one(b), zero(zero(T388)))
addCI_in_aag(zero(T404), one(T405), zero(T403)) → U16_aag(T404, T405, T403, addCI_in_aag(T404, T405, T403))
addCI_in_aag(one(b), zero(zero(T431)), zero(one(T431))) → U17_aag(T431, binaryZA_in_g(T431))
U17_aag(T431, binaryZA_out_g(T431)) → addCI_out_aag(one(b), zero(zero(T431)), zero(one(T431)))
addCI_in_aag(one(b), zero(one(T443)), zero(zero(T442))) → U18_aag(T443, T442, succG_in_ag(T443, T442))
U18_aag(T443, T442, succG_out_ag(T443, T442)) → addCI_out_aag(one(b), zero(one(T443)), zero(zero(T442)))
addCI_in_aag(one(T458), zero(T459), zero(T457)) → U19_aag(T458, T459, T457, addCI_in_aag(T458, T459, T457))
addCI_in_aag(one(T472), one(T473), one(T471)) → U20_aag(T472, T473, T471, addcF_in_aag(T472, T473, T471))
U20_aag(T472, T473, T471, addcF_out_aag(T472, T473, T471)) → addCI_out_aag(one(T472), one(T473), one(T471))
U19_aag(T458, T459, T457, addCI_out_aag(T458, T459, T457)) → addCI_out_aag(one(T458), zero(T459), zero(T457))
U16_aag(T404, T405, T403, addCI_out_aag(T404, T405, T403)) → addCI_out_aag(zero(T404), one(T405), zero(T403))
U23_aag(T330, T331, T329, addCI_out_aag(T330, T331, T329)) → addcF_out_aag(T330, T331, T329)
U8_aag(T264, T265, T263, addcF_out_aag(T264, T265, T263)) → addzC_out_aag(one(T264), one(T265), zero(T263))
U29_aag(T250, T251, T249, addzC_out_aag(T250, T251, T249)) → addyE_out_aag(T250, T251, T249)
U7_aag(T222, T223, T221, addyE_out_aag(T222, T223, T221)) → addzC_out_aag(one(T222), zero(T223), one(T221))
U26_aag(T202, T203, T201, addzC_out_aag(T202, T203, T201)) → addxD_out_aag(T202, T203, T201)
U6_aag(T174, T175, T173, addxD_out_aag(T174, T175, T173)) → addzC_out_aag(zero(T174), one(T175), one(T173))
U5_aag(T154, T155, T153, addzC_out_aag(T154, T155, T153)) → addzC_out_aag(zero(T154), zero(T155), zero(T153))
U30_aag(T134, T135, T133, addzC_out_aag(T134, T135, T133)) → addzJ_out_aag(zero(T134), zero(T135), zero(T133))
addzJ_in_aag(zero(T489), one(T490), one(T488)) → U31_aag(T489, T490, T488, addxD_in_aag(T489, T490, T488))
U31_aag(T489, T490, T488, addxD_out_aag(T489, T490, T488)) → addzJ_out_aag(zero(T489), one(T490), one(T488))
addzJ_in_aag(one(T507), zero(T508), one(T506)) → U32_aag(T507, T508, T506, addyE_in_aag(T507, T508, T506))
U32_aag(T507, T508, T506, addyE_out_aag(T507, T508, T506)) → addzJ_out_aag(one(T507), zero(T508), one(T506))
addzJ_in_aag(one(T519), one(T520), zero(T518)) → U33_aag(T519, T520, T518, addcF_in_aag(T519, T520, T518))
U33_aag(T519, T520, T518, addcF_out_aag(T519, T520, T518)) → addzJ_out_aag(one(T519), one(T520), zero(T518))
U37_aag(T114, T115, T113, addzJ_out_aag(T114, T115, T113)) → addK_out_aag(T114, T115, T113)
addK_in_aag(b, zero(T527), zero(T527)) → U38_aag(T527, binaryZA_in_g(T527))
U38_aag(T527, binaryZA_out_g(T527)) → addK_out_aag(b, zero(T527), zero(T527))
addK_in_aag(b, one(T533), one(T533)) → U39_aag(T533, binaryB_in_g(T533))
U39_aag(T533, binaryB_out_g(T533)) → addK_out_aag(b, one(T533), one(T533))
addK_in_aag(T548, T549, T547) → U40_aag(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
U40_aag(T548, T549, T547, addzJ_out_aag(T548, T549, T547)) → addK_out_aag(T548, T549, T547)
addK_in_aag(zero(T576), zero(T577), zero(T575)) → U41_aag(T576, T577, T575, addzC_in_aag(T576, T577, T575))
U41_aag(T576, T577, T575, addzC_out_aag(T576, T577, T575)) → addK_out_aag(zero(T576), zero(T577), zero(T575))
addK_in_aag(zero(T596), one(T597), one(T595)) → U42_aag(T596, T597, T595, addxD_in_aag(T596, T597, T595))
U42_aag(T596, T597, T595, addxD_out_aag(T596, T597, T595)) → addK_out_aag(zero(T596), one(T597), one(T595))
addK_in_aag(one(T614), zero(T615), one(T613)) → U43_aag(T614, T615, T613, addyE_in_aag(T614, T615, T613))
U43_aag(T614, T615, T613, addyE_out_aag(T614, T615, T613)) → addK_out_aag(one(T614), zero(T615), one(T613))
addK_in_aag(one(T626), one(T627), zero(T625)) → U44_aag(T626, T627, T625, addcF_in_aag(T626, T627, T625))
U44_aag(T626, T627, T625, addcF_out_aag(T626, T627, T625)) → addK_out_aag(one(T626), one(T627), zero(T625))

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

BINARYZA_IN_G(one(T79)) → BINARYB_IN_G(T79)
BINARYB_IN_G(zero(T84)) → BINARYZA_IN_G(T84)
BINARYZA_IN_G(zero(T75)) → BINARYZA_IN_G(T75)
BINARYB_IN_G(one(T88)) → BINARYB_IN_G(T88)

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

(12) PiDPToQDPProof (EQUIVALENT transformation)

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

(13) Obligation:

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

BINARYZA_IN_G(one(T79)) → BINARYB_IN_G(T79)
BINARYB_IN_G(zero(T84)) → BINARYZA_IN_G(T84)
BINARYZA_IN_G(zero(T75)) → BINARYZA_IN_G(T75)
BINARYB_IN_G(one(T88)) → BINARYB_IN_G(T88)

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

(14) 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:

BINARYB_IN_G(zero(T84)) → BINARYZA_IN_G(T84)
The graph contains the following edges 1 > 1
BINARYB_IN_G(one(T88)) → BINARYB_IN_G(T88)
The graph contains the following edges 1 > 1
BINARYZA_IN_G(zero(T75)) → BINARYZA_IN_G(T75)
The graph contains the following edges 1 > 1
BINARYZA_IN_G(one(T79)) → BINARYB_IN_G(T79)
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

SUCCG_IN_AG(one(T303), zero(T302)) → SUCCG_IN_AG(T303, T302)

The TRS R consists of the following rules:

addK_in_aag(b, b, b) → addK_out_aag(b, b, b)
addK_in_aag(zero(T69), b, zero(T69)) → U34_aag(T69, binaryZA_in_g(T69))
binaryZA_in_g(zero(T75)) → U1_g(T75, binaryZA_in_g(T75))
binaryZA_in_g(one(T79)) → U2_g(T79, binaryB_in_g(T79))
binaryB_in_g(b) → binaryB_out_g(b)
binaryB_in_g(zero(T84)) → U3_g(T84, binaryZA_in_g(T84))
U3_g(T84, binaryZA_out_g(T84)) → binaryB_out_g(zero(T84))
binaryB_in_g(one(T88)) → U4_g(T88, binaryB_in_g(T88))
U4_g(T88, binaryB_out_g(T88)) → binaryB_out_g(one(T88))
U2_g(T79, binaryB_out_g(T79)) → binaryZA_out_g(one(T79))
U1_g(T75, binaryZA_out_g(T75)) → binaryZA_out_g(zero(T75))
U34_aag(T69, binaryZA_out_g(T69)) → addK_out_aag(zero(T69), b, zero(T69))
addK_in_aag(one(T93), b, one(T93)) → U35_aag(T93, binaryB_in_g(T93))
U35_aag(T93, binaryB_out_g(T93)) → addK_out_aag(one(T93), b, one(T93))
addK_in_aag(b, T98, T98) → U36_aag(T98, binaryZA_in_g(T98))
U36_aag(T98, binaryZA_out_g(T98)) → addK_out_aag(b, T98, T98)
addK_in_aag(T114, T115, T113) → U37_aag(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
addzJ_in_aag(zero(T134), zero(T135), zero(T133)) → U30_aag(T134, T135, T133, addzC_in_aag(T134, T135, T133))
addzC_in_aag(zero(T154), zero(T155), zero(T153)) → U5_aag(T154, T155, T153, addzC_in_aag(T154, T155, T153))
addzC_in_aag(zero(T174), one(T175), one(T173)) → U6_aag(T174, T175, T173, addxD_in_aag(T174, T175, T173))
addxD_in_aag(one(T181), b, one(T181)) → U24_aag(T181, binaryB_in_g(T181))
U24_aag(T181, binaryB_out_g(T181)) → addxD_out_aag(one(T181), b, one(T181))
addxD_in_aag(zero(T186), b, zero(T186)) → U25_aag(T186, binaryZA_in_g(T186))
U25_aag(T186, binaryZA_out_g(T186)) → addxD_out_aag(zero(T186), b, zero(T186))
addxD_in_aag(T202, T203, T201) → U26_aag(T202, T203, T201, addzC_in_aag(T202, T203, T201))
addzC_in_aag(one(T222), zero(T223), one(T221)) → U7_aag(T222, T223, T221, addyE_in_aag(T222, T223, T221))
addyE_in_aag(b, one(T229), one(T229)) → U27_aag(T229, binaryB_in_g(T229))
U27_aag(T229, binaryB_out_g(T229)) → addyE_out_aag(b, one(T229), one(T229))
addyE_in_aag(b, zero(T234), zero(T234)) → U28_aag(T234, binaryZA_in_g(T234))
U28_aag(T234, binaryZA_out_g(T234)) → addyE_out_aag(b, zero(T234), zero(T234))
addyE_in_aag(T250, T251, T249) → U29_aag(T250, T251, T249, addzC_in_aag(T250, T251, T249))
addzC_in_aag(one(T264), one(T265), zero(T263)) → U8_aag(T264, T265, T263, addcF_in_aag(T264, T265, T263))
addcF_in_aag(b, b, one(b)) → addcF_out_aag(b, b, one(b))
addcF_in_aag(T276, b, T275) → U21_aag(T276, T275, succZH_in_ag(T276, T275))
succZH_in_ag(zero(T282), one(T282)) → U11_ag(T282, binaryZA_in_g(T282))
U11_ag(T282, binaryZA_out_g(T282)) → succZH_out_ag(zero(T282), one(T282))
succZH_in_ag(one(T290), zero(T289)) → U12_ag(T290, T289, succG_in_ag(T290, T289))
succG_in_ag(b, one(b)) → succG_out_ag(b, one(b))
succG_in_ag(zero(T295), one(T295)) → U9_ag(T295, binaryZA_in_g(T295))
U9_ag(T295, binaryZA_out_g(T295)) → succG_out_ag(zero(T295), one(T295))
succG_in_ag(one(T303), zero(T302)) → U10_ag(T303, T302, succG_in_ag(T303, T302))
U10_ag(T303, T302, succG_out_ag(T303, T302)) → succG_out_ag(one(T303), zero(T302))
U12_ag(T290, T289, succG_out_ag(T290, T289)) → succZH_out_ag(one(T290), zero(T289))
U21_aag(T276, T275, succZH_out_ag(T276, T275)) → addcF_out_aag(T276, b, T275)
addcF_in_aag(b, T314, T313) → U22_aag(T314, T313, succZH_in_ag(T314, T313))
U22_aag(T314, T313, succZH_out_ag(T314, T313)) → addcF_out_aag(b, T314, T313)
addcF_in_aag(T330, T331, T329) → U23_aag(T330, T331, T329, addCI_in_aag(T330, T331, T329))
addCI_in_aag(zero(T350), zero(T351), one(T349)) → U13_aag(T350, T351, T349, addzC_in_aag(T350, T351, T349))
U13_aag(T350, T351, T349, addzC_out_aag(T350, T351, T349)) → addCI_out_aag(zero(T350), zero(T351), one(T349))
addCI_in_aag(zero(zero(T377)), one(b), zero(one(T377))) → U14_aag(T377, binaryZA_in_g(T377))
U14_aag(T377, binaryZA_out_g(T377)) → addCI_out_aag(zero(zero(T377)), one(b), zero(one(T377)))
addCI_in_aag(zero(one(T389)), one(b), zero(zero(T388))) → U15_aag(T389, T388, succG_in_ag(T389, T388))
U15_aag(T389, T388, succG_out_ag(T389, T388)) → addCI_out_aag(zero(one(T389)), one(b), zero(zero(T388)))
addCI_in_aag(zero(T404), one(T405), zero(T403)) → U16_aag(T404, T405, T403, addCI_in_aag(T404, T405, T403))
addCI_in_aag(one(b), zero(zero(T431)), zero(one(T431))) → U17_aag(T431, binaryZA_in_g(T431))
U17_aag(T431, binaryZA_out_g(T431)) → addCI_out_aag(one(b), zero(zero(T431)), zero(one(T431)))
addCI_in_aag(one(b), zero(one(T443)), zero(zero(T442))) → U18_aag(T443, T442, succG_in_ag(T443, T442))
U18_aag(T443, T442, succG_out_ag(T443, T442)) → addCI_out_aag(one(b), zero(one(T443)), zero(zero(T442)))
addCI_in_aag(one(T458), zero(T459), zero(T457)) → U19_aag(T458, T459, T457, addCI_in_aag(T458, T459, T457))
addCI_in_aag(one(T472), one(T473), one(T471)) → U20_aag(T472, T473, T471, addcF_in_aag(T472, T473, T471))
U20_aag(T472, T473, T471, addcF_out_aag(T472, T473, T471)) → addCI_out_aag(one(T472), one(T473), one(T471))
U19_aag(T458, T459, T457, addCI_out_aag(T458, T459, T457)) → addCI_out_aag(one(T458), zero(T459), zero(T457))
U16_aag(T404, T405, T403, addCI_out_aag(T404, T405, T403)) → addCI_out_aag(zero(T404), one(T405), zero(T403))
U23_aag(T330, T331, T329, addCI_out_aag(T330, T331, T329)) → addcF_out_aag(T330, T331, T329)
U8_aag(T264, T265, T263, addcF_out_aag(T264, T265, T263)) → addzC_out_aag(one(T264), one(T265), zero(T263))
U29_aag(T250, T251, T249, addzC_out_aag(T250, T251, T249)) → addyE_out_aag(T250, T251, T249)
U7_aag(T222, T223, T221, addyE_out_aag(T222, T223, T221)) → addzC_out_aag(one(T222), zero(T223), one(T221))
U26_aag(T202, T203, T201, addzC_out_aag(T202, T203, T201)) → addxD_out_aag(T202, T203, T201)
U6_aag(T174, T175, T173, addxD_out_aag(T174, T175, T173)) → addzC_out_aag(zero(T174), one(T175), one(T173))
U5_aag(T154, T155, T153, addzC_out_aag(T154, T155, T153)) → addzC_out_aag(zero(T154), zero(T155), zero(T153))
U30_aag(T134, T135, T133, addzC_out_aag(T134, T135, T133)) → addzJ_out_aag(zero(T134), zero(T135), zero(T133))
addzJ_in_aag(zero(T489), one(T490), one(T488)) → U31_aag(T489, T490, T488, addxD_in_aag(T489, T490, T488))
U31_aag(T489, T490, T488, addxD_out_aag(T489, T490, T488)) → addzJ_out_aag(zero(T489), one(T490), one(T488))
addzJ_in_aag(one(T507), zero(T508), one(T506)) → U32_aag(T507, T508, T506, addyE_in_aag(T507, T508, T506))
U32_aag(T507, T508, T506, addyE_out_aag(T507, T508, T506)) → addzJ_out_aag(one(T507), zero(T508), one(T506))
addzJ_in_aag(one(T519), one(T520), zero(T518)) → U33_aag(T519, T520, T518, addcF_in_aag(T519, T520, T518))
U33_aag(T519, T520, T518, addcF_out_aag(T519, T520, T518)) → addzJ_out_aag(one(T519), one(T520), zero(T518))
U37_aag(T114, T115, T113, addzJ_out_aag(T114, T115, T113)) → addK_out_aag(T114, T115, T113)
addK_in_aag(b, zero(T527), zero(T527)) → U38_aag(T527, binaryZA_in_g(T527))
U38_aag(T527, binaryZA_out_g(T527)) → addK_out_aag(b, zero(T527), zero(T527))
addK_in_aag(b, one(T533), one(T533)) → U39_aag(T533, binaryB_in_g(T533))
U39_aag(T533, binaryB_out_g(T533)) → addK_out_aag(b, one(T533), one(T533))
addK_in_aag(T548, T549, T547) → U40_aag(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
U40_aag(T548, T549, T547, addzJ_out_aag(T548, T549, T547)) → addK_out_aag(T548, T549, T547)
addK_in_aag(zero(T576), zero(T577), zero(T575)) → U41_aag(T576, T577, T575, addzC_in_aag(T576, T577, T575))
U41_aag(T576, T577, T575, addzC_out_aag(T576, T577, T575)) → addK_out_aag(zero(T576), zero(T577), zero(T575))
addK_in_aag(zero(T596), one(T597), one(T595)) → U42_aag(T596, T597, T595, addxD_in_aag(T596, T597, T595))
U42_aag(T596, T597, T595, addxD_out_aag(T596, T597, T595)) → addK_out_aag(zero(T596), one(T597), one(T595))
addK_in_aag(one(T614), zero(T615), one(T613)) → U43_aag(T614, T615, T613, addyE_in_aag(T614, T615, T613))
U43_aag(T614, T615, T613, addyE_out_aag(T614, T615, T613)) → addK_out_aag(one(T614), zero(T615), one(T613))
addK_in_aag(one(T626), one(T627), zero(T625)) → U44_aag(T626, T627, T625, addcF_in_aag(T626, T627, T625))
U44_aag(T626, T627, T625, addcF_out_aag(T626, T627, T625)) → addK_out_aag(one(T626), one(T627), zero(T625))

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

SUCCG_IN_AG(one(T303), zero(T302)) → SUCCG_IN_AG(T303, T302)

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

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

SUCCG_IN_AG(zero(T302)) → SUCCG_IN_AG(T302)

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

(21) 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:

SUCCG_IN_AG(zero(T302)) → SUCCG_IN_AG(T302)
The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

ADDXD_IN_AAG(T202, T203, T201) → ADDZC_IN_AAG(T202, T203, T201)
ADDZC_IN_AAG(zero(T154), zero(T155), zero(T153)) → ADDZC_IN_AAG(T154, T155, T153)
ADDZC_IN_AAG(zero(T174), one(T175), one(T173)) → ADDXD_IN_AAG(T174, T175, T173)
ADDZC_IN_AAG(one(T222), zero(T223), one(T221)) → ADDYE_IN_AAG(T222, T223, T221)
ADDYE_IN_AAG(T250, T251, T249) → ADDZC_IN_AAG(T250, T251, T249)
ADDZC_IN_AAG(one(T264), one(T265), zero(T263)) → ADDCF_IN_AAG(T264, T265, T263)
ADDCF_IN_AAG(T330, T331, T329) → ADDCI_IN_AAG(T330, T331, T329)
ADDCI_IN_AAG(zero(T350), zero(T351), one(T349)) → ADDZC_IN_AAG(T350, T351, T349)
ADDCI_IN_AAG(zero(T404), one(T405), zero(T403)) → ADDCI_IN_AAG(T404, T405, T403)
ADDCI_IN_AAG(one(T458), zero(T459), zero(T457)) → ADDCI_IN_AAG(T458, T459, T457)
ADDCI_IN_AAG(one(T472), one(T473), one(T471)) → ADDCF_IN_AAG(T472, T473, T471)

The TRS R consists of the following rules:

addK_in_aag(b, b, b) → addK_out_aag(b, b, b)
addK_in_aag(zero(T69), b, zero(T69)) → U34_aag(T69, binaryZA_in_g(T69))
binaryZA_in_g(zero(T75)) → U1_g(T75, binaryZA_in_g(T75))
binaryZA_in_g(one(T79)) → U2_g(T79, binaryB_in_g(T79))
binaryB_in_g(b) → binaryB_out_g(b)
binaryB_in_g(zero(T84)) → U3_g(T84, binaryZA_in_g(T84))
U3_g(T84, binaryZA_out_g(T84)) → binaryB_out_g(zero(T84))
binaryB_in_g(one(T88)) → U4_g(T88, binaryB_in_g(T88))
U4_g(T88, binaryB_out_g(T88)) → binaryB_out_g(one(T88))
U2_g(T79, binaryB_out_g(T79)) → binaryZA_out_g(one(T79))
U1_g(T75, binaryZA_out_g(T75)) → binaryZA_out_g(zero(T75))
U34_aag(T69, binaryZA_out_g(T69)) → addK_out_aag(zero(T69), b, zero(T69))
addK_in_aag(one(T93), b, one(T93)) → U35_aag(T93, binaryB_in_g(T93))
U35_aag(T93, binaryB_out_g(T93)) → addK_out_aag(one(T93), b, one(T93))
addK_in_aag(b, T98, T98) → U36_aag(T98, binaryZA_in_g(T98))
U36_aag(T98, binaryZA_out_g(T98)) → addK_out_aag(b, T98, T98)
addK_in_aag(T114, T115, T113) → U37_aag(T114, T115, T113, addzJ_in_aag(T114, T115, T113))
addzJ_in_aag(zero(T134), zero(T135), zero(T133)) → U30_aag(T134, T135, T133, addzC_in_aag(T134, T135, T133))
addzC_in_aag(zero(T154), zero(T155), zero(T153)) → U5_aag(T154, T155, T153, addzC_in_aag(T154, T155, T153))
addzC_in_aag(zero(T174), one(T175), one(T173)) → U6_aag(T174, T175, T173, addxD_in_aag(T174, T175, T173))
addxD_in_aag(one(T181), b, one(T181)) → U24_aag(T181, binaryB_in_g(T181))
U24_aag(T181, binaryB_out_g(T181)) → addxD_out_aag(one(T181), b, one(T181))
addxD_in_aag(zero(T186), b, zero(T186)) → U25_aag(T186, binaryZA_in_g(T186))
U25_aag(T186, binaryZA_out_g(T186)) → addxD_out_aag(zero(T186), b, zero(T186))
addxD_in_aag(T202, T203, T201) → U26_aag(T202, T203, T201, addzC_in_aag(T202, T203, T201))
addzC_in_aag(one(T222), zero(T223), one(T221)) → U7_aag(T222, T223, T221, addyE_in_aag(T222, T223, T221))
addyE_in_aag(b, one(T229), one(T229)) → U27_aag(T229, binaryB_in_g(T229))
U27_aag(T229, binaryB_out_g(T229)) → addyE_out_aag(b, one(T229), one(T229))
addyE_in_aag(b, zero(T234), zero(T234)) → U28_aag(T234, binaryZA_in_g(T234))
U28_aag(T234, binaryZA_out_g(T234)) → addyE_out_aag(b, zero(T234), zero(T234))
addyE_in_aag(T250, T251, T249) → U29_aag(T250, T251, T249, addzC_in_aag(T250, T251, T249))
addzC_in_aag(one(T264), one(T265), zero(T263)) → U8_aag(T264, T265, T263, addcF_in_aag(T264, T265, T263))
addcF_in_aag(b, b, one(b)) → addcF_out_aag(b, b, one(b))
addcF_in_aag(T276, b, T275) → U21_aag(T276, T275, succZH_in_ag(T276, T275))
succZH_in_ag(zero(T282), one(T282)) → U11_ag(T282, binaryZA_in_g(T282))
U11_ag(T282, binaryZA_out_g(T282)) → succZH_out_ag(zero(T282), one(T282))
succZH_in_ag(one(T290), zero(T289)) → U12_ag(T290, T289, succG_in_ag(T290, T289))
succG_in_ag(b, one(b)) → succG_out_ag(b, one(b))
succG_in_ag(zero(T295), one(T295)) → U9_ag(T295, binaryZA_in_g(T295))
U9_ag(T295, binaryZA_out_g(T295)) → succG_out_ag(zero(T295), one(T295))
succG_in_ag(one(T303), zero(T302)) → U10_ag(T303, T302, succG_in_ag(T303, T302))
U10_ag(T303, T302, succG_out_ag(T303, T302)) → succG_out_ag(one(T303), zero(T302))
U12_ag(T290, T289, succG_out_ag(T290, T289)) → succZH_out_ag(one(T290), zero(T289))
U21_aag(T276, T275, succZH_out_ag(T276, T275)) → addcF_out_aag(T276, b, T275)
addcF_in_aag(b, T314, T313) → U22_aag(T314, T313, succZH_in_ag(T314, T313))
U22_aag(T314, T313, succZH_out_ag(T314, T313)) → addcF_out_aag(b, T314, T313)
addcF_in_aag(T330, T331, T329) → U23_aag(T330, T331, T329, addCI_in_aag(T330, T331, T329))
addCI_in_aag(zero(T350), zero(T351), one(T349)) → U13_aag(T350, T351, T349, addzC_in_aag(T350, T351, T349))
U13_aag(T350, T351, T349, addzC_out_aag(T350, T351, T349)) → addCI_out_aag(zero(T350), zero(T351), one(T349))
addCI_in_aag(zero(zero(T377)), one(b), zero(one(T377))) → U14_aag(T377, binaryZA_in_g(T377))
U14_aag(T377, binaryZA_out_g(T377)) → addCI_out_aag(zero(zero(T377)), one(b), zero(one(T377)))
addCI_in_aag(zero(one(T389)), one(b), zero(zero(T388))) → U15_aag(T389, T388, succG_in_ag(T389, T388))
U15_aag(T389, T388, succG_out_ag(T389, T388)) → addCI_out_aag(zero(one(T389)), one(b), zero(zero(T388)))
addCI_in_aag(zero(T404), one(T405), zero(T403)) → U16_aag(T404, T405, T403, addCI_in_aag(T404, T405, T403))
addCI_in_aag(one(b), zero(zero(T431)), zero(one(T431))) → U17_aag(T431, binaryZA_in_g(T431))
U17_aag(T431, binaryZA_out_g(T431)) → addCI_out_aag(one(b), zero(zero(T431)), zero(one(T431)))
addCI_in_aag(one(b), zero(one(T443)), zero(zero(T442))) → U18_aag(T443, T442, succG_in_ag(T443, T442))
U18_aag(T443, T442, succG_out_ag(T443, T442)) → addCI_out_aag(one(b), zero(one(T443)), zero(zero(T442)))
addCI_in_aag(one(T458), zero(T459), zero(T457)) → U19_aag(T458, T459, T457, addCI_in_aag(T458, T459, T457))
addCI_in_aag(one(T472), one(T473), one(T471)) → U20_aag(T472, T473, T471, addcF_in_aag(T472, T473, T471))
U20_aag(T472, T473, T471, addcF_out_aag(T472, T473, T471)) → addCI_out_aag(one(T472), one(T473), one(T471))
U19_aag(T458, T459, T457, addCI_out_aag(T458, T459, T457)) → addCI_out_aag(one(T458), zero(T459), zero(T457))
U16_aag(T404, T405, T403, addCI_out_aag(T404, T405, T403)) → addCI_out_aag(zero(T404), one(T405), zero(T403))
U23_aag(T330, T331, T329, addCI_out_aag(T330, T331, T329)) → addcF_out_aag(T330, T331, T329)
U8_aag(T264, T265, T263, addcF_out_aag(T264, T265, T263)) → addzC_out_aag(one(T264), one(T265), zero(T263))
U29_aag(T250, T251, T249, addzC_out_aag(T250, T251, T249)) → addyE_out_aag(T250, T251, T249)
U7_aag(T222, T223, T221, addyE_out_aag(T222, T223, T221)) → addzC_out_aag(one(T222), zero(T223), one(T221))
U26_aag(T202, T203, T201, addzC_out_aag(T202, T203, T201)) → addxD_out_aag(T202, T203, T201)
U6_aag(T174, T175, T173, addxD_out_aag(T174, T175, T173)) → addzC_out_aag(zero(T174), one(T175), one(T173))
U5_aag(T154, T155, T153, addzC_out_aag(T154, T155, T153)) → addzC_out_aag(zero(T154), zero(T155), zero(T153))
U30_aag(T134, T135, T133, addzC_out_aag(T134, T135, T133)) → addzJ_out_aag(zero(T134), zero(T135), zero(T133))
addzJ_in_aag(zero(T489), one(T490), one(T488)) → U31_aag(T489, T490, T488, addxD_in_aag(T489, T490, T488))
U31_aag(T489, T490, T488, addxD_out_aag(T489, T490, T488)) → addzJ_out_aag(zero(T489), one(T490), one(T488))
addzJ_in_aag(one(T507), zero(T508), one(T506)) → U32_aag(T507, T508, T506, addyE_in_aag(T507, T508, T506))
U32_aag(T507, T508, T506, addyE_out_aag(T507, T508, T506)) → addzJ_out_aag(one(T507), zero(T508), one(T506))
addzJ_in_aag(one(T519), one(T520), zero(T518)) → U33_aag(T519, T520, T518, addcF_in_aag(T519, T520, T518))
U33_aag(T519, T520, T518, addcF_out_aag(T519, T520, T518)) → addzJ_out_aag(one(T519), one(T520), zero(T518))
U37_aag(T114, T115, T113, addzJ_out_aag(T114, T115, T113)) → addK_out_aag(T114, T115, T113)
addK_in_aag(b, zero(T527), zero(T527)) → U38_aag(T527, binaryZA_in_g(T527))
U38_aag(T527, binaryZA_out_g(T527)) → addK_out_aag(b, zero(T527), zero(T527))
addK_in_aag(b, one(T533), one(T533)) → U39_aag(T533, binaryB_in_g(T533))
U39_aag(T533, binaryB_out_g(T533)) → addK_out_aag(b, one(T533), one(T533))
addK_in_aag(T548, T549, T547) → U40_aag(T548, T549, T547, addzJ_in_aag(T548, T549, T547))
U40_aag(T548, T549, T547, addzJ_out_aag(T548, T549, T547)) → addK_out_aag(T548, T549, T547)
addK_in_aag(zero(T576), zero(T577), zero(T575)) → U41_aag(T576, T577, T575, addzC_in_aag(T576, T577, T575))
U41_aag(T576, T577, T575, addzC_out_aag(T576, T577, T575)) → addK_out_aag(zero(T576), zero(T577), zero(T575))
addK_in_aag(zero(T596), one(T597), one(T595)) → U42_aag(T596, T597, T595, addxD_in_aag(T596, T597, T595))
U42_aag(T596, T597, T595, addxD_out_aag(T596, T597, T595)) → addK_out_aag(zero(T596), one(T597), one(T595))
addK_in_aag(one(T614), zero(T615), one(T613)) → U43_aag(T614, T615, T613, addyE_in_aag(T614, T615, T613))
U43_aag(T614, T615, T613, addyE_out_aag(T614, T615, T613)) → addK_out_aag(one(T614), zero(T615), one(T613))
addK_in_aag(one(T626), one(T627), zero(T625)) → U44_aag(T626, T627, T625, addcF_in_aag(T626, T627, T625))
U44_aag(T626, T627, T625, addcF_out_aag(T626, T627, T625)) → addK_out_aag(one(T626), one(T627), zero(T625))

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

ADDXD_IN_AAG(T202, T203, T201) → ADDZC_IN_AAG(T202, T203, T201)
ADDZC_IN_AAG(zero(T154), zero(T155), zero(T153)) → ADDZC_IN_AAG(T154, T155, T153)
ADDZC_IN_AAG(zero(T174), one(T175), one(T173)) → ADDXD_IN_AAG(T174, T175, T173)
ADDZC_IN_AAG(one(T222), zero(T223), one(T221)) → ADDYE_IN_AAG(T222, T223, T221)
ADDYE_IN_AAG(T250, T251, T249) → ADDZC_IN_AAG(T250, T251, T249)
ADDZC_IN_AAG(one(T264), one(T265), zero(T263)) → ADDCF_IN_AAG(T264, T265, T263)
ADDCF_IN_AAG(T330, T331, T329) → ADDCI_IN_AAG(T330, T331, T329)
ADDCI_IN_AAG(zero(T350), zero(T351), one(T349)) → ADDZC_IN_AAG(T350, T351, T349)
ADDCI_IN_AAG(zero(T404), one(T405), zero(T403)) → ADDCI_IN_AAG(T404, T405, T403)
ADDCI_IN_AAG(one(T458), zero(T459), zero(T457)) → ADDCI_IN_AAG(T458, T459, T457)
ADDCI_IN_AAG(one(T472), one(T473), one(T471)) → ADDCF_IN_AAG(T472, T473, T471)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1) = zero(x1)
one(x1) = one(x1)
ADDZC_IN_AAG(x1, x2, x3) = ADDZC_IN_AAG(x3)
ADDXD_IN_AAG(x1, x2, x3) = ADDXD_IN_AAG(x3)
ADDYE_IN_AAG(x1, x2, x3) = ADDYE_IN_AAG(x3)
ADDCF_IN_AAG(x1, x2, x3) = ADDCF_IN_AAG(x3)
ADDCI_IN_AAG(x1, x2, x3) = ADDCI_IN_AAG(x3)

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

(26) PiDPToQDPProof (SOUND transformation)

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

(27) Obligation:

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

ADDXD_IN_AAG(T201) → ADDZC_IN_AAG(T201)
ADDZC_IN_AAG(zero(T153)) → ADDZC_IN_AAG(T153)
ADDZC_IN_AAG(one(T173)) → ADDXD_IN_AAG(T173)
ADDZC_IN_AAG(one(T221)) → ADDYE_IN_AAG(T221)
ADDYE_IN_AAG(T249) → ADDZC_IN_AAG(T249)
ADDZC_IN_AAG(zero(T263)) → ADDCF_IN_AAG(T263)
ADDCF_IN_AAG(T329) → ADDCI_IN_AAG(T329)
ADDCI_IN_AAG(one(T349)) → ADDZC_IN_AAG(T349)
ADDCI_IN_AAG(zero(T403)) → ADDCI_IN_AAG(T403)
ADDCI_IN_AAG(one(T471)) → ADDCF_IN_AAG(T471)

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

(28) 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:

ADDZC_IN_AAG(one(T173)) → ADDXD_IN_AAG(T173)
The graph contains the following edges 1 > 1
ADDZC_IN_AAG(zero(T153)) → ADDZC_IN_AAG(T153)
The graph contains the following edges 1 > 1
ADDXD_IN_AAG(T201) → ADDZC_IN_AAG(T201)
The graph contains the following edges 1 >= 1
ADDYE_IN_AAG(T249) → ADDZC_IN_AAG(T249)
The graph contains the following edges 1 >= 1
ADDCI_IN_AAG(one(T349)) → ADDZC_IN_AAG(T349)
The graph contains the following edges 1 > 1
ADDZC_IN_AAG(one(T221)) → ADDYE_IN_AAG(T221)
The graph contains the following edges 1 > 1
ADDZC_IN_AAG(zero(T263)) → ADDCF_IN_AAG(T263)
The graph contains the following edges 1 > 1
ADDCF_IN_AAG(T329) → ADDCI_IN_AAG(T329)
The graph contains the following edges 1 >= 1
ADDCI_IN_AAG(one(T471)) → ADDCF_IN_AAG(T471)
The graph contains the following edges 1 > 1
ADDCI_IN_AAG(zero(T403)) → ADDCI_IN_AAG(T403)
The graph contains the following edges 1 > 1

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (EQUIVALENT transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (SOUND transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) YES