Left Termination of the query pattern add_in_3(a, a, g) w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

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

Queries:

add(a,a,g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

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\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(T27, T28, b)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: addz(T27, T28, b), SCOPE: 4, CLAUSE: 10 | addz(T27, T28, b), SCOPE: 4, CLAUSE: 11 | addz(T27, T28, b), SCOPE: 4, CLAUSE: 12 | addz(T27, T28, b), SCOPE: 4, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: addz(T27, T28, b), SCOPE: 4, CLAUSE: 11 | addz(T27, T28, b), SCOPE: 4, CLAUSE: 12 | addz(T27, T28, b), SCOPE: 4, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: addz(T27, T28, b), SCOPE: 4, CLAUSE: 12 | addz(T27, T28, b), SCOPE: 4, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: addz(T27, T28, 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\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\nadd(T1, T2, b) !=? add(X2, b, X2)\nadd(T1, T2, b) !=? add(b, X62, X62)", 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\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\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\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\nadd(T1, T2, b) !=? add(X2, b, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: addz(T63, T64, b)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: addz(T77, T78, b)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: addz(T77, T78, b), SCOPE: 6, CLAUSE: 10 | addz(T77, T78, b), SCOPE: 6, CLAUSE: 11 | addz(T77, T78, b), SCOPE: 6, CLAUSE: 12 | addz(T77, T78, b), SCOPE: 6, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: addz(T77, T78, b), SCOPE: 6, CLAUSE: 11 | addz(T77, T78, b), SCOPE: 6, CLAUSE: 12 | addz(T77, T78, b), SCOPE: 6, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: addz(T77, T78, b), SCOPE: 6, CLAUSE: 12 | addz(T77, T78, b), SCOPE: 6, CLAUSE: 13\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: addz(T77, T78, 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(T88) | add(T1, T2, T88), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 3\n\nT88 is ground\nadd(T1, T2, T88) !=? 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\nadd(T1, T2, T3) !=? add(b, b, b)\nadd(T1, T2, T3) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: binaryZ(T88), SCOPE: 7, CLAUSE: 31 | binaryZ(T88), SCOPE: 7, CLAUSE: 32 | ?_7 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 3\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: binaryZ(T88), SCOPE: 7, CLAUSE: 31\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: binaryZ(T88), SCOPE: 7, CLAUSE: 32 | ?_7 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 3\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: binaryZ(T93)\n\nT93 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: binaryZ(T93), SCOPE: 8, CLAUSE: 31 | binaryZ(T93), SCOPE: 8, CLAUSE: 32\n\nT93 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: binaryZ(T93), SCOPE: 8, CLAUSE: 31\n\nT93 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: binaryZ(T93), SCOPE: 8, CLAUSE: 32\n\nT93 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: binaryZ(T99)\n\nT99 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: binary(T103)\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: binary(T103), SCOPE: 9, CLAUSE: 28 | binary(T103), SCOPE: 9, CLAUSE: 29 | binary(T103), SCOPE: 9, CLAUSE: 30\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: binary(T103), SCOPE: 9, CLAUSE: 28\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: binary(T103), SCOPE: 9, CLAUSE: 29 | binary(T103), SCOPE: 9, CLAUSE: 30\n\nT103 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(T103), SCOPE: 9, CLAUSE: 29\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: binary(T103), SCOPE: 9, CLAUSE: 30\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: binaryZ(T108)\n\nT108 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: binary(T112)\n\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: binaryZ(T88), SCOPE: 7, CLAUSE: 32\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ?_7 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 3\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: binary(T117)\n\nT117 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, T88), SCOPE: 1, CLAUSE: 2 | add(T1, T2, T88), SCOPE: 1, CLAUSE: 3\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: add(T1, T2, T88), SCOPE: 1, CLAUSE: 2\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: add(T1, T2, T88), SCOPE: 1, CLAUSE: 3\n\nT88 is ground\nadd(T1, T2, T88) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: binaryZ(T122)\n\nT122 is ground\nadd(T1, T2, T122) !=? 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(T138, T139, T137)\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: addz(T138, T139, T137), SCOPE: 10, CLAUSE: 10 | addz(T138, T139, T137), SCOPE: 10, CLAUSE: 11 | addz(T138, T139, T137), SCOPE: 10, CLAUSE: 12 | addz(T138, T139, T137), SCOPE: 10, CLAUSE: 13\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: addz(T138, T139, T137), SCOPE: 10, CLAUSE: 10\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: addz(T138, T139, T137), SCOPE: 10, CLAUSE: 11 | addz(T138, T139, T137), SCOPE: 10, CLAUSE: 12 | addz(T138, T139, T137), SCOPE: 10, CLAUSE: 13\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: addz(T158, T159, T157)\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: addz(T158, T159, T157), SCOPE: 11, CLAUSE: 10 | addz(T158, T159, T157), SCOPE: 11, CLAUSE: 11 | addz(T158, T159, T157), SCOPE: 11, CLAUSE: 12 | addz(T158, T159, T157), SCOPE: 11, CLAUSE: 13\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: addz(T158, T159, T157), SCOPE: 11, CLAUSE: 10\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: addz(T158, T159, T157), SCOPE: 11, CLAUSE: 11 | addz(T158, T159, T157), SCOPE: 11, CLAUSE: 12 | addz(T158, T159, T157), SCOPE: 11, CLAUSE: 13\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: addz(T178, T179, T177)\n\nT177 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: addz(T158, T159, T157), SCOPE: 11, CLAUSE: 11\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: addz(T158, T159, T157), SCOPE: 11, CLAUSE: 12 | addz(T158, T159, T157), SCOPE: 11, CLAUSE: 13\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: addx(T198, T199, T197)\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: addx(T198, T199, T197), SCOPE: 12, CLAUSE: 4 | addx(T198, T199, T197), SCOPE: 12, CLAUSE: 5 | addx(T198, T199, T197), SCOPE: 12, CLAUSE: 6\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: addx(T198, T199, T197), SCOPE: 12, CLAUSE: 4\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: addx(T198, T199, T197), SCOPE: 12, CLAUSE: 5 | addx(T198, T199, T197), SCOPE: 12, CLAUSE: 6\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: binary(T205)\n\nT205 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: addx(T198, T199, T197), SCOPE: 12, CLAUSE: 5\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: addx(T198, T199, T197), SCOPE: 12, CLAUSE: 6\n\nT197 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: binaryZ(T210)\n\nT210 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: addz(T226, T227, T225)\n\nT225 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: addz(T158, T159, T157), SCOPE: 11, CLAUSE: 12\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: addz(T158, T159, T157), SCOPE: 11, CLAUSE: 13\n\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: addy(T246, T247, T245)\n\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: addy(T246, T247, T245), SCOPE: 13, CLAUSE: 7 | addy(T246, T247, T245), SCOPE: 13, CLAUSE: 8 | addy(T246, T247, T245), SCOPE: 13, CLAUSE: 9\n\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: addy(T246, T247, T245), SCOPE: 13, CLAUSE: 7\n\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: addy(T246, T247, T245), SCOPE: 13, CLAUSE: 8 | addy(T246, T247, T245), SCOPE: 13, CLAUSE: 9\n\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: binary(T253)\n\nT253 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: addy(T246, T247, T245), SCOPE: 13, CLAUSE: 8\n\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: addy(T246, T247, T245), SCOPE: 13, CLAUSE: 9\n\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: binaryZ(T258)\n\nT258 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: addz(T274, T275, T273)\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: addc(T288, T289, T287)\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: addc(T288, T289, T287), SCOPE: 14, CLAUSE: 14 | addc(T288, T289, T287), SCOPE: 14, CLAUSE: 15 | addc(T288, T289, T287), SCOPE: 14, CLAUSE: 16 | addc(T288, T289, T287), SCOPE: 14, CLAUSE: 17\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: addc(T288, T289, T287), SCOPE: 14, CLAUSE: 14\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: addc(T288, T289, T287), SCOPE: 14, CLAUSE: 15 | addc(T288, T289, T287), SCOPE: 14, CLAUSE: 16 | addc(T288, T289, T287), SCOPE: 14, CLAUSE: 17\n\nT287 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(T288, T289, T287), SCOPE: 14, CLAUSE: 15\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: addc(T288, T289, T287), SCOPE: 14, CLAUSE: 16 | addc(T288, T289, T287), SCOPE: 14, CLAUSE: 17\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: succZ(T300, T299)\n\nT299 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: succZ(T300, T299), SCOPE: 15, CLAUSE: 36 | succZ(T300, T299), SCOPE: 15, CLAUSE: 37\n\nT299 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: succZ(T300, T299), SCOPE: 15, CLAUSE: 36\n\nT299 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: succZ(T300, T299), SCOPE: 15, CLAUSE: 37\n\nT299 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: binaryZ(T306)\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: succ(T314, T313)\n\nT313 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: succ(T314, T313), SCOPE: 16, CLAUSE: 33 | succ(T314, T313), SCOPE: 16, CLAUSE: 34 | succ(T314, T313), SCOPE: 16, CLAUSE: 35\n\nT313 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: succ(T314, T313), SCOPE: 16, CLAUSE: 33\n\nT313 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: succ(T314, T313), SCOPE: 16, CLAUSE: 34 | succ(T314, T313), SCOPE: 16, CLAUSE: 35\n\nT313 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(T314, T313), SCOPE: 16, CLAUSE: 34\n\nT313 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: succ(T314, T313), SCOPE: 16, CLAUSE: 35\n\nT313 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: binaryZ(T319)\n\nT319 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: succ(T327, T326)\n\nT326 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: addc(T288, T289, T287), SCOPE: 14, CLAUSE: 16\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: addc(T288, T289, T287), SCOPE: 14, CLAUSE: 17\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: succZ(T338, T337)\n\nT337 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: addC(T354, T355, T353)\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: addC(T354, T355, T353), SCOPE: 17, CLAUSE: 24 | addC(T354, T355, T353), SCOPE: 17, CLAUSE: 25 | addC(T354, T355, T353), SCOPE: 17, CLAUSE: 26 | addC(T354, T355, T353), SCOPE: 17, CLAUSE: 27\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: addC(T354, T355, T353), SCOPE: 17, CLAUSE: 24\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: addC(T354, T355, T353), SCOPE: 17, CLAUSE: 25 | addC(T354, T355, T353), SCOPE: 17, CLAUSE: 26 | addC(T354, T355, T353), SCOPE: 17, CLAUSE: 27\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: addz(T374, T375, T373)\n\nT373 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: addC(T354, T355, T353), SCOPE: 17, CLAUSE: 25\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: addC(T354, T355, T353), SCOPE: 17, CLAUSE: 26 | addC(T354, T355, T353), SCOPE: 17, CLAUSE: 27\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: addX(T394, T395, T393)\n\nT393 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: addX(T394, T395, T393), SCOPE: 18, CLAUSE: 18 | addX(T394, T395, T393), SCOPE: 18, CLAUSE: 19 | addX(T394, T395, T393), SCOPE: 18, CLAUSE: 20\n\nT393 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: addX(T394, T395, T393), SCOPE: 18, CLAUSE: 18\n\nT393 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: addX(T394, T395, T393), SCOPE: 18, CLAUSE: 19 | addX(T394, T395, T393), SCOPE: 18, CLAUSE: 20\n\nT393 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: binaryZ(T401)\n\nT401 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: addX(T394, T395, T393), SCOPE: 18, CLAUSE: 19\n\nT393 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: addX(T394, T395, T393), SCOPE: 18, CLAUSE: 20\n\nT393 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: succ(T413, T412)\n\nT412 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: addC(T428, T429, T427)\n\nT427 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: addC(T354, T355, T353), SCOPE: 17, CLAUSE: 26\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: addC(T354, T355, T353), SCOPE: 17, CLAUSE: 27\n\nT353 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: addY(T448, T449, T447)\n\nT447 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: addY(T448, T449, T447), SCOPE: 19, CLAUSE: 21 | addY(T448, T449, T447), SCOPE: 19, CLAUSE: 22 | addY(T448, T449, T447), SCOPE: 19, CLAUSE: 23\n\nT447 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: addY(T448, T449, T447), SCOPE: 19, CLAUSE: 21\n\nT447 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: addY(T448, T449, T447), SCOPE: 19, CLAUSE: 22 | addY(T448, T449, T447), SCOPE: 19, CLAUSE: 23\n\nT447 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: binaryZ(T455)\n\nT455 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: addY(T448, T449, T447), SCOPE: 19, CLAUSE: 22\n\nT447 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: addY(T448, T449, T447), SCOPE: 19, CLAUSE: 23\n\nT447 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: succ(T467, T466)\n\nT466 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: addC(T482, T483, T481)\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: addc(T496, T497, T495)\n\nT495 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: addz(T138, T139, T137), SCOPE: 10, CLAUSE: 11\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: addz(T138, T139, T137), SCOPE: 10, CLAUSE: 12 | addz(T138, T139, T137), SCOPE: 10, CLAUSE: 13\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: addx(T513, T514, T512)\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: addz(T138, T139, T137), SCOPE: 10, CLAUSE: 12\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: addz(T138, T139, T137), SCOPE: 10, CLAUSE: 13\n\nT137 is ground\nadd(T1, T2, T137) !=? add(b, b, b)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: addy(T531, T532, T530)\n\nT530 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: addc(T543, T544, T542)\n\nT542 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: binaryZ(T546) | add(T1, T2, T546), SCOPE: 1, CLAUSE: 3\n\nT546 is ground\nadd(T1, T2, T546) !=? add(b, b, b)\nadd(T1, T2, T546) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: add(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\nadd(T1, T2, T3) !=? add(b, b, b)\nadd(T1, T2, T3) !=? add(X118, b, X118)\nadd(T1, T2, T3) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: binaryZ(T546), SCOPE: 20, CLAUSE: 31 | binaryZ(T546), SCOPE: 20, CLAUSE: 32 | ?_20 | add(T1, T2, T546), SCOPE: 1, CLAUSE: 3\n\nT546 is ground\nadd(T1, T2, T546) !=? add(b, b, b)\nadd(T1, T2, T546) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: binaryZ(T546), SCOPE: 20, CLAUSE: 31\n\nT546 is ground\nadd(T1, T2, T546) !=? add(b, b, b)\nadd(T1, T2, T546) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: binaryZ(T546), SCOPE: 20, CLAUSE: 32 | ?_20 | add(T1, T2, T546), SCOPE: 1, CLAUSE: 3\n\nT546 is ground\nadd(T1, T2, T546) !=? add(b, b, b)\nadd(T1, T2, T546) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: binaryZ(T551)\n\nT551 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: binaryZ(T546), SCOPE: 20, CLAUSE: 32\n\nT546 is ground\nadd(T1, T2, T546) !=? add(b, b, b)\nadd(T1, T2, T546) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ?_20 | add(T1, T2, T546), SCOPE: 1, CLAUSE: 3\n\nT546 is ground\nadd(T1, T2, T546) !=? add(b, b, b)\nadd(T1, T2, T546) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: binary(T557)\n\nT557 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: add(T1, T2, T546), SCOPE: 1, CLAUSE: 3\n\nT546 is ground\nadd(T1, T2, T546) !=? add(b, b, b)\nadd(T1, T2, T546) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: addz(T572, T573, T571)\n\nT571 is ground\nadd(T1, T2, T571) !=? add(b, b, b)\nadd(T1, T2, T571) !=? add(X118, b, X118)", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: addz(T583, T584, T582)\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: addz(T583, T584, T582), SCOPE: 21, CLAUSE: 10 | addz(T583, T584, T582), SCOPE: 21, CLAUSE: 11 | addz(T583, T584, T582), SCOPE: 21, CLAUSE: 12 | addz(T583, T584, T582), SCOPE: 21, CLAUSE: 13\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: addz(T583, T584, T582), SCOPE: 21, CLAUSE: 10\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: addz(T583, T584, T582), SCOPE: 21, CLAUSE: 11 | addz(T583, T584, T582), SCOPE: 21, CLAUSE: 12 | addz(T583, T584, T582), SCOPE: 21, CLAUSE: 13\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: addz(T600, T601, T599)\n\nT599 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: addz(T583, T584, T582), SCOPE: 21, CLAUSE: 11\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: addz(T583, T584, T582), SCOPE: 21, CLAUSE: 12 | addz(T583, T584, T582), SCOPE: 21, CLAUSE: 13\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: addx(T620, T621, T619)\n\nT619 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: addz(T583, T584, T582), SCOPE: 21, CLAUSE: 12\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: addz(T583, T584, T582), SCOPE: 21, CLAUSE: 13\n\nT582 is ground\nadd(T1, T2, T582) !=? add(b, b, b)\nadd(T1, T2, T582) !=? add(X118, b, X118)\nadd(T1, T2, T582) !=? add(b, X586, X586)", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: addy(T638, T639, T637)\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: addc(T650, T651, T649)\n\nT649 is ground", 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 substitution\nT1 -> 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 = lightblue];
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(X118, b, X118) :- binaryZ(X118).\nand substitution\nT1 -> T88\nX118 -> T88\nT2 -> b\nT3 -> T88", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 226 [arrowhead = none ];
226 -> 38;

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

228 [label="EVAL with clause\nadd(X2, b, X2) :- binaryZ(X2).\nand substitution\nT1 -> 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 = lightblue];
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, X62, X62) :- binaryZ(X62).\nand substitution\nT1 -> b\nT2 -> b\nX62 -> b\nT46 -> b", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 231 [arrowhead = none ];
231 -> 25;

232 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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 = white];
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 = white];
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, X10, X10) :- binaryZ(X10).\nand substitution\nT1 -> b\nT2 -> b\nX10 -> b\nT10 -> b", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 238 [arrowhead = none ];
238 -> 14;

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

240 [label="ONLY EVAL with clause\nadd(X34, X35, X36) :- addz(X34, X35, X36).\nand substitution\nT1 -> T27\nX34 -> T27\nT2 -> T28\nX35 -> T28\nX36 -> b\nT25 -> T27\nT26 -> T28", fontsize=14, style = filled, fillcolor = white];
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 = white];
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 = white];
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 = white];
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 = white];
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 = white];
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 = white];
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(X102, X103, X104) :- addz(X102, X103, X104).\nand substitution\nT1 -> T77\nX102 -> T77\nT2 -> T78\nX103 -> T78\nX104 -> b\nT75 -> T77\nT76 -> T78", fontsize=14, style = filled, fillcolor = white];
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 = white];
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 = white];
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(X84, X85, X86) :- addz(X84, X85, X86).\nand substitution\nT1 -> T63\nX84 -> T63\nT2 -> T64\nX85 -> T64\nX86 -> b\nT61 -> T63\nT62 -> T64", fontsize=14, style = filled, fillcolor = white];
30 -> 254 [arrowhead = none ];
254 -> 31;

255 [label="INSTANCE with matching:\nT27 -> T63\nT28 -> T64", 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 = white];
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 = white];
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 = white];
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 = white];
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, X586, X586) :- binaryZ(X586).\nand substitution\nT1 -> b\nT2 -> T546\nX586 -> T546\nT3 -> T546", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 262 [arrowhead = none ];
262 -> 193;

263 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X124)) :- binaryZ(X124).\nand substitution\nX124 -> T93\nT88 -> zero(T93)", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 266 [arrowhead = none ];
266 -> 43;

267 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X131)) :- binaryZ(X131).\nand substitution\nX131 -> T99\nT93 -> zero(T99)", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 273 [arrowhead = none ];
273 -> 48;

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

275 [label="EVAL with clause\nbinaryZ(one(X136)) :- binary(X136).\nand substitution\nX136 -> T103\nT93 -> one(T103)", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 275 [arrowhead = none ];
275 -> 50;

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

277 [label="INSTANCE with matching:\nT93 -> T99", 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 substitution\nT103 -> b", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 281 [arrowhead = none ];
281 -> 55;

282 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X142)) :- binaryZ(X142).\nand substitution\nX142 -> T108\nT103 -> zero(T108)", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 286 [arrowhead = none ];
286 -> 60;

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

288 [label="EVAL with clause\nbinary(one(X147)) :- binary(X147).\nand substitution\nX147 -> T112\nT103 -> one(T112)", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 288 [arrowhead = none ];
288 -> 62;

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

290 [label="INSTANCE with matching:\nT93 -> T108", fontsize=14, style = filled, fillcolor = lightgrey];
60 -> 290 [arrowhead = none , style=dashed];
290 -> 43[style=dashed];

291 [label="INSTANCE with matching:\nT103 -> T112", fontsize=14, style = filled, fillcolor = lightgrey];
62 -> 291 [arrowhead = none , style=dashed];
291 -> 50[style=dashed];

292 [label="EVAL with clause\nbinaryZ(one(X153)) :- binary(X153).\nand substitution\nX153 -> T117\nT88 -> one(T117)", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 292 [arrowhead = none ];
292 -> 66;

293 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT103 -> T117", 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, X159, X159) :- binaryZ(X159).\nand substitution\nT1 -> b\nT2 -> T122\nX159 -> T122\nT88 -> T122", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 298 [arrowhead = none ];
298 -> 71;

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

300 [label="ONLY EVAL with clause\nadd(X171, X172, X173) :- addz(X171, X172, X173).\nand substitution\nT1 -> T138\nX171 -> T138\nT2 -> T139\nX172 -> T139\nT88 -> T137\nX173 -> T137\nT135 -> T138\nT136 -> T139", fontsize=14, style = filled, fillcolor = white];
70 -> 300 [arrowhead = none ];
300 -> 73;

301 [label="INSTANCE with matching:\nT93 -> T122", 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(X189), zero(X190), zero(X191)) :- addz(X189, X190, X191).\nand substitution\nX189 -> T158\nT138 -> zero(T158)\nX190 -> T159\nT139 -> zero(T159)\nX191 -> T157\nT137 -> zero(T157)\nT155 -> T158\nT156 -> T159", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 305 [arrowhead = none ];
305 -> 77;

306 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X210), zero(X211), zero(X212)) :- addz(X210, X211, X212).\nand substitution\nX210 -> T178\nT158 -> zero(T178)\nX211 -> T179\nT159 -> zero(T179)\nX212 -> T177\nT157 -> zero(T177)\nT175 -> T178\nT176 -> T179", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 312 [arrowhead = none ];
312 -> 82;

313 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT158 -> T178\nT159 -> T179\nT157 -> T177", fontsize=14, style = filled, fillcolor = lightgrey];
82 -> 316 [arrowhead = none , style=dashed];
316 -> 77[style=dashed];

317 [label="EVAL with clause\naddz(zero(X231), one(X232), one(X233)) :- addx(X231, X232, X233).\nand substitution\nX231 -> T198\nT158 -> zero(T198)\nX232 -> T199\nT159 -> one(T199)\nX233 -> T197\nT157 -> one(T197)\nT195 -> T198\nT196 -> T199", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 317 [arrowhead = none ];
317 -> 86;

318 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X242), b, one(X242)) :- binary(X242).\nand substitution\nX242 -> T205\nT198 -> one(T205)\nT199 -> b\nT197 -> one(T205)", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 324 [arrowhead = none ];
324 -> 91;

325 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT117 -> T205", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 328 [arrowhead = none , style=dashed];
328 -> 66[style=dashed];

329 [label="EVAL with clause\naddx(zero(X248), b, zero(X248)) :- binaryZ(X248).\nand substitution\nX248 -> T210\nT198 -> zero(T210)\nT199 -> b\nT197 -> zero(T210)", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 329 [arrowhead = none ];
329 -> 95;

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

331 [label="ONLY EVAL with clause\naddx(X260, X261, X262) :- addz(X260, X261, X262).\nand substitution\nT198 -> T226\nX260 -> T226\nT199 -> T227\nX261 -> T227\nT197 -> T225\nX262 -> T225\nT223 -> T226\nT224 -> T227", fontsize=14, style = filled, fillcolor = white];
94 -> 331 [arrowhead = none ];
331 -> 97;

332 [label="INSTANCE with matching:\nT93 -> T210", fontsize=14, style = filled, fillcolor = lightgrey];
95 -> 332 [arrowhead = none , style=dashed];
332 -> 43[style=dashed];

333 [label="INSTANCE with matching:\nT158 -> T226\nT159 -> T227\nT157 -> T225", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 333 [arrowhead = none , style=dashed];
333 -> 77[style=dashed];

334 [label="EVAL with clause\naddz(one(X278), zero(X279), one(X280)) :- addy(X278, X279, X280).\nand substitution\nX278 -> T246\nT158 -> one(T246)\nX279 -> T247\nT159 -> zero(T247)\nX280 -> T245\nT157 -> one(T245)\nT243 -> T246\nT244 -> T247", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 334 [arrowhead = none ];
334 -> 100;

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

336 [label="EVAL with clause\naddz(one(X319), one(X320), zero(X321)) :- addc(X319, X320, X321).\nand substitution\nX319 -> T288\nT158 -> one(T288)\nX320 -> T289\nT159 -> one(T289)\nX321 -> T287\nT157 -> zero(T287)\nT285 -> T288\nT286 -> T289", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 336 [arrowhead = none ];
336 -> 112;

337 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X289), one(X289)) :- binary(X289).\nand substitution\nT246 -> b\nX289 -> T253\nT247 -> one(T253)\nT245 -> one(T253)", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 341 [arrowhead = none ];
341 -> 105;

342 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT117 -> T253", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 345 [arrowhead = none , style=dashed];
345 -> 66[style=dashed];

346 [label="EVAL with clause\naddy(b, zero(X295), zero(X295)) :- binaryZ(X295).\nand substitution\nT246 -> b\nX295 -> T258\nT247 -> zero(T258)\nT245 -> zero(T258)", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 346 [arrowhead = none ];
346 -> 109;

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

348 [label="ONLY EVAL with clause\naddy(X307, X308, X309) :- addz(X307, X308, X309).\nand substitution\nT246 -> T274\nX307 -> T274\nT247 -> T275\nX308 -> T275\nT245 -> T273\nX309 -> T273\nT271 -> T274\nT272 -> T275", fontsize=14, style = filled, fillcolor = white];
108 -> 348 [arrowhead = none ];
348 -> 111;

349 [label="INSTANCE with matching:\nT93 -> T258", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 349 [arrowhead = none , style=dashed];
349 -> 43[style=dashed];

350 [label="INSTANCE with matching:\nT158 -> T274\nT159 -> T275\nT157 -> T273", 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 substitution\nT288 -> b\nT289 -> b\nT287 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 354 [arrowhead = none ];
354 -> 117;

355 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X333, b, X334) :- succZ(X333, X334).\nand substitution\nT288 -> T300\nX333 -> T300\nT289 -> b\nT287 -> T299\nX334 -> T299\nT298 -> T300", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 359 [arrowhead = none ];
359 -> 122;

360 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X342), one(X342)) :- binaryZ(X342).\nand substitution\nX342 -> T306\nT300 -> zero(T306)\nT299 -> one(T306)", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 366 [arrowhead = none ];
366 -> 127;

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

368 [label="EVAL with clause\nsuccZ(one(X349), zero(X350)) :- succ(X349, X350).\nand substitution\nX349 -> T314\nT300 -> one(T314)\nX350 -> T313\nT299 -> zero(T313)\nT312 -> T314", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 368 [arrowhead = none ];
368 -> 129;

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

370 [label="INSTANCE with matching:\nT93 -> T306", 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 substitution\nT314 -> b\nT313 -> one(b)", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 374 [arrowhead = none ];
374 -> 134;

375 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X357), one(X357)) :- binaryZ(X357).\nand substitution\nX357 -> T319\nT314 -> zero(T319)\nT313 -> one(T319)", fontsize=14, style = filled, fillcolor = lightblue];
137 -> 379 [arrowhead = none ];
379 -> 139;

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

381 [label="EVAL with clause\nsucc(one(X364), zero(X365)) :- succ(X364, X365).\nand substitution\nX364 -> T327\nT314 -> one(T327)\nX365 -> T326\nT313 -> zero(T326)\nT325 -> T327", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 381 [arrowhead = none ];
381 -> 141;

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

383 [label="INSTANCE with matching:\nT93 -> T319", fontsize=14, style = filled, fillcolor = lightgrey];
139 -> 383 [arrowhead = none , style=dashed];
383 -> 43[style=dashed];

384 [label="INSTANCE with matching:\nT314 -> T327\nT313 -> T326", fontsize=14, style = filled, fillcolor = lightgrey];
141 -> 384 [arrowhead = none , style=dashed];
384 -> 129[style=dashed];

385 [label="EVAL with clause\naddc(b, X376, X377) :- succZ(X376, X377).\nand substitution\nT288 -> b\nT289 -> T338\nX376 -> T338\nT287 -> T337\nX377 -> T337\nT336 -> T338", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 385 [arrowhead = none ];
385 -> 145;

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

387 [label="ONLY EVAL with clause\naddc(X390, X391, X392) :- addC(X390, X391, X392).\nand substitution\nT288 -> T354\nX390 -> T354\nT289 -> T355\nX391 -> T355\nT287 -> T353\nX392 -> T353\nT351 -> T354\nT352 -> T355", fontsize=14, style = filled, fillcolor = white];
144 -> 387 [arrowhead = none ];
387 -> 147;

388 [label="INSTANCE with matching:\nT300 -> T338\nT299 -> T337", 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(X408), zero(X409), one(X410)) :- addz(X408, X409, X410).\nand substitution\nX408 -> T374\nT354 -> zero(T374)\nX409 -> T375\nT355 -> zero(T375)\nX410 -> T373\nT353 -> one(T373)\nT371 -> T374\nT372 -> T375", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 392 [arrowhead = none ];
392 -> 151;

393 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT158 -> T374\nT159 -> T375\nT157 -> T373", fontsize=14, style = filled, fillcolor = lightgrey];
151 -> 396 [arrowhead = none , style=dashed];
396 -> 77[style=dashed];

397 [label="EVAL with clause\naddC(zero(X429), one(X430), zero(X431)) :- addX(X429, X430, X431).\nand substitution\nX429 -> T394\nT354 -> zero(T394)\nX430 -> T395\nT355 -> one(T395)\nX431 -> T393\nT353 -> zero(T393)\nT391 -> T394\nT392 -> T395", fontsize=14, style = filled, fillcolor = lightblue];
153 -> 397 [arrowhead = none ];
397 -> 155;

398 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X440), b, one(X440)) :- binaryZ(X440).\nand substitution\nX440 -> T401\nT394 -> zero(T401)\nT395 -> b\nT393 -> one(T401)", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 404 [arrowhead = none ];
404 -> 160;

405 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT93 -> T401", fontsize=14, style = filled, fillcolor = lightgrey];
160 -> 408 [arrowhead = none , style=dashed];
408 -> 43[style=dashed];

409 [label="EVAL with clause\naddX(one(X451), b, zero(X452)) :- succ(X451, X452).\nand substitution\nX451 -> T413\nT394 -> one(T413)\nT395 -> b\nX452 -> T412\nT393 -> zero(T412)\nT411 -> T413", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 409 [arrowhead = none ];
409 -> 164;

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

411 [label="ONLY EVAL with clause\naddX(X464, X465, X466) :- addC(X464, X465, X466).\nand substitution\nT394 -> T428\nX464 -> T428\nT395 -> T429\nX465 -> T429\nT393 -> T427\nX466 -> T427\nT425 -> T428\nT426 -> T429", fontsize=14, style = filled, fillcolor = white];
163 -> 411 [arrowhead = none ];
411 -> 166;

412 [label="INSTANCE with matching:\nT314 -> T413\nT313 -> T412", fontsize=14, style = filled, fillcolor = lightgrey];
164 -> 412 [arrowhead = none , style=dashed];
412 -> 129[style=dashed];

413 [label="INSTANCE with matching:\nT354 -> T428\nT355 -> T429\nT353 -> T427", fontsize=14, style = filled, fillcolor = lightgrey];
166 -> 413 [arrowhead = none , style=dashed];
413 -> 147[style=dashed];

414 [label="EVAL with clause\naddC(one(X482), zero(X483), zero(X484)) :- addY(X482, X483, X484).\nand substitution\nX482 -> T448\nT354 -> one(T448)\nX483 -> T449\nT355 -> zero(T449)\nX484 -> T447\nT353 -> zero(T447)\nT445 -> T448\nT446 -> T449", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 414 [arrowhead = none ];
414 -> 169;

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

416 [label="EVAL with clause\naddC(one(X529), one(X530), one(X531)) :- addc(X529, X530, X531).\nand substitution\nX529 -> T496\nT354 -> one(T496)\nX530 -> T497\nT355 -> one(T497)\nX531 -> T495\nT353 -> one(T495)\nT493 -> T496\nT494 -> T497", fontsize=14, style = filled, fillcolor = lightblue];
168 -> 416 [arrowhead = none ];
416 -> 181;

417 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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(X493), one(X493)) :- binaryZ(X493).\nand substitution\nT448 -> b\nX493 -> T455\nT449 -> zero(T455)\nT447 -> one(T455)", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 421 [arrowhead = none ];
421 -> 174;

422 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT93 -> T455", fontsize=14, style = filled, fillcolor = lightgrey];
174 -> 425 [arrowhead = none , style=dashed];
425 -> 43[style=dashed];

426 [label="EVAL with clause\naddY(b, one(X504), zero(X505)) :- succ(X504, X505).\nand substitution\nT448 -> b\nX504 -> T467\nT449 -> one(T467)\nX505 -> T466\nT447 -> zero(T466)\nT465 -> T467", fontsize=14, style = filled, fillcolor = lightblue];
176 -> 426 [arrowhead = none ];
426 -> 178;

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

428 [label="ONLY EVAL with clause\naddY(X517, X518, X519) :- addC(X517, X518, X519).\nand substitution\nT448 -> T482\nX517 -> T482\nT449 -> T483\nX518 -> T483\nT447 -> T481\nX519 -> T481\nT479 -> T482\nT480 -> T483", fontsize=14, style = filled, fillcolor = white];
177 -> 428 [arrowhead = none ];
428 -> 180;

429 [label="INSTANCE with matching:\nT314 -> T467\nT313 -> T466", fontsize=14, style = filled, fillcolor = lightgrey];
178 -> 429 [arrowhead = none , style=dashed];
429 -> 129[style=dashed];

430 [label="INSTANCE with matching:\nT354 -> T482\nT355 -> T483\nT353 -> T481", fontsize=14, style = filled, fillcolor = lightgrey];
180 -> 430 [arrowhead = none , style=dashed];
430 -> 147[style=dashed];

431 [label="INSTANCE with matching:\nT288 -> T496\nT289 -> T497\nT287 -> T495", fontsize=14, style = filled, fillcolor = lightgrey];
181 -> 431 [arrowhead = none , style=dashed];
431 -> 112[style=dashed];

432 [label="EVAL with clause\naddz(zero(X547), one(X548), one(X549)) :- addx(X547, X548, X549).\nand substitution\nX547 -> T513\nT138 -> zero(T513)\nX548 -> T514\nT139 -> one(T514)\nX549 -> T512\nT137 -> one(T512)\nT510 -> T513\nT511 -> T514", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 432 [arrowhead = none ];
432 -> 185;

433 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT198 -> T513\nT199 -> T514\nT197 -> T512", fontsize=14, style = filled, fillcolor = lightgrey];
185 -> 436 [arrowhead = none , style=dashed];
436 -> 86[style=dashed];

437 [label="EVAL with clause\naddz(one(X566), zero(X567), one(X568)) :- addy(X566, X567, X568).\nand substitution\nX566 -> T531\nT138 -> one(T531)\nX567 -> T532\nT139 -> zero(T532)\nX568 -> T530\nT137 -> one(T530)\nT528 -> T531\nT529 -> T532", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 437 [arrowhead = none ];
437 -> 189;

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

439 [label="EVAL with clause\naddz(one(X579), one(X580), zero(X581)) :- addc(X579, X580, X581).\nand substitution\nX579 -> T543\nT138 -> one(T543)\nX580 -> T544\nT139 -> one(T544)\nX581 -> T542\nT137 -> zero(T542)\nT540 -> T543\nT541 -> T544", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 439 [arrowhead = none ];
439 -> 191;

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

441 [label="INSTANCE with matching:\nT246 -> T531\nT247 -> T532\nT245 -> T530", fontsize=14, style = filled, fillcolor = lightgrey];
189 -> 441 [arrowhead = none , style=dashed];
441 -> 100[style=dashed];

442 [label="INSTANCE with matching:\nT288 -> T543\nT289 -> T544\nT287 -> T542", 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(X619, X620, X621) :- addz(X619, X620, X621).\nand substitution\nT1 -> T583\nX619 -> T583\nT2 -> T584\nX620 -> T584\nT3 -> T582\nX621 -> T582\nT580 -> T583\nT581 -> T584", fontsize=14, style = filled, fillcolor = white];
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(X592)) :- binaryZ(X592).\nand substitution\nX592 -> T551\nT546 -> zero(T551)", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 447 [arrowhead = none ];
447 -> 198;

448 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT93 -> T551", fontsize=14, style = filled, fillcolor = lightgrey];
198 -> 451 [arrowhead = none , style=dashed];
451 -> 43[style=dashed];

452 [label="EVAL with clause\nbinaryZ(one(X599)) :- binary(X599).\nand substitution\nX599 -> T557\nT546 -> one(T557)", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 452 [arrowhead = none ];
452 -> 202;

453 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT117 -> T557", fontsize=14, style = filled, fillcolor = lightgrey];
202 -> 455 [arrowhead = none , style=dashed];
455 -> 66[style=dashed];

456 [label="ONLY EVAL with clause\nadd(X610, X611, X612) :- addz(X610, X611, X612).\nand substitution\nT1 -> T572\nX610 -> T572\nT2 -> T573\nX611 -> T573\nT546 -> T571\nX612 -> T571\nT569 -> T572\nT570 -> T573", fontsize=14, style = filled, fillcolor = white];
204 -> 456 [arrowhead = none ];
456 -> 205;

457 [label="INSTANCE with matching:\nT138 -> T572\nT139 -> T573\nT137 -> T571", 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(X634), zero(X635), zero(X636)) :- addz(X634, X635, X636).\nand substitution\nX634 -> T600\nT583 -> zero(T600)\nX635 -> T601\nT584 -> zero(T601)\nX636 -> T599\nT582 -> zero(T599)\nT597 -> T600\nT598 -> T601", fontsize=14, style = filled, fillcolor = lightblue];
208 -> 461 [arrowhead = none ];
461 -> 210;

462 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT158 -> T600\nT159 -> T601\nT157 -> T599", fontsize=14, style = filled, fillcolor = lightgrey];
210 -> 465 [arrowhead = none , style=dashed];
465 -> 77[style=dashed];

466 [label="EVAL with clause\naddz(zero(X655), one(X656), one(X657)) :- addx(X655, X656, X657).\nand substitution\nX655 -> T620\nT583 -> zero(T620)\nX656 -> T621\nT584 -> one(T621)\nX657 -> T619\nT582 -> one(T619)\nT617 -> T620\nT618 -> T621", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 466 [arrowhead = none ];
466 -> 214;

467 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
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:\nT513 -> T620\nT514 -> T621\nT512 -> T619", fontsize=14, style = filled, fillcolor = lightgrey];
214 -> 470 [arrowhead = none , style=dashed];
470 -> 185[style=dashed];

471 [label="EVAL with clause\naddz(one(X674), zero(X675), one(X676)) :- addy(X674, X675, X676).\nand substitution\nX674 -> T638\nT583 -> one(T638)\nX675 -> T639\nT584 -> zero(T639)\nX676 -> T637\nT582 -> one(T637)\nT635 -> T638\nT636 -> T639", fontsize=14, style = filled, fillcolor = lightblue];
216 -> 471 [arrowhead = none ];
471 -> 218;

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

473 [label="EVAL with clause\naddz(one(X687), one(X688), zero(X689)) :- addc(X687, X688, X689).\nand substitution\nX687 -> T650\nT583 -> one(T650)\nX688 -> T651\nT584 -> one(T651)\nX689 -> T649\nT582 -> zero(T649)\nT647 -> T650\nT648 -> T651", fontsize=14, style = filled, fillcolor = lightblue];
217 -> 473 [arrowhead = none ];
473 -> 220;

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

475 [label="INSTANCE with matching:\nT531 -> T638\nT532 -> T639\nT530 -> T637", fontsize=14, style = filled, fillcolor = lightgrey];
218 -> 475 [arrowhead = none , style=dashed];
475 -> 189[style=dashed];

476 [label="INSTANCE with matching:\nT543 -> T650\nT544 -> T651\nT542 -> T649", fontsize=14, style = filled, fillcolor = lightgrey];
220 -> 476 [arrowhead = none , style=dashed];
476 -> 191[style=dashed];

}

(2) Obligation:

Clauses:

binaryZ43(zero(T99)) :- binaryZ43(T99).
binaryZ43(one(T103)) :- binary50(T103).
binary50(b).
binary50(zero(T108)) :- binaryZ43(T108).
binary50(one(T112)) :- binary50(T112).
addz77(zero(T178), zero(T179), zero(T177)) :- addz77(T178, T179, T177).
addz77(zero(T198), one(T199), one(T197)) :- addx86(T198, T199, T197).
addz77(one(T246), zero(T247), one(T245)) :- addy100(T246, T247, T245).
addz77(one(T288), one(T289), zero(T287)) :- addc112(T288, T289, T287).
succ129(b, one(b)).
succ129(zero(T319), one(T319)) :- binaryZ43(T319).
succ129(one(T327), zero(T326)) :- succ129(T327, T326).
succZ122(zero(T306), one(T306)) :- binaryZ43(T306).
succZ122(one(T314), zero(T313)) :- succ129(T314, T313).
addC147(zero(T374), zero(T375), one(T373)) :- addz77(T374, T375, T373).
addC147(zero(zero(T401)), one(b), zero(one(T401))) :- binaryZ43(T401).
addC147(zero(one(T413)), one(b), zero(zero(T412))) :- succ129(T413, T412).
addC147(zero(T428), one(T429), zero(T427)) :- addC147(T428, T429, T427).
addC147(one(b), zero(zero(T455)), zero(one(T455))) :- binaryZ43(T455).
addC147(one(b), zero(one(T467)), zero(zero(T466))) :- succ129(T467, T466).
addC147(one(T482), zero(T483), zero(T481)) :- addC147(T482, T483, T481).
addC147(one(T496), one(T497), one(T495)) :- addc112(T496, T497, T495).
addc112(b, b, one(b)).
addc112(T300, b, T299) :- succZ122(T300, T299).
addc112(b, T338, T337) :- succZ122(T338, T337).
addc112(T354, T355, T353) :- addC147(T354, T355, T353).
addx86(one(T205), b, one(T205)) :- binary50(T205).
addx86(zero(T210), b, zero(T210)) :- binaryZ43(T210).
addx86(T226, T227, T225) :- addz77(T226, T227, T225).
addy100(b, one(T253), one(T253)) :- binary50(T253).
addy100(b, zero(T258), zero(T258)) :- binaryZ43(T258).
addy100(T274, T275, T273) :- addz77(T274, T275, T273).
addz73(zero(T158), zero(T159), zero(T157)) :- addz77(T158, T159, T157).
addz73(zero(T513), one(T514), one(T512)) :- addx86(T513, T514, T512).
addz73(one(T531), zero(T532), one(T530)) :- addy100(T531, T532, T530).
addz73(one(T543), one(T544), zero(T542)) :- addc112(T543, T544, T542).
add1(b, b, b).
add1(zero(T93), b, zero(T93)) :- binaryZ43(T93).
add1(one(T117), b, one(T117)) :- binary50(T117).
add1(b, T122, T122) :- binaryZ43(T122).
add1(T138, T139, T137) :- addz73(T138, T139, T137).
add1(b, zero(T551), zero(T551)) :- binaryZ43(T551).
add1(b, one(T557), one(T557)) :- binary50(T557).
add1(T572, T573, T571) :- addz73(T572, T573, T571).
add1(zero(T600), zero(T601), zero(T599)) :- addz77(T600, T601, T599).
add1(zero(T620), one(T621), one(T619)) :- addx86(T620, T621, T619).
add1(one(T638), zero(T639), one(T637)) :- addy100(T638, T639, T637).
add1(one(T650), one(T651), zero(T649)) :- addc112(T650, T651, T649).

Queries:

add1(a,a,g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
add1_in: (f,f,b)
binaryZ43_in: (b)
binary50_in: (b)
addz73_in: (f,f,b)
addz77_in: (f,f,b)
addx86_in: (f,f,b)
addy100_in: (f,f,b)
addc112_in: (f,f,b)
succZ122_in: (f,b)
succ129_in: (f,b)
addC147_in: (f,f,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

add1_in_aag(b, b, b) → add1_out_aag(b, b, b)
add1_in_aag(zero(T93), b, zero(T93)) → U34_aag(T93, binaryZ43_in_g(T93))
binaryZ43_in_g(zero(T99)) → U1_g(T99, binaryZ43_in_g(T99))
binaryZ43_in_g(one(T103)) → U2_g(T103, binary50_in_g(T103))
binary50_in_g(b) → binary50_out_g(b)
binary50_in_g(zero(T108)) → U3_g(T108, binaryZ43_in_g(T108))
U3_g(T108, binaryZ43_out_g(T108)) → binary50_out_g(zero(T108))
binary50_in_g(one(T112)) → U4_g(T112, binary50_in_g(T112))
U4_g(T112, binary50_out_g(T112)) → binary50_out_g(one(T112))
U2_g(T103, binary50_out_g(T103)) → binaryZ43_out_g(one(T103))
U1_g(T99, binaryZ43_out_g(T99)) → binaryZ43_out_g(zero(T99))
U34_aag(T93, binaryZ43_out_g(T93)) → add1_out_aag(zero(T93), b, zero(T93))
add1_in_aag(one(T117), b, one(T117)) → U35_aag(T117, binary50_in_g(T117))
U35_aag(T117, binary50_out_g(T117)) → add1_out_aag(one(T117), b, one(T117))
add1_in_aag(b, T122, T122) → U36_aag(T122, binaryZ43_in_g(T122))
U36_aag(T122, binaryZ43_out_g(T122)) → add1_out_aag(b, T122, T122)
add1_in_aag(T138, T139, T137) → U37_aag(T138, T139, T137, addz73_in_aag(T138, T139, T137))
addz73_in_aag(zero(T158), zero(T159), zero(T157)) → U30_aag(T158, T159, T157, addz77_in_aag(T158, T159, T157))
addz77_in_aag(zero(T178), zero(T179), zero(T177)) → U5_aag(T178, T179, T177, addz77_in_aag(T178, T179, T177))
addz77_in_aag(zero(T198), one(T199), one(T197)) → U6_aag(T198, T199, T197, addx86_in_aag(T198, T199, T197))
addx86_in_aag(one(T205), b, one(T205)) → U24_aag(T205, binary50_in_g(T205))
U24_aag(T205, binary50_out_g(T205)) → addx86_out_aag(one(T205), b, one(T205))
addx86_in_aag(zero(T210), b, zero(T210)) → U25_aag(T210, binaryZ43_in_g(T210))
U25_aag(T210, binaryZ43_out_g(T210)) → addx86_out_aag(zero(T210), b, zero(T210))
addx86_in_aag(T226, T227, T225) → U26_aag(T226, T227, T225, addz77_in_aag(T226, T227, T225))
addz77_in_aag(one(T246), zero(T247), one(T245)) → U7_aag(T246, T247, T245, addy100_in_aag(T246, T247, T245))
addy100_in_aag(b, one(T253), one(T253)) → U27_aag(T253, binary50_in_g(T253))
U27_aag(T253, binary50_out_g(T253)) → addy100_out_aag(b, one(T253), one(T253))
addy100_in_aag(b, zero(T258), zero(T258)) → U28_aag(T258, binaryZ43_in_g(T258))
U28_aag(T258, binaryZ43_out_g(T258)) → addy100_out_aag(b, zero(T258), zero(T258))
addy100_in_aag(T274, T275, T273) → U29_aag(T274, T275, T273, addz77_in_aag(T274, T275, T273))
addz77_in_aag(one(T288), one(T289), zero(T287)) → U8_aag(T288, T289, T287, addc112_in_aag(T288, T289, T287))
addc112_in_aag(b, b, one(b)) → addc112_out_aag(b, b, one(b))
addc112_in_aag(T300, b, T299) → U21_aag(T300, T299, succZ122_in_ag(T300, T299))
succZ122_in_ag(zero(T306), one(T306)) → U11_ag(T306, binaryZ43_in_g(T306))
U11_ag(T306, binaryZ43_out_g(T306)) → succZ122_out_ag(zero(T306), one(T306))
succZ122_in_ag(one(T314), zero(T313)) → U12_ag(T314, T313, succ129_in_ag(T314, T313))
succ129_in_ag(b, one(b)) → succ129_out_ag(b, one(b))
succ129_in_ag(zero(T319), one(T319)) → U9_ag(T319, binaryZ43_in_g(T319))
U9_ag(T319, binaryZ43_out_g(T319)) → succ129_out_ag(zero(T319), one(T319))
succ129_in_ag(one(T327), zero(T326)) → U10_ag(T327, T326, succ129_in_ag(T327, T326))
U10_ag(T327, T326, succ129_out_ag(T327, T326)) → succ129_out_ag(one(T327), zero(T326))
U12_ag(T314, T313, succ129_out_ag(T314, T313)) → succZ122_out_ag(one(T314), zero(T313))
U21_aag(T300, T299, succZ122_out_ag(T300, T299)) → addc112_out_aag(T300, b, T299)
addc112_in_aag(b, T338, T337) → U22_aag(T338, T337, succZ122_in_ag(T338, T337))
U22_aag(T338, T337, succZ122_out_ag(T338, T337)) → addc112_out_aag(b, T338, T337)
addc112_in_aag(T354, T355, T353) → U23_aag(T354, T355, T353, addC147_in_aag(T354, T355, T353))
addC147_in_aag(zero(T374), zero(T375), one(T373)) → U13_aag(T374, T375, T373, addz77_in_aag(T374, T375, T373))
U13_aag(T374, T375, T373, addz77_out_aag(T374, T375, T373)) → addC147_out_aag(zero(T374), zero(T375), one(T373))
addC147_in_aag(zero(zero(T401)), one(b), zero(one(T401))) → U14_aag(T401, binaryZ43_in_g(T401))
U14_aag(T401, binaryZ43_out_g(T401)) → addC147_out_aag(zero(zero(T401)), one(b), zero(one(T401)))
addC147_in_aag(zero(one(T413)), one(b), zero(zero(T412))) → U15_aag(T413, T412, succ129_in_ag(T413, T412))
U15_aag(T413, T412, succ129_out_ag(T413, T412)) → addC147_out_aag(zero(one(T413)), one(b), zero(zero(T412)))
addC147_in_aag(zero(T428), one(T429), zero(T427)) → U16_aag(T428, T429, T427, addC147_in_aag(T428, T429, T427))
addC147_in_aag(one(b), zero(zero(T455)), zero(one(T455))) → U17_aag(T455, binaryZ43_in_g(T455))
U17_aag(T455, binaryZ43_out_g(T455)) → addC147_out_aag(one(b), zero(zero(T455)), zero(one(T455)))
addC147_in_aag(one(b), zero(one(T467)), zero(zero(T466))) → U18_aag(T467, T466, succ129_in_ag(T467, T466))
U18_aag(T467, T466, succ129_out_ag(T467, T466)) → addC147_out_aag(one(b), zero(one(T467)), zero(zero(T466)))
addC147_in_aag(one(T482), zero(T483), zero(T481)) → U19_aag(T482, T483, T481, addC147_in_aag(T482, T483, T481))
addC147_in_aag(one(T496), one(T497), one(T495)) → U20_aag(T496, T497, T495, addc112_in_aag(T496, T497, T495))
U20_aag(T496, T497, T495, addc112_out_aag(T496, T497, T495)) → addC147_out_aag(one(T496), one(T497), one(T495))
U19_aag(T482, T483, T481, addC147_out_aag(T482, T483, T481)) → addC147_out_aag(one(T482), zero(T483), zero(T481))
U16_aag(T428, T429, T427, addC147_out_aag(T428, T429, T427)) → addC147_out_aag(zero(T428), one(T429), zero(T427))
U23_aag(T354, T355, T353, addC147_out_aag(T354, T355, T353)) → addc112_out_aag(T354, T355, T353)
U8_aag(T288, T289, T287, addc112_out_aag(T288, T289, T287)) → addz77_out_aag(one(T288), one(T289), zero(T287))
U29_aag(T274, T275, T273, addz77_out_aag(T274, T275, T273)) → addy100_out_aag(T274, T275, T273)
U7_aag(T246, T247, T245, addy100_out_aag(T246, T247, T245)) → addz77_out_aag(one(T246), zero(T247), one(T245))
U26_aag(T226, T227, T225, addz77_out_aag(T226, T227, T225)) → addx86_out_aag(T226, T227, T225)
U6_aag(T198, T199, T197, addx86_out_aag(T198, T199, T197)) → addz77_out_aag(zero(T198), one(T199), one(T197))
U5_aag(T178, T179, T177, addz77_out_aag(T178, T179, T177)) → addz77_out_aag(zero(T178), zero(T179), zero(T177))
U30_aag(T158, T159, T157, addz77_out_aag(T158, T159, T157)) → addz73_out_aag(zero(T158), zero(T159), zero(T157))
addz73_in_aag(zero(T513), one(T514), one(T512)) → U31_aag(T513, T514, T512, addx86_in_aag(T513, T514, T512))
U31_aag(T513, T514, T512, addx86_out_aag(T513, T514, T512)) → addz73_out_aag(zero(T513), one(T514), one(T512))
addz73_in_aag(one(T531), zero(T532), one(T530)) → U32_aag(T531, T532, T530, addy100_in_aag(T531, T532, T530))
U32_aag(T531, T532, T530, addy100_out_aag(T531, T532, T530)) → addz73_out_aag(one(T531), zero(T532), one(T530))
addz73_in_aag(one(T543), one(T544), zero(T542)) → U33_aag(T543, T544, T542, addc112_in_aag(T543, T544, T542))
U33_aag(T543, T544, T542, addc112_out_aag(T543, T544, T542)) → addz73_out_aag(one(T543), one(T544), zero(T542))
U37_aag(T138, T139, T137, addz73_out_aag(T138, T139, T137)) → add1_out_aag(T138, T139, T137)
add1_in_aag(b, zero(T551), zero(T551)) → U38_aag(T551, binaryZ43_in_g(T551))
U38_aag(T551, binaryZ43_out_g(T551)) → add1_out_aag(b, zero(T551), zero(T551))
add1_in_aag(b, one(T557), one(T557)) → U39_aag(T557, binary50_in_g(T557))
U39_aag(T557, binary50_out_g(T557)) → add1_out_aag(b, one(T557), one(T557))
add1_in_aag(T572, T573, T571) → U40_aag(T572, T573, T571, addz73_in_aag(T572, T573, T571))
U40_aag(T572, T573, T571, addz73_out_aag(T572, T573, T571)) → add1_out_aag(T572, T573, T571)
add1_in_aag(zero(T600), zero(T601), zero(T599)) → U41_aag(T600, T601, T599, addz77_in_aag(T600, T601, T599))
U41_aag(T600, T601, T599, addz77_out_aag(T600, T601, T599)) → add1_out_aag(zero(T600), zero(T601), zero(T599))
add1_in_aag(zero(T620), one(T621), one(T619)) → U42_aag(T620, T621, T619, addx86_in_aag(T620, T621, T619))
U42_aag(T620, T621, T619, addx86_out_aag(T620, T621, T619)) → add1_out_aag(zero(T620), one(T621), one(T619))
add1_in_aag(one(T638), zero(T639), one(T637)) → U43_aag(T638, T639, T637, addy100_in_aag(T638, T639, T637))
U43_aag(T638, T639, T637, addy100_out_aag(T638, T639, T637)) → add1_out_aag(one(T638), zero(T639), one(T637))
add1_in_aag(one(T650), one(T651), zero(T649)) → U44_aag(T650, T651, T649, addc112_in_aag(T650, T651, T649))
U44_aag(T650, T651, T649, addc112_out_aag(T650, T651, T649)) → add1_out_aag(one(T650), one(T651), zero(T649))

The argument filtering Pi contains the following mapping:
add1_in_aag(x1, x2, x3)  =  add1_in_aag(x3)
b  =  b
add1_out_aag(x1, x2, x3)  =  add1_out_aag(x1, x2, x3)
zero(x1)  =  zero(x1)
U34_aag(x1, x2)  =  U34_aag(x1, x2)
binaryZ43_in_g(x1)  =  binaryZ43_in_g(x1)
U1_g(x1, x2)  =  U1_g(x1, x2)
one(x1)  =  one(x1)
U2_g(x1, x2)  =  U2_g(x1, x2)
binary50_in_g(x1)  =  binary50_in_g(x1)
binary50_out_g(x1)  =  binary50_out_g(x1)
U3_g(x1, x2)  =  U3_g(x1, x2)
binaryZ43_out_g(x1)  =  binaryZ43_out_g(x1)
U4_g(x1, x2)  =  U4_g(x1, 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(x3, x4)
addz73_in_aag(x1, x2, x3)  =  addz73_in_aag(x3)
U30_aag(x1, x2, x3, x4)  =  U30_aag(x3, x4)
addz77_in_aag(x1, x2, x3)  =  addz77_in_aag(x3)
U5_aag(x1, x2, x3, x4)  =  U5_aag(x3, x4)
U6_aag(x1, x2, x3, x4)  =  U6_aag(x3, x4)
addx86_in_aag(x1, x2, x3)  =  addx86_in_aag(x3)
U24_aag(x1, x2)  =  U24_aag(x1, x2)
addx86_out_aag(x1, x2, x3)  =  addx86_out_aag(x1, x2, x3)
U25_aag(x1, x2)  =  U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x3, x4)
U7_aag(x1, x2, x3, x4)  =  U7_aag(x3, x4)
addy100_in_aag(x1, x2, x3)  =  addy100_in_aag(x3)
U27_aag(x1, x2)  =  U27_aag(x1, x2)
addy100_out_aag(x1, x2, x3)  =  addy100_out_aag(x1, x2, x3)
U28_aag(x1, x2)  =  U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4)  =  U29_aag(x3, x4)
U8_aag(x1, x2, x3, x4)  =  U8_aag(x3, x4)
addc112_in_aag(x1, x2, x3)  =  addc112_in_aag(x3)
addc112_out_aag(x1, x2, x3)  =  addc112_out_aag(x1, x2, x3)
U21_aag(x1, x2, x3)  =  U21_aag(x2, x3)
succZ122_in_ag(x1, x2)  =  succZ122_in_ag(x2)
U11_ag(x1, x2)  =  U11_ag(x1, x2)
succZ122_out_ag(x1, x2)  =  succZ122_out_ag(x1, x2)
U12_ag(x1, x2, x3)  =  U12_ag(x2, x3)
succ129_in_ag(x1, x2)  =  succ129_in_ag(x2)
succ129_out_ag(x1, x2)  =  succ129_out_ag(x1, x2)
U9_ag(x1, x2)  =  U9_ag(x1, x2)
U10_ag(x1, x2, x3)  =  U10_ag(x2, x3)
U22_aag(x1, x2, x3)  =  U22_aag(x2, x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x3, x4)
addC147_in_aag(x1, x2, x3)  =  addC147_in_aag(x3)
U13_aag(x1, x2, x3, x4)  =  U13_aag(x3, x4)
addz77_out_aag(x1, x2, x3)  =  addz77_out_aag(x1, x2, x3)
addC147_out_aag(x1, x2, x3)  =  addC147_out_aag(x1, x2, x3)
U14_aag(x1, x2)  =  U14_aag(x1, x2)
U15_aag(x1, x2, x3)  =  U15_aag(x2, x3)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x3, x4)
U17_aag(x1, x2)  =  U17_aag(x1, x2)
U18_aag(x1, x2, x3)  =  U18_aag(x2, x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x3, x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x3, x4)
addz73_out_aag(x1, x2, x3)  =  addz73_out_aag(x1, x2, x3)
U31_aag(x1, x2, x3, x4)  =  U31_aag(x3, x4)
U32_aag(x1, x2, x3, x4)  =  U32_aag(x3, x4)
U33_aag(x1, x2, x3, x4)  =  U33_aag(x3, 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(x3, x4)
U41_aag(x1, x2, x3, x4)  =  U41_aag(x3, x4)
U42_aag(x1, x2, x3, x4)  =  U42_aag(x3, x4)
U43_aag(x1, x2, x3, x4)  =  U43_aag(x3, x4)
U44_aag(x1, x2, x3, x4)  =  U44_aag(x3, x4)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

add1_in_aag(b, b, b) → add1_out_aag(b, b, b)
add1_in_aag(zero(T93), b, zero(T93)) → U34_aag(T93, binaryZ43_in_g(T93))
binaryZ43_in_g(zero(T99)) → U1_g(T99, binaryZ43_in_g(T99))
binaryZ43_in_g(one(T103)) → U2_g(T103, binary50_in_g(T103))
binary50_in_g(b) → binary50_out_g(b)
binary50_in_g(zero(T108)) → U3_g(T108, binaryZ43_in_g(T108))
U3_g(T108, binaryZ43_out_g(T108)) → binary50_out_g(zero(T108))
binary50_in_g(one(T112)) → U4_g(T112, binary50_in_g(T112))
U4_g(T112, binary50_out_g(T112)) → binary50_out_g(one(T112))
U2_g(T103, binary50_out_g(T103)) → binaryZ43_out_g(one(T103))
U1_g(T99, binaryZ43_out_g(T99)) → binaryZ43_out_g(zero(T99))
U34_aag(T93, binaryZ43_out_g(T93)) → add1_out_aag(zero(T93), b, zero(T93))
add1_in_aag(one(T117), b, one(T117)) → U35_aag(T117, binary50_in_g(T117))
U35_aag(T117, binary50_out_g(T117)) → add1_out_aag(one(T117), b, one(T117))
add1_in_aag(b, T122, T122) → U36_aag(T122, binaryZ43_in_g(T122))
U36_aag(T122, binaryZ43_out_g(T122)) → add1_out_aag(b, T122, T122)
add1_in_aag(T138, T139, T137) → U37_aag(T138, T139, T137, addz73_in_aag(T138, T139, T137))
addz73_in_aag(zero(T158), zero(T159), zero(T157)) → U30_aag(T158, T159, T157, addz77_in_aag(T158, T159, T157))
addz77_in_aag(zero(T178), zero(T179), zero(T177)) → U5_aag(T178, T179, T177, addz77_in_aag(T178, T179, T177))
addz77_in_aag(zero(T198), one(T199), one(T197)) → U6_aag(T198, T199, T197, addx86_in_aag(T198, T199, T197))
addx86_in_aag(one(T205), b, one(T205)) → U24_aag(T205, binary50_in_g(T205))
U24_aag(T205, binary50_out_g(T205)) → addx86_out_aag(one(T205), b, one(T205))
addx86_in_aag(zero(T210), b, zero(T210)) → U25_aag(T210, binaryZ43_in_g(T210))
U25_aag(T210, binaryZ43_out_g(T210)) → addx86_out_aag(zero(T210), b, zero(T210))
addx86_in_aag(T226, T227, T225) → U26_aag(T226, T227, T225, addz77_in_aag(T226, T227, T225))
addz77_in_aag(one(T246), zero(T247), one(T245)) → U7_aag(T246, T247, T245, addy100_in_aag(T246, T247, T245))
addy100_in_aag(b, one(T253), one(T253)) → U27_aag(T253, binary50_in_g(T253))
U27_aag(T253, binary50_out_g(T253)) → addy100_out_aag(b, one(T253), one(T253))
addy100_in_aag(b, zero(T258), zero(T258)) → U28_aag(T258, binaryZ43_in_g(T258))
U28_aag(T258, binaryZ43_out_g(T258)) → addy100_out_aag(b, zero(T258), zero(T258))
addy100_in_aag(T274, T275, T273) → U29_aag(T274, T275, T273, addz77_in_aag(T274, T275, T273))
addz77_in_aag(one(T288), one(T289), zero(T287)) → U8_aag(T288, T289, T287, addc112_in_aag(T288, T289, T287))
addc112_in_aag(b, b, one(b)) → addc112_out_aag(b, b, one(b))
addc112_in_aag(T300, b, T299) → U21_aag(T300, T299, succZ122_in_ag(T300, T299))
succZ122_in_ag(zero(T306), one(T306)) → U11_ag(T306, binaryZ43_in_g(T306))
U11_ag(T306, binaryZ43_out_g(T306)) → succZ122_out_ag(zero(T306), one(T306))
succZ122_in_ag(one(T314), zero(T313)) → U12_ag(T314, T313, succ129_in_ag(T314, T313))
succ129_in_ag(b, one(b)) → succ129_out_ag(b, one(b))
succ129_in_ag(zero(T319), one(T319)) → U9_ag(T319, binaryZ43_in_g(T319))
U9_ag(T319, binaryZ43_out_g(T319)) → succ129_out_ag(zero(T319), one(T319))
succ129_in_ag(one(T327), zero(T326)) → U10_ag(T327, T326, succ129_in_ag(T327, T326))
U10_ag(T327, T326, succ129_out_ag(T327, T326)) → succ129_out_ag(one(T327), zero(T326))
U12_ag(T314, T313, succ129_out_ag(T314, T313)) → succZ122_out_ag(one(T314), zero(T313))
U21_aag(T300, T299, succZ122_out_ag(T300, T299)) → addc112_out_aag(T300, b, T299)
addc112_in_aag(b, T338, T337) → U22_aag(T338, T337, succZ122_in_ag(T338, T337))
U22_aag(T338, T337, succZ122_out_ag(T338, T337)) → addc112_out_aag(b, T338, T337)
addc112_in_aag(T354, T355, T353) → U23_aag(T354, T355, T353, addC147_in_aag(T354, T355, T353))
addC147_in_aag(zero(T374), zero(T375), one(T373)) → U13_aag(T374, T375, T373, addz77_in_aag(T374, T375, T373))
U13_aag(T374, T375, T373, addz77_out_aag(T374, T375, T373)) → addC147_out_aag(zero(T374), zero(T375), one(T373))
addC147_in_aag(zero(zero(T401)), one(b), zero(one(T401))) → U14_aag(T401, binaryZ43_in_g(T401))
U14_aag(T401, binaryZ43_out_g(T401)) → addC147_out_aag(zero(zero(T401)), one(b), zero(one(T401)))
addC147_in_aag(zero(one(T413)), one(b), zero(zero(T412))) → U15_aag(T413, T412, succ129_in_ag(T413, T412))
U15_aag(T413, T412, succ129_out_ag(T413, T412)) → addC147_out_aag(zero(one(T413)), one(b), zero(zero(T412)))
addC147_in_aag(zero(T428), one(T429), zero(T427)) → U16_aag(T428, T429, T427, addC147_in_aag(T428, T429, T427))
addC147_in_aag(one(b), zero(zero(T455)), zero(one(T455))) → U17_aag(T455, binaryZ43_in_g(T455))
U17_aag(T455, binaryZ43_out_g(T455)) → addC147_out_aag(one(b), zero(zero(T455)), zero(one(T455)))
addC147_in_aag(one(b), zero(one(T467)), zero(zero(T466))) → U18_aag(T467, T466, succ129_in_ag(T467, T466))
U18_aag(T467, T466, succ129_out_ag(T467, T466)) → addC147_out_aag(one(b), zero(one(T467)), zero(zero(T466)))
addC147_in_aag(one(T482), zero(T483), zero(T481)) → U19_aag(T482, T483, T481, addC147_in_aag(T482, T483, T481))
addC147_in_aag(one(T496), one(T497), one(T495)) → U20_aag(T496, T497, T495, addc112_in_aag(T496, T497, T495))
U20_aag(T496, T497, T495, addc112_out_aag(T496, T497, T495)) → addC147_out_aag(one(T496), one(T497), one(T495))
U19_aag(T482, T483, T481, addC147_out_aag(T482, T483, T481)) → addC147_out_aag(one(T482), zero(T483), zero(T481))
U16_aag(T428, T429, T427, addC147_out_aag(T428, T429, T427)) → addC147_out_aag(zero(T428), one(T429), zero(T427))
U23_aag(T354, T355, T353, addC147_out_aag(T354, T355, T353)) → addc112_out_aag(T354, T355, T353)
U8_aag(T288, T289, T287, addc112_out_aag(T288, T289, T287)) → addz77_out_aag(one(T288), one(T289), zero(T287))
U29_aag(T274, T275, T273, addz77_out_aag(T274, T275, T273)) → addy100_out_aag(T274, T275, T273)
U7_aag(T246, T247, T245, addy100_out_aag(T246, T247, T245)) → addz77_out_aag(one(T246), zero(T247), one(T245))
U26_aag(T226, T227, T225, addz77_out_aag(T226, T227, T225)) → addx86_out_aag(T226, T227, T225)
U6_aag(T198, T199, T197, addx86_out_aag(T198, T199, T197)) → addz77_out_aag(zero(T198), one(T199), one(T197))
U5_aag(T178, T179, T177, addz77_out_aag(T178, T179, T177)) → addz77_out_aag(zero(T178), zero(T179), zero(T177))
U30_aag(T158, T159, T157, addz77_out_aag(T158, T159, T157)) → addz73_out_aag(zero(T158), zero(T159), zero(T157))
addz73_in_aag(zero(T513), one(T514), one(T512)) → U31_aag(T513, T514, T512, addx86_in_aag(T513, T514, T512))
U31_aag(T513, T514, T512, addx86_out_aag(T513, T514, T512)) → addz73_out_aag(zero(T513), one(T514), one(T512))
addz73_in_aag(one(T531), zero(T532), one(T530)) → U32_aag(T531, T532, T530, addy100_in_aag(T531, T532, T530))
U32_aag(T531, T532, T530, addy100_out_aag(T531, T532, T530)) → addz73_out_aag(one(T531), zero(T532), one(T530))
addz73_in_aag(one(T543), one(T544), zero(T542)) → U33_aag(T543, T544, T542, addc112_in_aag(T543, T544, T542))
U33_aag(T543, T544, T542, addc112_out_aag(T543, T544, T542)) → addz73_out_aag(one(T543), one(T544), zero(T542))
U37_aag(T138, T139, T137, addz73_out_aag(T138, T139, T137)) → add1_out_aag(T138, T139, T137)
add1_in_aag(b, zero(T551), zero(T551)) → U38_aag(T551, binaryZ43_in_g(T551))
U38_aag(T551, binaryZ43_out_g(T551)) → add1_out_aag(b, zero(T551), zero(T551))
add1_in_aag(b, one(T557), one(T557)) → U39_aag(T557, binary50_in_g(T557))
U39_aag(T557, binary50_out_g(T557)) → add1_out_aag(b, one(T557), one(T557))
add1_in_aag(T572, T573, T571) → U40_aag(T572, T573, T571, addz73_in_aag(T572, T573, T571))
U40_aag(T572, T573, T571, addz73_out_aag(T572, T573, T571)) → add1_out_aag(T572, T573, T571)
add1_in_aag(zero(T600), zero(T601), zero(T599)) → U41_aag(T600, T601, T599, addz77_in_aag(T600, T601, T599))
U41_aag(T600, T601, T599, addz77_out_aag(T600, T601, T599)) → add1_out_aag(zero(T600), zero(T601), zero(T599))
add1_in_aag(zero(T620), one(T621), one(T619)) → U42_aag(T620, T621, T619, addx86_in_aag(T620, T621, T619))
U42_aag(T620, T621, T619, addx86_out_aag(T620, T621, T619)) → add1_out_aag(zero(T620), one(T621), one(T619))
add1_in_aag(one(T638), zero(T639), one(T637)) → U43_aag(T638, T639, T637, addy100_in_aag(T638, T639, T637))
U43_aag(T638, T639, T637, addy100_out_aag(T638, T639, T637)) → add1_out_aag(one(T638), zero(T639), one(T637))
add1_in_aag(one(T650), one(T651), zero(T649)) → U44_aag(T650, T651, T649, addc112_in_aag(T650, T651, T649))
U44_aag(T650, T651, T649, addc112_out_aag(T650, T651, T649)) → add1_out_aag(one(T650), one(T651), zero(T649))

The argument filtering Pi contains the following mapping:
add1_in_aag(x1, x2, x3)  =  add1_in_aag(x3)
b  =  b
add1_out_aag(x1, x2, x3)  =  add1_out_aag(x1, x2, x3)
zero(x1)  =  zero(x1)
U34_aag(x1, x2)  =  U34_aag(x1, x2)
binaryZ43_in_g(x1)  =  binaryZ43_in_g(x1)
U1_g(x1, x2)  =  U1_g(x1, x2)
one(x1)  =  one(x1)
U2_g(x1, x2)  =  U2_g(x1, x2)
binary50_in_g(x1)  =  binary50_in_g(x1)
binary50_out_g(x1)  =  binary50_out_g(x1)
U3_g(x1, x2)  =  U3_g(x1, x2)
binaryZ43_out_g(x1)  =  binaryZ43_out_g(x1)
U4_g(x1, x2)  =  U4_g(x1, 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(x3, x4)
addz73_in_aag(x1, x2, x3)  =  addz73_in_aag(x3)
U30_aag(x1, x2, x3, x4)  =  U30_aag(x3, x4)
addz77_in_aag(x1, x2, x3)  =  addz77_in_aag(x3)
U5_aag(x1, x2, x3, x4)  =  U5_aag(x3, x4)
U6_aag(x1, x2, x3, x4)  =  U6_aag(x3, x4)
addx86_in_aag(x1, x2, x3)  =  addx86_in_aag(x3)
U24_aag(x1, x2)  =  U24_aag(x1, x2)
addx86_out_aag(x1, x2, x3)  =  addx86_out_aag(x1, x2, x3)
U25_aag(x1, x2)  =  U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x3, x4)
U7_aag(x1, x2, x3, x4)  =  U7_aag(x3, x4)
addy100_in_aag(x1, x2, x3)  =  addy100_in_aag(x3)
U27_aag(x1, x2)  =  U27_aag(x1, x2)
addy100_out_aag(x1, x2, x3)  =  addy100_out_aag(x1, x2, x3)
U28_aag(x1, x2)  =  U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4)  =  U29_aag(x3, x4)
U8_aag(x1, x2, x3, x4)  =  U8_aag(x3, x4)
addc112_in_aag(x1, x2, x3)  =  addc112_in_aag(x3)
addc112_out_aag(x1, x2, x3)  =  addc112_out_aag(x1, x2, x3)
U21_aag(x1, x2, x3)  =  U21_aag(x2, x3)
succZ122_in_ag(x1, x2)  =  succZ122_in_ag(x2)
U11_ag(x1, x2)  =  U11_ag(x1, x2)
succZ122_out_ag(x1, x2)  =  succZ122_out_ag(x1, x2)
U12_ag(x1, x2, x3)  =  U12_ag(x2, x3)
succ129_in_ag(x1, x2)  =  succ129_in_ag(x2)
succ129_out_ag(x1, x2)  =  succ129_out_ag(x1, x2)
U9_ag(x1, x2)  =  U9_ag(x1, x2)
U10_ag(x1, x2, x3)  =  U10_ag(x2, x3)
U22_aag(x1, x2, x3)  =  U22_aag(x2, x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x3, x4)
addC147_in_aag(x1, x2, x3)  =  addC147_in_aag(x3)
U13_aag(x1, x2, x3, x4)  =  U13_aag(x3, x4)
addz77_out_aag(x1, x2, x3)  =  addz77_out_aag(x1, x2, x3)
addC147_out_aag(x1, x2, x3)  =  addC147_out_aag(x1, x2, x3)
U14_aag(x1, x2)  =  U14_aag(x1, x2)
U15_aag(x1, x2, x3)  =  U15_aag(x2, x3)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x3, x4)
U17_aag(x1, x2)  =  U17_aag(x1, x2)
U18_aag(x1, x2, x3)  =  U18_aag(x2, x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x3, x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x3, x4)
addz73_out_aag(x1, x2, x3)  =  addz73_out_aag(x1, x2, x3)
U31_aag(x1, x2, x3, x4)  =  U31_aag(x3, x4)
U32_aag(x1, x2, x3, x4)  =  U32_aag(x3, x4)
U33_aag(x1, x2, x3, x4)  =  U33_aag(x3, 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(x3, x4)
U41_aag(x1, x2, x3, x4)  =  U41_aag(x3, x4)
U42_aag(x1, x2, x3, x4)  =  U42_aag(x3, x4)
U43_aag(x1, x2, x3, x4)  =  U43_aag(x3, x4)
U44_aag(x1, x2, x3, x4)  =  U44_aag(x3, x4)

(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:

ADD1_IN_AAG(zero(T93), b, zero(T93)) → U34_AAG(T93, binaryZ43_in_g(T93))
ADD1_IN_AAG(zero(T93), b, zero(T93)) → BINARYZ43_IN_G(T93)
BINARYZ43_IN_G(zero(T99)) → U1_G(T99, binaryZ43_in_g(T99))
BINARYZ43_IN_G(zero(T99)) → BINARYZ43_IN_G(T99)
BINARYZ43_IN_G(one(T103)) → U2_G(T103, binary50_in_g(T103))
BINARYZ43_IN_G(one(T103)) → BINARY50_IN_G(T103)
BINARY50_IN_G(zero(T108)) → U3_G(T108, binaryZ43_in_g(T108))
BINARY50_IN_G(zero(T108)) → BINARYZ43_IN_G(T108)
BINARY50_IN_G(one(T112)) → U4_G(T112, binary50_in_g(T112))
BINARY50_IN_G(one(T112)) → BINARY50_IN_G(T112)
ADD1_IN_AAG(one(T117), b, one(T117)) → U35_AAG(T117, binary50_in_g(T117))
ADD1_IN_AAG(one(T117), b, one(T117)) → BINARY50_IN_G(T117)
ADD1_IN_AAG(b, T122, T122) → U36_AAG(T122, binaryZ43_in_g(T122))
ADD1_IN_AAG(b, T122, T122) → BINARYZ43_IN_G(T122)
ADD1_IN_AAG(T138, T139, T137) → U37_AAG(T138, T139, T137, addz73_in_aag(T138, T139, T137))
ADD1_IN_AAG(T138, T139, T137) → ADDZ73_IN_AAG(T138, T139, T137)
ADDZ73_IN_AAG(zero(T158), zero(T159), zero(T157)) → U30_AAG(T158, T159, T157, addz77_in_aag(T158, T159, T157))
ADDZ73_IN_AAG(zero(T158), zero(T159), zero(T157)) → ADDZ77_IN_AAG(T158, T159, T157)
ADDZ77_IN_AAG(zero(T178), zero(T179), zero(T177)) → U5_AAG(T178, T179, T177, addz77_in_aag(T178, T179, T177))
ADDZ77_IN_AAG(zero(T178), zero(T179), zero(T177)) → ADDZ77_IN_AAG(T178, T179, T177)
ADDZ77_IN_AAG(zero(T198), one(T199), one(T197)) → U6_AAG(T198, T199, T197, addx86_in_aag(T198, T199, T197))
ADDZ77_IN_AAG(zero(T198), one(T199), one(T197)) → ADDX86_IN_AAG(T198, T199, T197)
ADDX86_IN_AAG(one(T205), b, one(T205)) → U24_AAG(T205, binary50_in_g(T205))
ADDX86_IN_AAG(one(T205), b, one(T205)) → BINARY50_IN_G(T205)
ADDX86_IN_AAG(zero(T210), b, zero(T210)) → U25_AAG(T210, binaryZ43_in_g(T210))
ADDX86_IN_AAG(zero(T210), b, zero(T210)) → BINARYZ43_IN_G(T210)
ADDX86_IN_AAG(T226, T227, T225) → U26_AAG(T226, T227, T225, addz77_in_aag(T226, T227, T225))
ADDX86_IN_AAG(T226, T227, T225) → ADDZ77_IN_AAG(T226, T227, T225)
ADDZ77_IN_AAG(one(T246), zero(T247), one(T245)) → U7_AAG(T246, T247, T245, addy100_in_aag(T246, T247, T245))
ADDZ77_IN_AAG(one(T246), zero(T247), one(T245)) → ADDY100_IN_AAG(T246, T247, T245)
ADDY100_IN_AAG(b, one(T253), one(T253)) → U27_AAG(T253, binary50_in_g(T253))
ADDY100_IN_AAG(b, one(T253), one(T253)) → BINARY50_IN_G(T253)
ADDY100_IN_AAG(b, zero(T258), zero(T258)) → U28_AAG(T258, binaryZ43_in_g(T258))
ADDY100_IN_AAG(b, zero(T258), zero(T258)) → BINARYZ43_IN_G(T258)
ADDY100_IN_AAG(T274, T275, T273) → U29_AAG(T274, T275, T273, addz77_in_aag(T274, T275, T273))
ADDY100_IN_AAG(T274, T275, T273) → ADDZ77_IN_AAG(T274, T275, T273)
ADDZ77_IN_AAG(one(T288), one(T289), zero(T287)) → U8_AAG(T288, T289, T287, addc112_in_aag(T288, T289, T287))
ADDZ77_IN_AAG(one(T288), one(T289), zero(T287)) → ADDC112_IN_AAG(T288, T289, T287)
ADDC112_IN_AAG(T300, b, T299) → U21_AAG(T300, T299, succZ122_in_ag(T300, T299))
ADDC112_IN_AAG(T300, b, T299) → SUCCZ122_IN_AG(T300, T299)
SUCCZ122_IN_AG(zero(T306), one(T306)) → U11_AG(T306, binaryZ43_in_g(T306))
SUCCZ122_IN_AG(zero(T306), one(T306)) → BINARYZ43_IN_G(T306)
SUCCZ122_IN_AG(one(T314), zero(T313)) → U12_AG(T314, T313, succ129_in_ag(T314, T313))
SUCCZ122_IN_AG(one(T314), zero(T313)) → SUCC129_IN_AG(T314, T313)
SUCC129_IN_AG(zero(T319), one(T319)) → U9_AG(T319, binaryZ43_in_g(T319))
SUCC129_IN_AG(zero(T319), one(T319)) → BINARYZ43_IN_G(T319)
SUCC129_IN_AG(one(T327), zero(T326)) → U10_AG(T327, T326, succ129_in_ag(T327, T326))
SUCC129_IN_AG(one(T327), zero(T326)) → SUCC129_IN_AG(T327, T326)
ADDC112_IN_AAG(b, T338, T337) → U22_AAG(T338, T337, succZ122_in_ag(T338, T337))
ADDC112_IN_AAG(b, T338, T337) → SUCCZ122_IN_AG(T338, T337)
ADDC112_IN_AAG(T354, T355, T353) → U23_AAG(T354, T355, T353, addC147_in_aag(T354, T355, T353))
ADDC112_IN_AAG(T354, T355, T353) → ADDC147_IN_AAG(T354, T355, T353)
ADDC147_IN_AAG(zero(T374), zero(T375), one(T373)) → U13_AAG(T374, T375, T373, addz77_in_aag(T374, T375, T373))
ADDC147_IN_AAG(zero(T374), zero(T375), one(T373)) → ADDZ77_IN_AAG(T374, T375, T373)
ADDC147_IN_AAG(zero(zero(T401)), one(b), zero(one(T401))) → U14_AAG(T401, binaryZ43_in_g(T401))
ADDC147_IN_AAG(zero(zero(T401)), one(b), zero(one(T401))) → BINARYZ43_IN_G(T401)
ADDC147_IN_AAG(zero(one(T413)), one(b), zero(zero(T412))) → U15_AAG(T413, T412, succ129_in_ag(T413, T412))
ADDC147_IN_AAG(zero(one(T413)), one(b), zero(zero(T412))) → SUCC129_IN_AG(T413, T412)
ADDC147_IN_AAG(zero(T428), one(T429), zero(T427)) → U16_AAG(T428, T429, T427, addC147_in_aag(T428, T429, T427))
ADDC147_IN_AAG(zero(T428), one(T429), zero(T427)) → ADDC147_IN_AAG(T428, T429, T427)
ADDC147_IN_AAG(one(b), zero(zero(T455)), zero(one(T455))) → U17_AAG(T455, binaryZ43_in_g(T455))
ADDC147_IN_AAG(one(b), zero(zero(T455)), zero(one(T455))) → BINARYZ43_IN_G(T455)
ADDC147_IN_AAG(one(b), zero(one(T467)), zero(zero(T466))) → U18_AAG(T467, T466, succ129_in_ag(T467, T466))
ADDC147_IN_AAG(one(b), zero(one(T467)), zero(zero(T466))) → SUCC129_IN_AG(T467, T466)
ADDC147_IN_AAG(one(T482), zero(T483), zero(T481)) → U19_AAG(T482, T483, T481, addC147_in_aag(T482, T483, T481))
ADDC147_IN_AAG(one(T482), zero(T483), zero(T481)) → ADDC147_IN_AAG(T482, T483, T481)
ADDC147_IN_AAG(one(T496), one(T497), one(T495)) → U20_AAG(T496, T497, T495, addc112_in_aag(T496, T497, T495))
ADDC147_IN_AAG(one(T496), one(T497), one(T495)) → ADDC112_IN_AAG(T496, T497, T495)
ADDZ73_IN_AAG(zero(T513), one(T514), one(T512)) → U31_AAG(T513, T514, T512, addx86_in_aag(T513, T514, T512))
ADDZ73_IN_AAG(zero(T513), one(T514), one(T512)) → ADDX86_IN_AAG(T513, T514, T512)
ADDZ73_IN_AAG(one(T531), zero(T532), one(T530)) → U32_AAG(T531, T532, T530, addy100_in_aag(T531, T532, T530))
ADDZ73_IN_AAG(one(T531), zero(T532), one(T530)) → ADDY100_IN_AAG(T531, T532, T530)
ADDZ73_IN_AAG(one(T543), one(T544), zero(T542)) → U33_AAG(T543, T544, T542, addc112_in_aag(T543, T544, T542))
ADDZ73_IN_AAG(one(T543), one(T544), zero(T542)) → ADDC112_IN_AAG(T543, T544, T542)
ADD1_IN_AAG(b, zero(T551), zero(T551)) → U38_AAG(T551, binaryZ43_in_g(T551))
ADD1_IN_AAG(b, zero(T551), zero(T551)) → BINARYZ43_IN_G(T551)
ADD1_IN_AAG(b, one(T557), one(T557)) → U39_AAG(T557, binary50_in_g(T557))
ADD1_IN_AAG(b, one(T557), one(T557)) → BINARY50_IN_G(T557)
ADD1_IN_AAG(T572, T573, T571) → U40_AAG(T572, T573, T571, addz73_in_aag(T572, T573, T571))
ADD1_IN_AAG(zero(T600), zero(T601), zero(T599)) → U41_AAG(T600, T601, T599, addz77_in_aag(T600, T601, T599))
ADD1_IN_AAG(zero(T600), zero(T601), zero(T599)) → ADDZ77_IN_AAG(T600, T601, T599)
ADD1_IN_AAG(zero(T620), one(T621), one(T619)) → U42_AAG(T620, T621, T619, addx86_in_aag(T620, T621, T619))
ADD1_IN_AAG(zero(T620), one(T621), one(T619)) → ADDX86_IN_AAG(T620, T621, T619)
ADD1_IN_AAG(one(T638), zero(T639), one(T637)) → U43_AAG(T638, T639, T637, addy100_in_aag(T638, T639, T637))
ADD1_IN_AAG(one(T638), zero(T639), one(T637)) → ADDY100_IN_AAG(T638, T639, T637)
ADD1_IN_AAG(one(T650), one(T651), zero(T649)) → U44_AAG(T650, T651, T649, addc112_in_aag(T650, T651, T649))
ADD1_IN_AAG(one(T650), one(T651), zero(T649)) → ADDC112_IN_AAG(T650, T651, T649)

The TRS R consists of the following rules:

add1_in_aag(b, b, b) → add1_out_aag(b, b, b)
add1_in_aag(zero(T93), b, zero(T93)) → U34_aag(T93, binaryZ43_in_g(T93))
binaryZ43_in_g(zero(T99)) → U1_g(T99, binaryZ43_in_g(T99))
binaryZ43_in_g(one(T103)) → U2_g(T103, binary50_in_g(T103))
binary50_in_g(b) → binary50_out_g(b)
binary50_in_g(zero(T108)) → U3_g(T108, binaryZ43_in_g(T108))
U3_g(T108, binaryZ43_out_g(T108)) → binary50_out_g(zero(T108))
binary50_in_g(one(T112)) → U4_g(T112, binary50_in_g(T112))
U4_g(T112, binary50_out_g(T112)) → binary50_out_g(one(T112))
U2_g(T103, binary50_out_g(T103)) → binaryZ43_out_g(one(T103))
U1_g(T99, binaryZ43_out_g(T99)) → binaryZ43_out_g(zero(T99))
U34_aag(T93, binaryZ43_out_g(T93)) → add1_out_aag(zero(T93), b, zero(T93))
add1_in_aag(one(T117), b, one(T117)) → U35_aag(T117, binary50_in_g(T117))
U35_aag(T117, binary50_out_g(T117)) → add1_out_aag(one(T117), b, one(T117))
add1_in_aag(b, T122, T122) → U36_aag(T122, binaryZ43_in_g(T122))
U36_aag(T122, binaryZ43_out_g(T122)) → add1_out_aag(b, T122, T122)
add1_in_aag(T138, T139, T137) → U37_aag(T138, T139, T137, addz73_in_aag(T138, T139, T137))
addz73_in_aag(zero(T158), zero(T159), zero(T157)) → U30_aag(T158, T159, T157, addz77_in_aag(T158, T159, T157))
addz77_in_aag(zero(T178), zero(T179), zero(T177)) → U5_aag(T178, T179, T177, addz77_in_aag(T178, T179, T177))
addz77_in_aag(zero(T198), one(T199), one(T197)) → U6_aag(T198, T199, T197, addx86_in_aag(T198, T199, T197))
addx86_in_aag(one(T205), b, one(T205)) → U24_aag(T205, binary50_in_g(T205))
U24_aag(T205, binary50_out_g(T205)) → addx86_out_aag(one(T205), b, one(T205))
addx86_in_aag(zero(T210), b, zero(T210)) → U25_aag(T210, binaryZ43_in_g(T210))
U25_aag(T210, binaryZ43_out_g(T210)) → addx86_out_aag(zero(T210), b, zero(T210))
addx86_in_aag(T226, T227, T225) → U26_aag(T226, T227, T225, addz77_in_aag(T226, T227, T225))
addz77_in_aag(one(T246), zero(T247), one(T245)) → U7_aag(T246, T247, T245, addy100_in_aag(T246, T247, T245))
addy100_in_aag(b, one(T253), one(T253)) → U27_aag(T253, binary50_in_g(T253))
U27_aag(T253, binary50_out_g(T253)) → addy100_out_aag(b, one(T253), one(T253))
addy100_in_aag(b, zero(T258), zero(T258)) → U28_aag(T258, binaryZ43_in_g(T258))
U28_aag(T258, binaryZ43_out_g(T258)) → addy100_out_aag(b, zero(T258), zero(T258))
addy100_in_aag(T274, T275, T273) → U29_aag(T274, T275, T273, addz77_in_aag(T274, T275, T273))
addz77_in_aag(one(T288), one(T289), zero(T287)) → U8_aag(T288, T289, T287, addc112_in_aag(T288, T289, T287))
addc112_in_aag(b, b, one(b)) → addc112_out_aag(b, b, one(b))
addc112_in_aag(T300, b, T299) → U21_aag(T300, T299, succZ122_in_ag(T300, T299))
succZ122_in_ag(zero(T306), one(T306)) → U11_ag(T306, binaryZ43_in_g(T306))
U11_ag(T306, binaryZ43_out_g(T306)) → succZ122_out_ag(zero(T306), one(T306))
succZ122_in_ag(one(T314), zero(T313)) → U12_ag(T314, T313, succ129_in_ag(T314, T313))
succ129_in_ag(b, one(b)) → succ129_out_ag(b, one(b))
succ129_in_ag(zero(T319), one(T319)) → U9_ag(T319, binaryZ43_in_g(T319))
U9_ag(T319, binaryZ43_out_g(T319)) → succ129_out_ag(zero(T319), one(T319))
succ129_in_ag(one(T327), zero(T326)) → U10_ag(T327, T326, succ129_in_ag(T327, T326))
U10_ag(T327, T326, succ129_out_ag(T327, T326)) → succ129_out_ag(one(T327), zero(T326))
U12_ag(T314, T313, succ129_out_ag(T314, T313)) → succZ122_out_ag(one(T314), zero(T313))
U21_aag(T300, T299, succZ122_out_ag(T300, T299)) → addc112_out_aag(T300, b, T299)
addc112_in_aag(b, T338, T337) → U22_aag(T338, T337, succZ122_in_ag(T338, T337))
U22_aag(T338, T337, succZ122_out_ag(T338, T337)) → addc112_out_aag(b, T338, T337)
addc112_in_aag(T354, T355, T353) → U23_aag(T354, T355, T353, addC147_in_aag(T354, T355, T353))
addC147_in_aag(zero(T374), zero(T375), one(T373)) → U13_aag(T374, T375, T373, addz77_in_aag(T374, T375, T373))
U13_aag(T374, T375, T373, addz77_out_aag(T374, T375, T373)) → addC147_out_aag(zero(T374), zero(T375), one(T373))
addC147_in_aag(zero(zero(T401)), one(b), zero(one(T401))) → U14_aag(T401, binaryZ43_in_g(T401))
U14_aag(T401, binaryZ43_out_g(T401)) → addC147_out_aag(zero(zero(T401)), one(b), zero(one(T401)))
addC147_in_aag(zero(one(T413)), one(b), zero(zero(T412))) → U15_aag(T413, T412, succ129_in_ag(T413, T412))
U15_aag(T413, T412, succ129_out_ag(T413, T412)) → addC147_out_aag(zero(one(T413)), one(b), zero(zero(T412)))
addC147_in_aag(zero(T428), one(T429), zero(T427)) → U16_aag(T428, T429, T427, addC147_in_aag(T428, T429, T427))
addC147_in_aag(one(b), zero(zero(T455)), zero(one(T455))) → U17_aag(T455, binaryZ43_in_g(T455))
U17_aag(T455, binaryZ43_out_g(T455)) → addC147_out_aag(one(b), zero(zero(T455)), zero(one(T455)))
addC147_in_aag(one(b), zero(one(T467)), zero(zero(T466))) → U18_aag(T467, T466, succ129_in_ag(T467, T466))
U18_aag(T467, T466, succ129_out_ag(T467, T466)) → addC147_out_aag(one(b), zero(one(T467)), zero(zero(T466)))
addC147_in_aag(one(T482), zero(T483), zero(T481)) → U19_aag(T482, T483, T481, addC147_in_aag(T482, T483, T481))
addC147_in_aag(one(T496), one(T497), one(T495)) → U20_aag(T496, T497, T495, addc112_in_aag(T496, T497, T495))
U20_aag(T496, T497, T495, addc112_out_aag(T496, T497, T495)) → addC147_out_aag(one(T496), one(T497), one(T495))
U19_aag(T482, T483, T481, addC147_out_aag(T482, T483, T481)) → addC147_out_aag(one(T482), zero(T483), zero(T481))
U16_aag(T428, T429, T427, addC147_out_aag(T428, T429, T427)) → addC147_out_aag(zero(T428), one(T429), zero(T427))
U23_aag(T354, T355, T353, addC147_out_aag(T354, T355, T353)) → addc112_out_aag(T354, T355, T353)
U8_aag(T288, T289, T287, addc112_out_aag(T288, T289, T287)) → addz77_out_aag(one(T288), one(T289), zero(T287))
U29_aag(T274, T275, T273, addz77_out_aag(T274, T275, T273)) → addy100_out_aag(T274, T275, T273)
U7_aag(T246, T247, T245, addy100_out_aag(T246, T247, T245)) → addz77_out_aag(one(T246), zero(T247), one(T245))
U26_aag(T226, T227, T225, addz77_out_aag(T226, T227, T225)) → addx86_out_aag(T226, T227, T225)
U6_aag(T198, T199, T197, addx86_out_aag(T198, T199, T197)) → addz77_out_aag(zero(T198), one(T199), one(T197))
U5_aag(T178, T179, T177, addz77_out_aag(T178, T179, T177)) → addz77_out_aag(zero(T178), zero(T179), zero(T177))
U30_aag(T158, T159, T157, addz77_out_aag(T158, T159, T157)) → addz73_out_aag(zero(T158), zero(T159), zero(T157))
addz73_in_aag(zero(T513), one(T514), one(T512)) → U31_aag(T513, T514, T512, addx86_in_aag(T513, T514, T512))
U31_aag(T513, T514, T512, addx86_out_aag(T513, T514, T512)) → addz73_out_aag(zero(T513), one(T514), one(T512))
addz73_in_aag(one(T531), zero(T532), one(T530)) → U32_aag(T531, T532, T530, addy100_in_aag(T531, T532, T530))
U32_aag(T531, T532, T530, addy100_out_aag(T531, T532, T530)) → addz73_out_aag(one(T531), zero(T532), one(T530))
addz73_in_aag(one(T543), one(T544), zero(T542)) → U33_aag(T543, T544, T542, addc112_in_aag(T543, T544, T542))
U33_aag(T543, T544, T542, addc112_out_aag(T543, T544, T542)) → addz73_out_aag(one(T543), one(T544), zero(T542))
U37_aag(T138, T139, T137, addz73_out_aag(T138, T139, T137)) → add1_out_aag(T138, T139, T137)
add1_in_aag(b, zero(T551), zero(T551)) → U38_aag(T551, binaryZ43_in_g(T551))
U38_aag(T551, binaryZ43_out_g(T551)) → add1_out_aag(b, zero(T551), zero(T551))
add1_in_aag(b, one(T557), one(T557)) → U39_aag(T557, binary50_in_g(T557))
U39_aag(T557, binary50_out_g(T557)) → add1_out_aag(b, one(T557), one(T557))
add1_in_aag(T572, T573, T571) → U40_aag(T572, T573, T571, addz73_in_aag(T572, T573, T571))
U40_aag(T572, T573, T571, addz73_out_aag(T572, T573, T571)) → add1_out_aag(T572, T573, T571)
add1_in_aag(zero(T600), zero(T601), zero(T599)) → U41_aag(T600, T601, T599, addz77_in_aag(T600, T601, T599))
U41_aag(T600, T601, T599, addz77_out_aag(T600, T601, T599)) → add1_out_aag(zero(T600), zero(T601), zero(T599))
add1_in_aag(zero(T620), one(T621), one(T619)) → U42_aag(T620, T621, T619, addx86_in_aag(T620, T621, T619))
U42_aag(T620, T621, T619, addx86_out_aag(T620, T621, T619)) → add1_out_aag(zero(T620), one(T621), one(T619))
add1_in_aag(one(T638), zero(T639), one(T637)) → U43_aag(T638, T639, T637, addy100_in_aag(T638, T639, T637))
U43_aag(T638, T639, T637, addy100_out_aag(T638, T639, T637)) → add1_out_aag(one(T638), zero(T639), one(T637))
add1_in_aag(one(T650), one(T651), zero(T649)) → U44_aag(T650, T651, T649, addc112_in_aag(T650, T651, T649))
U44_aag(T650, T651, T649, addc112_out_aag(T650, T651, T649)) → add1_out_aag(one(T650), one(T651), zero(T649))

The argument filtering Pi contains the following mapping:
add1_in_aag(x1, x2, x3)  =  add1_in_aag(x3)
b  =  b
add1_out_aag(x1, x2, x3)  =  add1_out_aag(x1, x2, x3)
zero(x1)  =  zero(x1)
U34_aag(x1, x2)  =  U34_aag(x1, x2)
binaryZ43_in_g(x1)  =  binaryZ43_in_g(x1)
U1_g(x1, x2)  =  U1_g(x1, x2)
one(x1)  =  one(x1)
U2_g(x1, x2)  =  U2_g(x1, x2)
binary50_in_g(x1)  =  binary50_in_g(x1)
binary50_out_g(x1)  =  binary50_out_g(x1)
U3_g(x1, x2)  =  U3_g(x1, x2)
binaryZ43_out_g(x1)  =  binaryZ43_out_g(x1)
U4_g(x1, x2)  =  U4_g(x1, 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(x3, x4)
addz73_in_aag(x1, x2, x3)  =  addz73_in_aag(x3)
U30_aag(x1, x2, x3, x4)  =  U30_aag(x3, x4)
addz77_in_aag(x1, x2, x3)  =  addz77_in_aag(x3)
U5_aag(x1, x2, x3, x4)  =  U5_aag(x3, x4)
U6_aag(x1, x2, x3, x4)  =  U6_aag(x3, x4)
addx86_in_aag(x1, x2, x3)  =  addx86_in_aag(x3)
U24_aag(x1, x2)  =  U24_aag(x1, x2)
addx86_out_aag(x1, x2, x3)  =  addx86_out_aag(x1, x2, x3)
U25_aag(x1, x2)  =  U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x3, x4)
U7_aag(x1, x2, x3, x4)  =  U7_aag(x3, x4)
addy100_in_aag(x1, x2, x3)  =  addy100_in_aag(x3)
U27_aag(x1, x2)  =  U27_aag(x1, x2)
addy100_out_aag(x1, x2, x3)  =  addy100_out_aag(x1, x2, x3)
U28_aag(x1, x2)  =  U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4)  =  U29_aag(x3, x4)
U8_aag(x1, x2, x3, x4)  =  U8_aag(x3, x4)
addc112_in_aag(x1, x2, x3)  =  addc112_in_aag(x3)
addc112_out_aag(x1, x2, x3)  =  addc112_out_aag(x1, x2, x3)
U21_aag(x1, x2, x3)  =  U21_aag(x2, x3)
succZ122_in_ag(x1, x2)  =  succZ122_in_ag(x2)
U11_ag(x1, x2)  =  U11_ag(x1, x2)
succZ122_out_ag(x1, x2)  =  succZ122_out_ag(x1, x2)
U12_ag(x1, x2, x3)  =  U12_ag(x2, x3)
succ129_in_ag(x1, x2)  =  succ129_in_ag(x2)
succ129_out_ag(x1, x2)  =  succ129_out_ag(x1, x2)
U9_ag(x1, x2)  =  U9_ag(x1, x2)
U10_ag(x1, x2, x3)  =  U10_ag(x2, x3)
U22_aag(x1, x2, x3)  =  U22_aag(x2, x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x3, x4)
addC147_in_aag(x1, x2, x3)  =  addC147_in_aag(x3)
U13_aag(x1, x2, x3, x4)  =  U13_aag(x3, x4)
addz77_out_aag(x1, x2, x3)  =  addz77_out_aag(x1, x2, x3)
addC147_out_aag(x1, x2, x3)  =  addC147_out_aag(x1, x2, x3)
U14_aag(x1, x2)  =  U14_aag(x1, x2)
U15_aag(x1, x2, x3)  =  U15_aag(x2, x3)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x3, x4)
U17_aag(x1, x2)  =  U17_aag(x1, x2)
U18_aag(x1, x2, x3)  =  U18_aag(x2, x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x3, x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x3, x4)
addz73_out_aag(x1, x2, x3)  =  addz73_out_aag(x1, x2, x3)
U31_aag(x1, x2, x3, x4)  =  U31_aag(x3, x4)
U32_aag(x1, x2, x3, x4)  =  U32_aag(x3, x4)
U33_aag(x1, x2, x3, x4)  =  U33_aag(x3, 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(x3, x4)
U41_aag(x1, x2, x3, x4)  =  U41_aag(x3, x4)
U42_aag(x1, x2, x3, x4)  =  U42_aag(x3, x4)
U43_aag(x1, x2, x3, x4)  =  U43_aag(x3, x4)
U44_aag(x1, x2, x3, x4)  =  U44_aag(x3, x4)
ADD1_IN_AAG(x1, x2, x3)  =  ADD1_IN_AAG(x3)
U34_AAG(x1, x2)  =  U34_AAG(x1, x2)
BINARYZ43_IN_G(x1)  =  BINARYZ43_IN_G(x1)
U1_G(x1, x2)  =  U1_G(x1, x2)
U2_G(x1, x2)  =  U2_G(x1, x2)
BINARY50_IN_G(x1)  =  BINARY50_IN_G(x1)
U3_G(x1, x2)  =  U3_G(x1, x2)
U4_G(x1, x2)  =  U4_G(x1, 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(x3, x4)
ADDZ73_IN_AAG(x1, x2, x3)  =  ADDZ73_IN_AAG(x3)
U30_AAG(x1, x2, x3, x4)  =  U30_AAG(x3, x4)
ADDZ77_IN_AAG(x1, x2, x3)  =  ADDZ77_IN_AAG(x3)
U5_AAG(x1, x2, x3, x4)  =  U5_AAG(x3, x4)
U6_AAG(x1, x2, x3, x4)  =  U6_AAG(x3, x4)
ADDX86_IN_AAG(x1, x2, x3)  =  ADDX86_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(x3, x4)
U7_AAG(x1, x2, x3, x4)  =  U7_AAG(x3, x4)
ADDY100_IN_AAG(x1, x2, x3)  =  ADDY100_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(x3, x4)
U8_AAG(x1, x2, x3, x4)  =  U8_AAG(x3, x4)
ADDC112_IN_AAG(x1, x2, x3)  =  ADDC112_IN_AAG(x3)
U21_AAG(x1, x2, x3)  =  U21_AAG(x2, x3)
SUCCZ122_IN_AG(x1, x2)  =  SUCCZ122_IN_AG(x2)
U11_AG(x1, x2)  =  U11_AG(x1, x2)
U12_AG(x1, x2, x3)  =  U12_AG(x2, x3)
SUCC129_IN_AG(x1, x2)  =  SUCC129_IN_AG(x2)
U9_AG(x1, x2)  =  U9_AG(x1, x2)
U10_AG(x1, x2, x3)  =  U10_AG(x2, x3)
U22_AAG(x1, x2, x3)  =  U22_AAG(x2, x3)
U23_AAG(x1, x2, x3, x4)  =  U23_AAG(x3, x4)
ADDC147_IN_AAG(x1, x2, x3)  =  ADDC147_IN_AAG(x3)
U13_AAG(x1, x2, x3, x4)  =  U13_AAG(x3, x4)
U14_AAG(x1, x2)  =  U14_AAG(x1, x2)
U15_AAG(x1, x2, x3)  =  U15_AAG(x2, x3)
U16_AAG(x1, x2, x3, x4)  =  U16_AAG(x3, x4)
U17_AAG(x1, x2)  =  U17_AAG(x1, x2)
U18_AAG(x1, x2, x3)  =  U18_AAG(x2, x3)
U19_AAG(x1, x2, x3, x4)  =  U19_AAG(x3, x4)
U20_AAG(x1, x2, x3, x4)  =  U20_AAG(x3, x4)
U31_AAG(x1, x2, x3, x4)  =  U31_AAG(x3, x4)
U32_AAG(x1, x2, x3, x4)  =  U32_AAG(x3, x4)
U33_AAG(x1, x2, x3, x4)  =  U33_AAG(x3, 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(x3, x4)
U41_AAG(x1, x2, x3, x4)  =  U41_AAG(x3, x4)
U42_AAG(x1, x2, x3, x4)  =  U42_AAG(x3, x4)
U43_AAG(x1, x2, x3, x4)  =  U43_AAG(x3, x4)
U44_AAG(x1, x2, x3, x4)  =  U44_AAG(x3, x4)

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

(6) Obligation:

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

ADD1_IN_AAG(zero(T93), b, zero(T93)) → U34_AAG(T93, binaryZ43_in_g(T93))
ADD1_IN_AAG(zero(T93), b, zero(T93)) → BINARYZ43_IN_G(T93)
BINARYZ43_IN_G(zero(T99)) → U1_G(T99, binaryZ43_in_g(T99))
BINARYZ43_IN_G(zero(T99)) → BINARYZ43_IN_G(T99)
BINARYZ43_IN_G(one(T103)) → U2_G(T103, binary50_in_g(T103))
BINARYZ43_IN_G(one(T103)) → BINARY50_IN_G(T103)
BINARY50_IN_G(zero(T108)) → U3_G(T108, binaryZ43_in_g(T108))
BINARY50_IN_G(zero(T108)) → BINARYZ43_IN_G(T108)
BINARY50_IN_G(one(T112)) → U4_G(T112, binary50_in_g(T112))
BINARY50_IN_G(one(T112)) → BINARY50_IN_G(T112)
ADD1_IN_AAG(one(T117), b, one(T117)) → U35_AAG(T117, binary50_in_g(T117))
ADD1_IN_AAG(one(T117), b, one(T117)) → BINARY50_IN_G(T117)
ADD1_IN_AAG(b, T122, T122) → U36_AAG(T122, binaryZ43_in_g(T122))
ADD1_IN_AAG(b, T122, T122) → BINARYZ43_IN_G(T122)
ADD1_IN_AAG(T138, T139, T137) → U37_AAG(T138, T139, T137, addz73_in_aag(T138, T139, T137))
ADD1_IN_AAG(T138, T139, T137) → ADDZ73_IN_AAG(T138, T139, T137)
ADDZ73_IN_AAG(zero(T158), zero(T159), zero(T157)) → U30_AAG(T158, T159, T157, addz77_in_aag(T158, T159, T157))
ADDZ73_IN_AAG(zero(T158), zero(T159), zero(T157)) → ADDZ77_IN_AAG(T158, T159, T157)
ADDZ77_IN_AAG(zero(T178), zero(T179), zero(T177)) → U5_AAG(T178, T179, T177, addz77_in_aag(T178, T179, T177))
ADDZ77_IN_AAG(zero(T178), zero(T179), zero(T177)) → ADDZ77_IN_AAG(T178, T179, T177)
ADDZ77_IN_AAG(zero(T198), one(T199), one(T197)) → U6_AAG(T198, T199, T197, addx86_in_aag(T198, T199, T197))
ADDZ77_IN_AAG(zero(T198), one(T199), one(T197)) → ADDX86_IN_AAG(T198, T199, T197)
ADDX86_IN_AAG(one(T205), b, one(T205)) → U24_AAG(T205, binary50_in_g(T205))
ADDX86_IN_AAG(one(T205), b, one(T205)) → BINARY50_IN_G(T205)
ADDX86_IN_AAG(zero(T210), b, zero(T210)) → U25_AAG(T210, binaryZ43_in_g(T210))
ADDX86_IN_AAG(zero(T210), b, zero(T210)) → BINARYZ43_IN_G(T210)
ADDX86_IN_AAG(T226, T227, T225) → U26_AAG(T226, T227, T225, addz77_in_aag(T226, T227, T225))
ADDX86_IN_AAG(T226, T227, T225) → ADDZ77_IN_AAG(T226, T227, T225)
ADDZ77_IN_AAG(one(T246), zero(T247), one(T245)) → U7_AAG(T246, T247, T245, addy100_in_aag(T246, T247, T245))
ADDZ77_IN_AAG(one(T246), zero(T247), one(T245)) → ADDY100_IN_AAG(T246, T247, T245)
ADDY100_IN_AAG(b, one(T253), one(T253)) → U27_AAG(T253, binary50_in_g(T253))
ADDY100_IN_AAG(b, one(T253), one(T253)) → BINARY50_IN_G(T253)
ADDY100_IN_AAG(b, zero(T258), zero(T258)) → U28_AAG(T258, binaryZ43_in_g(T258))
ADDY100_IN_AAG(b, zero(T258), zero(T258)) → BINARYZ43_IN_G(T258)
ADDY100_IN_AAG(T274, T275, T273) → U29_AAG(T274, T275, T273, addz77_in_aag(T274, T275, T273))
ADDY100_IN_AAG(T274, T275, T273) → ADDZ77_IN_AAG(T274, T275, T273)
ADDZ77_IN_AAG(one(T288), one(T289), zero(T287)) → U8_AAG(T288, T289, T287, addc112_in_aag(T288, T289, T287))
ADDZ77_IN_AAG(one(T288), one(T289), zero(T287)) → ADDC112_IN_AAG(T288, T289, T287)
ADDC112_IN_AAG(T300, b, T299) → U21_AAG(T300, T299, succZ122_in_ag(T300, T299))
ADDC112_IN_AAG(T300, b, T299) → SUCCZ122_IN_AG(T300, T299)
SUCCZ122_IN_AG(zero(T306), one(T306)) → U11_AG(T306, binaryZ43_in_g(T306))
SUCCZ122_IN_AG(zero(T306), one(T306)) → BINARYZ43_IN_G(T306)
SUCCZ122_IN_AG(one(T314), zero(T313)) → U12_AG(T314, T313, succ129_in_ag(T314, T313))
SUCCZ122_IN_AG(one(T314), zero(T313)) → SUCC129_IN_AG(T314, T313)
SUCC129_IN_AG(zero(T319), one(T319)) → U9_AG(T319, binaryZ43_in_g(T319))
SUCC129_IN_AG(zero(T319), one(T319)) → BINARYZ43_IN_G(T319)
SUCC129_IN_AG(one(T327), zero(T326)) → U10_AG(T327, T326, succ129_in_ag(T327, T326))
SUCC129_IN_AG(one(T327), zero(T326)) → SUCC129_IN_AG(T327, T326)
ADDC112_IN_AAG(b, T338, T337) → U22_AAG(T338, T337, succZ122_in_ag(T338, T337))
ADDC112_IN_AAG(b, T338, T337) → SUCCZ122_IN_AG(T338, T337)
ADDC112_IN_AAG(T354, T355, T353) → U23_AAG(T354, T355, T353, addC147_in_aag(T354, T355, T353))
ADDC112_IN_AAG(T354, T355, T353) → ADDC147_IN_AAG(T354, T355, T353)
ADDC147_IN_AAG(zero(T374), zero(T375), one(T373)) → U13_AAG(T374, T375, T373, addz77_in_aag(T374, T375, T373))
ADDC147_IN_AAG(zero(T374), zero(T375), one(T373)) → ADDZ77_IN_AAG(T374, T375, T373)
ADDC147_IN_AAG(zero(zero(T401)), one(b), zero(one(T401))) → U14_AAG(T401, binaryZ43_in_g(T401))
ADDC147_IN_AAG(zero(zero(T401)), one(b), zero(one(T401))) → BINARYZ43_IN_G(T401)
ADDC147_IN_AAG(zero(one(T413)), one(b), zero(zero(T412))) → U15_AAG(T413, T412, succ129_in_ag(T413, T412))
ADDC147_IN_AAG(zero(one(T413)), one(b), zero(zero(T412))) → SUCC129_IN_AG(T413, T412)
ADDC147_IN_AAG(zero(T428), one(T429), zero(T427)) → U16_AAG(T428, T429, T427, addC147_in_aag(T428, T429, T427))
ADDC147_IN_AAG(zero(T428), one(T429), zero(T427)) → ADDC147_IN_AAG(T428, T429, T427)
ADDC147_IN_AAG(one(b), zero(zero(T455)), zero(one(T455))) → U17_AAG(T455, binaryZ43_in_g(T455))
ADDC147_IN_AAG(one(b), zero(zero(T455)), zero(one(T455))) → BINARYZ43_IN_G(T455)
ADDC147_IN_AAG(one(b), zero(one(T467)), zero(zero(T466))) → U18_AAG(T467, T466, succ129_in_ag(T467, T466))
ADDC147_IN_AAG(one(b), zero(one(T467)), zero(zero(T466))) → SUCC129_IN_AG(T467, T466)
ADDC147_IN_AAG(one(T482), zero(T483), zero(T481)) → U19_AAG(T482, T483, T481, addC147_in_aag(T482, T483, T481))
ADDC147_IN_AAG(one(T482), zero(T483), zero(T481)) → ADDC147_IN_AAG(T482, T483, T481)
ADDC147_IN_AAG(one(T496), one(T497), one(T495)) → U20_AAG(T496, T497, T495, addc112_in_aag(T496, T497, T495))
ADDC147_IN_AAG(one(T496), one(T497), one(T495)) → ADDC112_IN_AAG(T496, T497, T495)
ADDZ73_IN_AAG(zero(T513), one(T514), one(T512)) → U31_AAG(T513, T514, T512, addx86_in_aag(T513, T514, T512))
ADDZ73_IN_AAG(zero(T513), one(T514), one(T512)) → ADDX86_IN_AAG(T513, T514, T512)
ADDZ73_IN_AAG(one(T531), zero(T532), one(T530)) → U32_AAG(T531, T532, T530, addy100_in_aag(T531, T532, T530))
ADDZ73_IN_AAG(one(T531), zero(T532), one(T530)) → ADDY100_IN_AAG(T531, T532, T530)
ADDZ73_IN_AAG(one(T543), one(T544), zero(T542)) → U33_AAG(T543, T544, T542, addc112_in_aag(T543, T544, T542))
ADDZ73_IN_AAG(one(T543), one(T544), zero(T542)) → ADDC112_IN_AAG(T543, T544, T542)
ADD1_IN_AAG(b, zero(T551), zero(T551)) → U38_AAG(T551, binaryZ43_in_g(T551))
ADD1_IN_AAG(b, zero(T551), zero(T551)) → BINARYZ43_IN_G(T551)
ADD1_IN_AAG(b, one(T557), one(T557)) → U39_AAG(T557, binary50_in_g(T557))
ADD1_IN_AAG(b, one(T557), one(T557)) → BINARY50_IN_G(T557)
ADD1_IN_AAG(T572, T573, T571) → U40_AAG(T572, T573, T571, addz73_in_aag(T572, T573, T571))
ADD1_IN_AAG(zero(T600), zero(T601), zero(T599)) → U41_AAG(T600, T601, T599, addz77_in_aag(T600, T601, T599))
ADD1_IN_AAG(zero(T600), zero(T601), zero(T599)) → ADDZ77_IN_AAG(T600, T601, T599)
ADD1_IN_AAG(zero(T620), one(T621), one(T619)) → U42_AAG(T620, T621, T619, addx86_in_aag(T620, T621, T619))
ADD1_IN_AAG(zero(T620), one(T621), one(T619)) → ADDX86_IN_AAG(T620, T621, T619)
ADD1_IN_AAG(one(T638), zero(T639), one(T637)) → U43_AAG(T638, T639, T637, addy100_in_aag(T638, T639, T637))
ADD1_IN_AAG(one(T638), zero(T639), one(T637)) → ADDY100_IN_AAG(T638, T639, T637)
ADD1_IN_AAG(one(T650), one(T651), zero(T649)) → U44_AAG(T650, T651, T649, addc112_in_aag(T650, T651, T649))
ADD1_IN_AAG(one(T650), one(T651), zero(T649)) → ADDC112_IN_AAG(T650, T651, T649)

The TRS R consists of the following rules:

add1_in_aag(b, b, b) → add1_out_aag(b, b, b)
add1_in_aag(zero(T93), b, zero(T93)) → U34_aag(T93, binaryZ43_in_g(T93))
binaryZ43_in_g(zero(T99)) → U1_g(T99, binaryZ43_in_g(T99))
binaryZ43_in_g(one(T103)) → U2_g(T103, binary50_in_g(T103))
binary50_in_g(b) → binary50_out_g(b)
binary50_in_g(zero(T108)) → U3_g(T108, binaryZ43_in_g(T108))
U3_g(T108, binaryZ43_out_g(T108)) → binary50_out_g(zero(T108))
binary50_in_g(one(T112)) → U4_g(T112, binary50_in_g(T112))
U4_g(T112, binary50_out_g(T112)) → binary50_out_g(one(T112))
U2_g(T103, binary50_out_g(T103)) → binaryZ43_out_g(one(T103))
U1_g(T99, binaryZ43_out_g(T99)) → binaryZ43_out_g(zero(T99))
U34_aag(T93, binaryZ43_out_g(T93)) → add1_out_aag(zero(T93), b, zero(T93))
add1_in_aag(one(T117), b, one(T117)) → U35_aag(T117, binary50_in_g(T117))
U35_aag(T117, binary50_out_g(T117)) → add1_out_aag(one(T117), b, one(T117))
add1_in_aag(b, T122, T122) → U36_aag(T122, binaryZ43_in_g(T122))
U36_aag(T122, binaryZ43_out_g(T122)) → add1_out_aag(b, T122, T122)
add1_in_aag(T138, T139, T137) → U37_aag(T138, T139, T137, addz73_in_aag(T138, T139, T137))
addz73_in_aag(zero(T158), zero(T159), zero(T157)) → U30_aag(T158, T159, T157, addz77_in_aag(T158, T159, T157))
addz77_in_aag(zero(T178), zero(T179), zero(T177)) → U5_aag(T178, T179, T177, addz77_in_aag(T178, T179, T177))
addz77_in_aag(zero(T198), one(T199), one(T197)) → U6_aag(T198, T199, T197, addx86_in_aag(T198, T199, T197))
addx86_in_aag(one(T205), b, one(T205)) → U24_aag(T205, binary50_in_g(T205))
U24_aag(T205, binary50_out_g(T205)) → addx86_out_aag(one(T205), b, one(T205))
addx86_in_aag(zero(T210), b, zero(T210)) → U25_aag(T210, binaryZ43_in_g(T210))
U25_aag(T210, binaryZ43_out_g(T210)) → addx86_out_aag(zero(T210), b, zero(T210))
addx86_in_aag(T226, T227, T225) → U26_aag(T226, T227, T225, addz77_in_aag(T226, T227, T225))
addz77_in_aag(one(T246), zero(T247), one(T245)) → U7_aag(T246, T247, T245, addy100_in_aag(T246, T247, T245))
addy100_in_aag(b, one(T253), one(T253)) → U27_aag(T253, binary50_in_g(T253))
U27_aag(T253, binary50_out_g(T253)) → addy100_out_aag(b, one(T253), one(T253))
addy100_in_aag(b, zero(T258), zero(T258)) → U28_aag(T258, binaryZ43_in_g(T258))
U28_aag(T258, binaryZ43_out_g(T258)) → addy100_out_aag(b, zero(T258), zero(T258))
addy100_in_aag(T274, T275, T273) → U29_aag(T274, T275, T273, addz77_in_aag(T274, T275, T273))
addz77_in_aag(one(T288), one(T289), zero(T287)) → U8_aag(T288, T289, T287, addc112_in_aag(T288, T289, T287))
addc112_in_aag(b, b, one(b)) → addc112_out_aag(b, b, one(b))
addc112_in_aag(T300, b, T299) → U21_aag(T300, T299, succZ122_in_ag(T300, T299))
succZ122_in_ag(zero(T306), one(T306)) → U11_ag(T306, binaryZ43_in_g(T306))
U11_ag(T306, binaryZ43_out_g(T306)) → succZ122_out_ag(zero(T306), one(T306))
succZ122_in_ag(one(T314), zero(T313)) → U12_ag(T314, T313, succ129_in_ag(T314, T313))
succ129_in_ag(b, one(b)) → succ129_out_ag(b, one(b))
succ129_in_ag(zero(T319), one(T319)) → U9_ag(T319, binaryZ43_in_g(T319))
U9_ag(T319, binaryZ43_out_g(T319)) → succ129_out_ag(zero(T319), one(T319))
succ129_in_ag(one(T327), zero(T326)) → U10_ag(T327, T326, succ129_in_ag(T327, T326))
U10_ag(T327, T326, succ129_out_ag(T327, T326)) → succ129_out_ag(one(T327), zero(T326))
U12_ag(T314, T313, succ129_out_ag(T314, T313)) → succZ122_out_ag(one(T314), zero(T313))
U21_aag(T300, T299, succZ122_out_ag(T300, T299)) → addc112_out_aag(T300, b, T299)
addc112_in_aag(b, T338, T337) → U22_aag(T338, T337, succZ122_in_ag(T338, T337))
U22_aag(T338, T337, succZ122_out_ag(T338, T337)) → addc112_out_aag(b, T338, T337)
addc112_in_aag(T354, T355, T353) → U23_aag(T354, T355, T353, addC147_in_aag(T354, T355, T353))
addC147_in_aag(zero(T374), zero(T375), one(T373)) → U13_aag(T374, T375, T373, addz77_in_aag(T374, T375, T373))
U13_aag(T374, T375, T373, addz77_out_aag(T374, T375, T373)) → addC147_out_aag(zero(T374), zero(T375), one(T373))
addC147_in_aag(zero(zero(T401)), one(b), zero(one(T401))) → U14_aag(T401, binaryZ43_in_g(T401))
U14_aag(T401, binaryZ43_out_g(T401)) → addC147_out_aag(zero(zero(T401)), one(b), zero(one(T401)))
addC147_in_aag(zero(one(T413)), one(b), zero(zero(T412))) → U15_aag(T413, T412, succ129_in_ag(T413, T412))
U15_aag(T413, T412, succ129_out_ag(T413, T412)) → addC147_out_aag(zero(one(T413)), one(b), zero(zero(T412)))
addC147_in_aag(zero(T428), one(T429), zero(T427)) → U16_aag(T428, T429, T427, addC147_in_aag(T428, T429, T427))
addC147_in_aag(one(b), zero(zero(T455)), zero(one(T455))) → U17_aag(T455, binaryZ43_in_g(T455))
U17_aag(T455, binaryZ43_out_g(T455)) → addC147_out_aag(one(b), zero(zero(T455)), zero(one(T455)))
addC147_in_aag(one(b), zero(one(T467)), zero(zero(T466))) → U18_aag(T467, T466, succ129_in_ag(T467, T466))
U18_aag(T467, T466, succ129_out_ag(T467, T466)) → addC147_out_aag(one(b), zero(one(T467)), zero(zero(T466)))
addC147_in_aag(one(T482), zero(T483), zero(T481)) → U19_aag(T482, T483, T481, addC147_in_aag(T482, T483, T481))
addC147_in_aag(one(T496), one(T497), one(T495)) → U20_aag(T496, T497, T495, addc112_in_aag(T496, T497, T495))
U20_aag(T496, T497, T495, addc112_out_aag(T496, T497, T495)) → addC147_out_aag(one(T496), one(T497), one(T495))
U19_aag(T482, T483, T481, addC147_out_aag(T482, T483, T481)) → addC147_out_aag(one(T482), zero(T483), zero(T481))
U16_aag(T428, T429, T427, addC147_out_aag(T428, T429, T427)) → addC147_out_aag(zero(T428), one(T429), zero(T427))
U23_aag(T354, T355, T353, addC147_out_aag(T354, T355, T353)) → addc112_out_aag(T354, T355, T353)
U8_aag(T288, T289, T287, addc112_out_aag(T288, T289, T287)) → addz77_out_aag(one(T288), one(T289), zero(T287))
U29_aag(T274, T275, T273, addz77_out_aag(T274, T275, T273)) → addy100_out_aag(T274, T275, T273)
U7_aag(T246, T247, T245, addy100_out_aag(T246, T247, T245)) → addz77_out_aag(one(T246), zero(T247), one(T245))
U26_aag(T226, T227, T225, addz77_out_aag(T226, T227, T225)) → addx86_out_aag(T226, T227, T225)
U6_aag(T198, T199, T197, addx86_out_aag(T198, T199, T197)) → addz77_out_aag(zero(T198), one(T199), one(T197))
U5_aag(T178, T179, T177, addz77_out_aag(T178, T179, T177)) → addz77_out_aag(zero(T178), zero(T179), zero(T177))
U30_aag(T158, T159, T157, addz77_out_aag(T158, T159, T157)) → addz73_out_aag(zero(T158), zero(T159), zero(T157))
addz73_in_aag(zero(T513), one(T514), one(T512)) → U31_aag(T513, T514, T512, addx86_in_aag(T513, T514, T512))
U31_aag(T513, T514, T512, addx86_out_aag(T513, T514, T512)) → addz73_out_aag(zero(T513), one(T514), one(T512))
addz73_in_aag(one(T531), zero(T532), one(T530)) → U32_aag(T531, T532, T530, addy100_in_aag(T531, T532, T530))
U32_aag(T531, T532, T530, addy100_out_aag(T531, T532, T530)) → addz73_out_aag(one(T531), zero(T532), one(T530))
addz73_in_aag(one(T543), one(T544), zero(T542)) → U33_aag(T543, T544, T542, addc112_in_aag(T543, T544, T542))
U33_aag(T543, T544, T542, addc112_out_aag(T543, T544, T542)) → addz73_out_aag(one(T543), one(T544), zero(T542))
U37_aag(T138, T139, T137, addz73_out_aag(T138, T139, T137)) → add1_out_aag(T138, T139, T137)
add1_in_aag(b, zero(T551), zero(T551)) → U38_aag(T551, binaryZ43_in_g(T551))
U38_aag(T551, binaryZ43_out_g(T551)) → add1_out_aag(b, zero(T551), zero(T551))
add1_in_aag(b, one(T557), one(T557)) → U39_aag(T557, binary50_in_g(T557))
U39_aag(T557, binary50_out_g(T557)) → add1_out_aag(b, one(T557), one(T557))
add1_in_aag(T572, T573, T571) → U40_aag(T572, T573, T571, addz73_in_aag(T572, T573, T571))
U40_aag(T572, T573, T571, addz73_out_aag(T572, T573, T571)) → add1_out_aag(T572, T573, T571)
add1_in_aag(zero(T600), zero(T601), zero(T599)) → U41_aag(T600, T601, T599, addz77_in_aag(T600, T601, T599))
U41_aag(T600, T601, T599, addz77_out_aag(T600, T601, T599)) → add1_out_aag(zero(T600), zero(T601), zero(T599))
add1_in_aag(zero(T620), one(T621), one(T619)) → U42_aag(T620, T621, T619, addx86_in_aag(T620, T621, T619))
U42_aag(T620, T621, T619, addx86_out_aag(T620, T621, T619)) → add1_out_aag(zero(T620), one(T621), one(T619))
add1_in_aag(one(T638), zero(T639), one(T637)) → U43_aag(T638, T639, T637, addy100_in_aag(T638, T639, T637))
U43_aag(T638, T639, T637, addy100_out_aag(T638, T639, T637)) → add1_out_aag(one(T638), zero(T639), one(T637))
add1_in_aag(one(T650), one(T651), zero(T649)) → U44_aag(T650, T651, T649, addc112_in_aag(T650, T651, T649))
U44_aag(T650, T651, T649, addc112_out_aag(T650, T651, T649)) → add1_out_aag(one(T650), one(T651), zero(T649))

The argument filtering Pi contains the following mapping:
add1_in_aag(x1, x2, x3)  =  add1_in_aag(x3)
b  =  b
add1_out_aag(x1, x2, x3)  =  add1_out_aag(x1, x2, x3)
zero(x1)  =  zero(x1)
U34_aag(x1, x2)  =  U34_aag(x1, x2)
binaryZ43_in_g(x1)  =  binaryZ43_in_g(x1)
U1_g(x1, x2)  =  U1_g(x1, x2)
one(x1)  =  one(x1)
U2_g(x1, x2)  =  U2_g(x1, x2)
binary50_in_g(x1)  =  binary50_in_g(x1)
binary50_out_g(x1)  =  binary50_out_g(x1)
U3_g(x1, x2)  =  U3_g(x1, x2)
binaryZ43_out_g(x1)  =  binaryZ43_out_g(x1)
U4_g(x1, x2)  =  U4_g(x1, 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(x3, x4)
addz73_in_aag(x1, x2, x3)  =  addz73_in_aag(x3)
U30_aag(x1, x2, x3, x4)  =  U30_aag(x3, x4)
addz77_in_aag(x1, x2, x3)  =  addz77_in_aag(x3)
U5_aag(x1, x2, x3, x4)  =  U5_aag(x3, x4)
U6_aag(x1, x2, x3, x4)  =  U6_aag(x3, x4)
addx86_in_aag(x1, x2, x3)  =  addx86_in_aag(x3)
U24_aag(x1, x2)  =  U24_aag(x1, x2)
addx86_out_aag(x1, x2, x3)  =  addx86_out_aag(x1, x2, x3)
U25_aag(x1, x2)  =  U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x3, x4)
U7_aag(x1, x2, x3, x4)  =  U7_aag(x3, x4)
addy100_in_aag(x1, x2, x3)  =  addy100_in_aag(x3)
U27_aag(x1, x2)  =  U27_aag(x1, x2)
addy100_out_aag(x1, x2, x3)  =  addy100_out_aag(x1, x2, x3)
U28_aag(x1, x2)  =  U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4)  =  U29_aag(x3, x4)
U8_aag(x1, x2, x3, x4)  =  U8_aag(x3, x4)
addc112_in_aag(x1, x2, x3)  =  addc112_in_aag(x3)
addc112_out_aag(x1, x2, x3)  =  addc112_out_aag(x1, x2, x3)
U21_aag(x1, x2, x3)  =  U21_aag(x2, x3)
succZ122_in_ag(x1, x2)  =  succZ122_in_ag(x2)
U11_ag(x1, x2)  =  U11_ag(x1, x2)
succZ122_out_ag(x1, x2)  =  succZ122_out_ag(x1, x2)
U12_ag(x1, x2, x3)  =  U12_ag(x2, x3)
succ129_in_ag(x1, x2)  =  succ129_in_ag(x2)
succ129_out_ag(x1, x2)  =  succ129_out_ag(x1, x2)
U9_ag(x1, x2)  =  U9_ag(x1, x2)
U10_ag(x1, x2, x3)  =  U10_ag(x2, x3)
U22_aag(x1, x2, x3)  =  U22_aag(x2, x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x3, x4)
addC147_in_aag(x1, x2, x3)  =  addC147_in_aag(x3)
U13_aag(x1, x2, x3, x4)  =  U13_aag(x3, x4)
addz77_out_aag(x1, x2, x3)  =  addz77_out_aag(x1, x2, x3)
addC147_out_aag(x1, x2, x3)  =  addC147_out_aag(x1, x2, x3)
U14_aag(x1, x2)  =  U14_aag(x1, x2)
U15_aag(x1, x2, x3)  =  U15_aag(x2, x3)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x3, x4)
U17_aag(x1, x2)  =  U17_aag(x1, x2)
U18_aag(x1, x2, x3)  =  U18_aag(x2, x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x3, x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x3, x4)
addz73_out_aag(x1, x2, x3)  =  addz73_out_aag(x1, x2, x3)
U31_aag(x1, x2, x3, x4)  =  U31_aag(x3, x4)
U32_aag(x1, x2, x3, x4)  =  U32_aag(x3, x4)
U33_aag(x1, x2, x3, x4)  =  U33_aag(x3, 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(x3, x4)
U41_aag(x1, x2, x3, x4)  =  U41_aag(x3, x4)
U42_aag(x1, x2, x3, x4)  =  U42_aag(x3, x4)
U43_aag(x1, x2, x3, x4)  =  U43_aag(x3, x4)
U44_aag(x1, x2, x3, x4)  =  U44_aag(x3, x4)
ADD1_IN_AAG(x1, x2, x3)  =  ADD1_IN_AAG(x3)
U34_AAG(x1, x2)  =  U34_AAG(x1, x2)
BINARYZ43_IN_G(x1)  =  BINARYZ43_IN_G(x1)
U1_G(x1, x2)  =  U1_G(x1, x2)
U2_G(x1, x2)  =  U2_G(x1, x2)
BINARY50_IN_G(x1)  =  BINARY50_IN_G(x1)
U3_G(x1, x2)  =  U3_G(x1, x2)
U4_G(x1, x2)  =  U4_G(x1, 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(x3, x4)
ADDZ73_IN_AAG(x1, x2, x3)  =  ADDZ73_IN_AAG(x3)
U30_AAG(x1, x2, x3, x4)  =  U30_AAG(x3, x4)
ADDZ77_IN_AAG(x1, x2, x3)  =  ADDZ77_IN_AAG(x3)
U5_AAG(x1, x2, x3, x4)  =  U5_AAG(x3, x4)
U6_AAG(x1, x2, x3, x4)  =  U6_AAG(x3, x4)
ADDX86_IN_AAG(x1, x2, x3)  =  ADDX86_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(x3, x4)
U7_AAG(x1, x2, x3, x4)  =  U7_AAG(x3, x4)
ADDY100_IN_AAG(x1, x2, x3)  =  ADDY100_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(x3, x4)
U8_AAG(x1, x2, x3, x4)  =  U8_AAG(x3, x4)
ADDC112_IN_AAG(x1, x2, x3)  =  ADDC112_IN_AAG(x3)
U21_AAG(x1, x2, x3)  =  U21_AAG(x2, x3)
SUCCZ122_IN_AG(x1, x2)  =  SUCCZ122_IN_AG(x2)
U11_AG(x1, x2)  =  U11_AG(x1, x2)
U12_AG(x1, x2, x3)  =  U12_AG(x2, x3)
SUCC129_IN_AG(x1, x2)  =  SUCC129_IN_AG(x2)
U9_AG(x1, x2)  =  U9_AG(x1, x2)
U10_AG(x1, x2, x3)  =  U10_AG(x2, x3)
U22_AAG(x1, x2, x3)  =  U22_AAG(x2, x3)
U23_AAG(x1, x2, x3, x4)  =  U23_AAG(x3, x4)
ADDC147_IN_AAG(x1, x2, x3)  =  ADDC147_IN_AAG(x3)
U13_AAG(x1, x2, x3, x4)  =  U13_AAG(x3, x4)
U14_AAG(x1, x2)  =  U14_AAG(x1, x2)
U15_AAG(x1, x2, x3)  =  U15_AAG(x2, x3)
U16_AAG(x1, x2, x3, x4)  =  U16_AAG(x3, x4)
U17_AAG(x1, x2)  =  U17_AAG(x1, x2)
U18_AAG(x1, x2, x3)  =  U18_AAG(x2, x3)
U19_AAG(x1, x2, x3, x4)  =  U19_AAG(x3, x4)
U20_AAG(x1, x2, x3, x4)  =  U20_AAG(x3, x4)
U31_AAG(x1, x2, x3, x4)  =  U31_AAG(x3, x4)
U32_AAG(x1, x2, x3, x4)  =  U32_AAG(x3, x4)
U33_AAG(x1, x2, x3, x4)  =  U33_AAG(x3, 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(x3, x4)
U41_AAG(x1, x2, x3, x4)  =  U41_AAG(x3, x4)
U42_AAG(x1, x2, x3, x4)  =  U42_AAG(x3, x4)
U43_AAG(x1, x2, x3, x4)  =  U43_AAG(x3, x4)
U44_AAG(x1, x2, x3, x4)  =  U44_AAG(x3, x4)

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

(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:

BINARYZ43_IN_G(one(T103)) → BINARY50_IN_G(T103)
BINARY50_IN_G(zero(T108)) → BINARYZ43_IN_G(T108)
BINARYZ43_IN_G(zero(T99)) → BINARYZ43_IN_G(T99)
BINARY50_IN_G(one(T112)) → BINARY50_IN_G(T112)

The TRS R consists of the following rules:

add1_in_aag(b, b, b) → add1_out_aag(b, b, b)
add1_in_aag(zero(T93), b, zero(T93)) → U34_aag(T93, binaryZ43_in_g(T93))
binaryZ43_in_g(zero(T99)) → U1_g(T99, binaryZ43_in_g(T99))
binaryZ43_in_g(one(T103)) → U2_g(T103, binary50_in_g(T103))
binary50_in_g(b) → binary50_out_g(b)
binary50_in_g(zero(T108)) → U3_g(T108, binaryZ43_in_g(T108))
U3_g(T108, binaryZ43_out_g(T108)) → binary50_out_g(zero(T108))
binary50_in_g(one(T112)) → U4_g(T112, binary50_in_g(T112))
U4_g(T112, binary50_out_g(T112)) → binary50_out_g(one(T112))
U2_g(T103, binary50_out_g(T103)) → binaryZ43_out_g(one(T103))
U1_g(T99, binaryZ43_out_g(T99)) → binaryZ43_out_g(zero(T99))
U34_aag(T93, binaryZ43_out_g(T93)) → add1_out_aag(zero(T93), b, zero(T93))
add1_in_aag(one(T117), b, one(T117)) → U35_aag(T117, binary50_in_g(T117))
U35_aag(T117, binary50_out_g(T117)) → add1_out_aag(one(T117), b, one(T117))
add1_in_aag(b, T122, T122) → U36_aag(T122, binaryZ43_in_g(T122))
U36_aag(T122, binaryZ43_out_g(T122)) → add1_out_aag(b, T122, T122)
add1_in_aag(T138, T139, T137) → U37_aag(T138, T139, T137, addz73_in_aag(T138, T139, T137))
addz73_in_aag(zero(T158), zero(T159), zero(T157)) → U30_aag(T158, T159, T157, addz77_in_aag(T158, T159, T157))
addz77_in_aag(zero(T178), zero(T179), zero(T177)) → U5_aag(T178, T179, T177, addz77_in_aag(T178, T179, T177))
addz77_in_aag(zero(T198), one(T199), one(T197)) → U6_aag(T198, T199, T197, addx86_in_aag(T198, T199, T197))
addx86_in_aag(one(T205), b, one(T205)) → U24_aag(T205, binary50_in_g(T205))
U24_aag(T205, binary50_out_g(T205)) → addx86_out_aag(one(T205), b, one(T205))
addx86_in_aag(zero(T210), b, zero(T210)) → U25_aag(T210, binaryZ43_in_g(T210))
U25_aag(T210, binaryZ43_out_g(T210)) → addx86_out_aag(zero(T210), b, zero(T210))
addx86_in_aag(T226, T227, T225) → U26_aag(T226, T227, T225, addz77_in_aag(T226, T227, T225))
addz77_in_aag(one(T246), zero(T247), one(T245)) → U7_aag(T246, T247, T245, addy100_in_aag(T246, T247, T245))
addy100_in_aag(b, one(T253), one(T253)) → U27_aag(T253, binary50_in_g(T253))
U27_aag(T253, binary50_out_g(T253)) → addy100_out_aag(b, one(T253), one(T253))
addy100_in_aag(b, zero(T258), zero(T258)) → U28_aag(T258, binaryZ43_in_g(T258))
U28_aag(T258, binaryZ43_out_g(T258)) → addy100_out_aag(b, zero(T258), zero(T258))
addy100_in_aag(T274, T275, T273) → U29_aag(T274, T275, T273, addz77_in_aag(T274, T275, T273))
addz77_in_aag(one(T288), one(T289), zero(T287)) → U8_aag(T288, T289, T287, addc112_in_aag(T288, T289, T287))
addc112_in_aag(b, b, one(b)) → addc112_out_aag(b, b, one(b))
addc112_in_aag(T300, b, T299) → U21_aag(T300, T299, succZ122_in_ag(T300, T299))
succZ122_in_ag(zero(T306), one(T306)) → U11_ag(T306, binaryZ43_in_g(T306))
U11_ag(T306, binaryZ43_out_g(T306)) → succZ122_out_ag(zero(T306), one(T306))
succZ122_in_ag(one(T314), zero(T313)) → U12_ag(T314, T313, succ129_in_ag(T314, T313))
succ129_in_ag(b, one(b)) → succ129_out_ag(b, one(b))
succ129_in_ag(zero(T319), one(T319)) → U9_ag(T319, binaryZ43_in_g(T319))
U9_ag(T319, binaryZ43_out_g(T319)) → succ129_out_ag(zero(T319), one(T319))
succ129_in_ag(one(T327), zero(T326)) → U10_ag(T327, T326, succ129_in_ag(T327, T326))
U10_ag(T327, T326, succ129_out_ag(T327, T326)) → succ129_out_ag(one(T327), zero(T326))
U12_ag(T314, T313, succ129_out_ag(T314, T313)) → succZ122_out_ag(one(T314), zero(T313))
U21_aag(T300, T299, succZ122_out_ag(T300, T299)) → addc112_out_aag(T300, b, T299)
addc112_in_aag(b, T338, T337) → U22_aag(T338, T337, succZ122_in_ag(T338, T337))
U22_aag(T338, T337, succZ122_out_ag(T338, T337)) → addc112_out_aag(b, T338, T337)
addc112_in_aag(T354, T355, T353) → U23_aag(T354, T355, T353, addC147_in_aag(T354, T355, T353))
addC147_in_aag(zero(T374), zero(T375), one(T373)) → U13_aag(T374, T375, T373, addz77_in_aag(T374, T375, T373))
U13_aag(T374, T375, T373, addz77_out_aag(T374, T375, T373)) → addC147_out_aag(zero(T374), zero(T375), one(T373))
addC147_in_aag(zero(zero(T401)), one(b), zero(one(T401))) → U14_aag(T401, binaryZ43_in_g(T401))
U14_aag(T401, binaryZ43_out_g(T401)) → addC147_out_aag(zero(zero(T401)), one(b), zero(one(T401)))
addC147_in_aag(zero(one(T413)), one(b), zero(zero(T412))) → U15_aag(T413, T412, succ129_in_ag(T413, T412))
U15_aag(T413, T412, succ129_out_ag(T413, T412)) → addC147_out_aag(zero(one(T413)), one(b), zero(zero(T412)))
addC147_in_aag(zero(T428), one(T429), zero(T427)) → U16_aag(T428, T429, T427, addC147_in_aag(T428, T429, T427))
addC147_in_aag(one(b), zero(zero(T455)), zero(one(T455))) → U17_aag(T455, binaryZ43_in_g(T455))
U17_aag(T455, binaryZ43_out_g(T455)) → addC147_out_aag(one(b), zero(zero(T455)), zero(one(T455)))
addC147_in_aag(one(b), zero(one(T467)), zero(zero(T466))) → U18_aag(T467, T466, succ129_in_ag(T467, T466))
U18_aag(T467, T466, succ129_out_ag(T467, T466)) → addC147_out_aag(one(b), zero(one(T467)), zero(zero(T466)))
addC147_in_aag(one(T482), zero(T483), zero(T481)) → U19_aag(T482, T483, T481, addC147_in_aag(T482, T483, T481))
addC147_in_aag(one(T496), one(T497), one(T495)) → U20_aag(T496, T497, T495, addc112_in_aag(T496, T497, T495))
U20_aag(T496, T497, T495, addc112_out_aag(T496, T497, T495)) → addC147_out_aag(one(T496), one(T497), one(T495))
U19_aag(T482, T483, T481, addC147_out_aag(T482, T483, T481)) → addC147_out_aag(one(T482), zero(T483), zero(T481))
U16_aag(T428, T429, T427, addC147_out_aag(T428, T429, T427)) → addC147_out_aag(zero(T428), one(T429), zero(T427))
U23_aag(T354, T355, T353, addC147_out_aag(T354, T355, T353)) → addc112_out_aag(T354, T355, T353)
U8_aag(T288, T289, T287, addc112_out_aag(T288, T289, T287)) → addz77_out_aag(one(T288), one(T289), zero(T287))
U29_aag(T274, T275, T273, addz77_out_aag(T274, T275, T273)) → addy100_out_aag(T274, T275, T273)
U7_aag(T246, T247, T245, addy100_out_aag(T246, T247, T245)) → addz77_out_aag(one(T246), zero(T247), one(T245))
U26_aag(T226, T227, T225, addz77_out_aag(T226, T227, T225)) → addx86_out_aag(T226, T227, T225)
U6_aag(T198, T199, T197, addx86_out_aag(T198, T199, T197)) → addz77_out_aag(zero(T198), one(T199), one(T197))
U5_aag(T178, T179, T177, addz77_out_aag(T178, T179, T177)) → addz77_out_aag(zero(T178), zero(T179), zero(T177))
U30_aag(T158, T159, T157, addz77_out_aag(T158, T159, T157)) → addz73_out_aag(zero(T158), zero(T159), zero(T157))
addz73_in_aag(zero(T513), one(T514), one(T512)) → U31_aag(T513, T514, T512, addx86_in_aag(T513, T514, T512))
U31_aag(T513, T514, T512, addx86_out_aag(T513, T514, T512)) → addz73_out_aag(zero(T513), one(T514), one(T512))
addz73_in_aag(one(T531), zero(T532), one(T530)) → U32_aag(T531, T532, T530, addy100_in_aag(T531, T532, T530))
U32_aag(T531, T532, T530, addy100_out_aag(T531, T532, T530)) → addz73_out_aag(one(T531), zero(T532), one(T530))
addz73_in_aag(one(T543), one(T544), zero(T542)) → U33_aag(T543, T544, T542, addc112_in_aag(T543, T544, T542))
U33_aag(T543, T544, T542, addc112_out_aag(T543, T544, T542)) → addz73_out_aag(one(T543), one(T544), zero(T542))
U37_aag(T138, T139, T137, addz73_out_aag(T138, T139, T137)) → add1_out_aag(T138, T139, T137)
add1_in_aag(b, zero(T551), zero(T551)) → U38_aag(T551, binaryZ43_in_g(T551))
U38_aag(T551, binaryZ43_out_g(T551)) → add1_out_aag(b, zero(T551), zero(T551))
add1_in_aag(b, one(T557), one(T557)) → U39_aag(T557, binary50_in_g(T557))
U39_aag(T557, binary50_out_g(T557)) → add1_out_aag(b, one(T557), one(T557))
add1_in_aag(T572, T573, T571) → U40_aag(T572, T573, T571, addz73_in_aag(T572, T573, T571))
U40_aag(T572, T573, T571, addz73_out_aag(T572, T573, T571)) → add1_out_aag(T572, T573, T571)
add1_in_aag(zero(T600), zero(T601), zero(T599)) → U41_aag(T600, T601, T599, addz77_in_aag(T600, T601, T599))
U41_aag(T600, T601, T599, addz77_out_aag(T600, T601, T599)) → add1_out_aag(zero(T600), zero(T601), zero(T599))
add1_in_aag(zero(T620), one(T621), one(T619)) → U42_aag(T620, T621, T619, addx86_in_aag(T620, T621, T619))
U42_aag(T620, T621, T619, addx86_out_aag(T620, T621, T619)) → add1_out_aag(zero(T620), one(T621), one(T619))
add1_in_aag(one(T638), zero(T639), one(T637)) → U43_aag(T638, T639, T637, addy100_in_aag(T638, T639, T637))
U43_aag(T638, T639, T637, addy100_out_aag(T638, T639, T637)) → add1_out_aag(one(T638), zero(T639), one(T637))
add1_in_aag(one(T650), one(T651), zero(T649)) → U44_aag(T650, T651, T649, addc112_in_aag(T650, T651, T649))
U44_aag(T650, T651, T649, addc112_out_aag(T650, T651, T649)) → add1_out_aag(one(T650), one(T651), zero(T649))

The argument filtering Pi contains the following mapping:
add1_in_aag(x1, x2, x3)  =  add1_in_aag(x3)
b  =  b
add1_out_aag(x1, x2, x3)  =  add1_out_aag(x1, x2, x3)
zero(x1)  =  zero(x1)
U34_aag(x1, x2)  =  U34_aag(x1, x2)
binaryZ43_in_g(x1)  =  binaryZ43_in_g(x1)
U1_g(x1, x2)  =  U1_g(x1, x2)
one(x1)  =  one(x1)
U2_g(x1, x2)  =  U2_g(x1, x2)
binary50_in_g(x1)  =  binary50_in_g(x1)
binary50_out_g(x1)  =  binary50_out_g(x1)
U3_g(x1, x2)  =  U3_g(x1, x2)
binaryZ43_out_g(x1)  =  binaryZ43_out_g(x1)
U4_g(x1, x2)  =  U4_g(x1, 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(x3, x4)
addz73_in_aag(x1, x2, x3)  =  addz73_in_aag(x3)
U30_aag(x1, x2, x3, x4)  =  U30_aag(x3, x4)
addz77_in_aag(x1, x2, x3)  =  addz77_in_aag(x3)
U5_aag(x1, x2, x3, x4)  =  U5_aag(x3, x4)
U6_aag(x1, x2, x3, x4)  =  U6_aag(x3, x4)
addx86_in_aag(x1, x2, x3)  =  addx86_in_aag(x3)
U24_aag(x1, x2)  =  U24_aag(x1, x2)
addx86_out_aag(x1, x2, x3)  =  addx86_out_aag(x1, x2, x3)
U25_aag(x1, x2)  =  U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x3, x4)
U7_aag(x1, x2, x3, x4)  =  U7_aag(x3, x4)
addy100_in_aag(x1, x2, x3)  =  addy100_in_aag(x3)
U27_aag(x1, x2)  =  U27_aag(x1, x2)
addy100_out_aag(x1, x2, x3)  =  addy100_out_aag(x1, x2, x3)
U28_aag(x1, x2)  =  U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4)  =  U29_aag(x3, x4)
U8_aag(x1, x2, x3, x4)  =  U8_aag(x3, x4)
addc112_in_aag(x1, x2, x3)  =  addc112_in_aag(x3)
addc112_out_aag(x1, x2, x3)  =  addc112_out_aag(x1, x2, x3)
U21_aag(x1, x2, x3)  =  U21_aag(x2, x3)
succZ122_in_ag(x1, x2)  =  succZ122_in_ag(x2)
U11_ag(x1, x2)  =  U11_ag(x1, x2)
succZ122_out_ag(x1, x2)  =  succZ122_out_ag(x1, x2)
U12_ag(x1, x2, x3)  =  U12_ag(x2, x3)
succ129_in_ag(x1, x2)  =  succ129_in_ag(x2)
succ129_out_ag(x1, x2)  =  succ129_out_ag(x1, x2)
U9_ag(x1, x2)  =  U9_ag(x1, x2)
U10_ag(x1, x2, x3)  =  U10_ag(x2, x3)
U22_aag(x1, x2, x3)  =  U22_aag(x2, x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x3, x4)
addC147_in_aag(x1, x2, x3)  =  addC147_in_aag(x3)
U13_aag(x1, x2, x3, x4)  =  U13_aag(x3, x4)
addz77_out_aag(x1, x2, x3)  =  addz77_out_aag(x1, x2, x3)
addC147_out_aag(x1, x2, x3)  =  addC147_out_aag(x1, x2, x3)
U14_aag(x1, x2)  =  U14_aag(x1, x2)
U15_aag(x1, x2, x3)  =  U15_aag(x2, x3)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x3, x4)
U17_aag(x1, x2)  =  U17_aag(x1, x2)
U18_aag(x1, x2, x3)  =  U18_aag(x2, x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x3, x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x3, x4)
addz73_out_aag(x1, x2, x3)  =  addz73_out_aag(x1, x2, x3)
U31_aag(x1, x2, x3, x4)  =  U31_aag(x3, x4)
U32_aag(x1, x2, x3, x4)  =  U32_aag(x3, x4)
U33_aag(x1, x2, x3, x4)  =  U33_aag(x3, 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(x3, x4)
U41_aag(x1, x2, x3, x4)  =  U41_aag(x3, x4)
U42_aag(x1, x2, x3, x4)  =  U42_aag(x3, x4)
U43_aag(x1, x2, x3, x4)  =  U43_aag(x3, x4)
U44_aag(x1, x2, x3, x4)  =  U44_aag(x3, x4)
BINARYZ43_IN_G(x1)  =  BINARYZ43_IN_G(x1)
BINARY50_IN_G(x1)  =  BINARY50_IN_G(x1)

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

(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:

BINARYZ43_IN_G(one(T103)) → BINARY50_IN_G(T103)
BINARY50_IN_G(zero(T108)) → BINARYZ43_IN_G(T108)
BINARYZ43_IN_G(zero(T99)) → BINARYZ43_IN_G(T99)
BINARY50_IN_G(one(T112)) → BINARY50_IN_G(T112)

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:

BINARYZ43_IN_G(one(T103)) → BINARY50_IN_G(T103)
BINARY50_IN_G(zero(T108)) → BINARYZ43_IN_G(T108)
BINARYZ43_IN_G(zero(T99)) → BINARYZ43_IN_G(T99)
BINARY50_IN_G(one(T112)) → BINARY50_IN_G(T112)

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:

• BINARY50_IN_G(zero(T108)) → BINARYZ43_IN_G(T108)
  The graph contains the following edges 1 > 1

• BINARY50_IN_G(one(T112)) → BINARY50_IN_G(T112)
  The graph contains the following edges 1 > 1

• BINARYZ43_IN_G(zero(T99)) → BINARYZ43_IN_G(T99)
  The graph contains the following edges 1 > 1

• BINARYZ43_IN_G(one(T103)) → BINARY50_IN_G(T103)
  The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

SUCC129_IN_AG(one(T327), zero(T326)) → SUCC129_IN_AG(T327, T326)

The TRS R consists of the following rules:

add1_in_aag(b, b, b) → add1_out_aag(b, b, b)
add1_in_aag(zero(T93), b, zero(T93)) → U34_aag(T93, binaryZ43_in_g(T93))
binaryZ43_in_g(zero(T99)) → U1_g(T99, binaryZ43_in_g(T99))
binaryZ43_in_g(one(T103)) → U2_g(T103, binary50_in_g(T103))
binary50_in_g(b) → binary50_out_g(b)
binary50_in_g(zero(T108)) → U3_g(T108, binaryZ43_in_g(T108))
U3_g(T108, binaryZ43_out_g(T108)) → binary50_out_g(zero(T108))
binary50_in_g(one(T112)) → U4_g(T112, binary50_in_g(T112))
U4_g(T112, binary50_out_g(T112)) → binary50_out_g(one(T112))
U2_g(T103, binary50_out_g(T103)) → binaryZ43_out_g(one(T103))
U1_g(T99, binaryZ43_out_g(T99)) → binaryZ43_out_g(zero(T99))
U34_aag(T93, binaryZ43_out_g(T93)) → add1_out_aag(zero(T93), b, zero(T93))
add1_in_aag(one(T117), b, one(T117)) → U35_aag(T117, binary50_in_g(T117))
U35_aag(T117, binary50_out_g(T117)) → add1_out_aag(one(T117), b, one(T117))
add1_in_aag(b, T122, T122) → U36_aag(T122, binaryZ43_in_g(T122))
U36_aag(T122, binaryZ43_out_g(T122)) → add1_out_aag(b, T122, T122)
add1_in_aag(T138, T139, T137) → U37_aag(T138, T139, T137, addz73_in_aag(T138, T139, T137))
addz73_in_aag(zero(T158), zero(T159), zero(T157)) → U30_aag(T158, T159, T157, addz77_in_aag(T158, T159, T157))
addz77_in_aag(zero(T178), zero(T179), zero(T177)) → U5_aag(T178, T179, T177, addz77_in_aag(T178, T179, T177))
addz77_in_aag(zero(T198), one(T199), one(T197)) → U6_aag(T198, T199, T197, addx86_in_aag(T198, T199, T197))
addx86_in_aag(one(T205), b, one(T205)) → U24_aag(T205, binary50_in_g(T205))
U24_aag(T205, binary50_out_g(T205)) → addx86_out_aag(one(T205), b, one(T205))
addx86_in_aag(zero(T210), b, zero(T210)) → U25_aag(T210, binaryZ43_in_g(T210))
U25_aag(T210, binaryZ43_out_g(T210)) → addx86_out_aag(zero(T210), b, zero(T210))
addx86_in_aag(T226, T227, T225) → U26_aag(T226, T227, T225, addz77_in_aag(T226, T227, T225))
addz77_in_aag(one(T246), zero(T247), one(T245)) → U7_aag(T246, T247, T245, addy100_in_aag(T246, T247, T245))
addy100_in_aag(b, one(T253), one(T253)) → U27_aag(T253, binary50_in_g(T253))
U27_aag(T253, binary50_out_g(T253)) → addy100_out_aag(b, one(T253), one(T253))
addy100_in_aag(b, zero(T258), zero(T258)) → U28_aag(T258, binaryZ43_in_g(T258))
U28_aag(T258, binaryZ43_out_g(T258)) → addy100_out_aag(b, zero(T258), zero(T258))
addy100_in_aag(T274, T275, T273) → U29_aag(T274, T275, T273, addz77_in_aag(T274, T275, T273))
addz77_in_aag(one(T288), one(T289), zero(T287)) → U8_aag(T288, T289, T287, addc112_in_aag(T288, T289, T287))
addc112_in_aag(b, b, one(b)) → addc112_out_aag(b, b, one(b))
addc112_in_aag(T300, b, T299) → U21_aag(T300, T299, succZ122_in_ag(T300, T299))
succZ122_in_ag(zero(T306), one(T306)) → U11_ag(T306, binaryZ43_in_g(T306))
U11_ag(T306, binaryZ43_out_g(T306)) → succZ122_out_ag(zero(T306), one(T306))
succZ122_in_ag(one(T314), zero(T313)) → U12_ag(T314, T313, succ129_in_ag(T314, T313))
succ129_in_ag(b, one(b)) → succ129_out_ag(b, one(b))
succ129_in_ag(zero(T319), one(T319)) → U9_ag(T319, binaryZ43_in_g(T319))
U9_ag(T319, binaryZ43_out_g(T319)) → succ129_out_ag(zero(T319), one(T319))
succ129_in_ag(one(T327), zero(T326)) → U10_ag(T327, T326, succ129_in_ag(T327, T326))
U10_ag(T327, T326, succ129_out_ag(T327, T326)) → succ129_out_ag(one(T327), zero(T326))
U12_ag(T314, T313, succ129_out_ag(T314, T313)) → succZ122_out_ag(one(T314), zero(T313))
U21_aag(T300, T299, succZ122_out_ag(T300, T299)) → addc112_out_aag(T300, b, T299)
addc112_in_aag(b, T338, T337) → U22_aag(T338, T337, succZ122_in_ag(T338, T337))
U22_aag(T338, T337, succZ122_out_ag(T338, T337)) → addc112_out_aag(b, T338, T337)
addc112_in_aag(T354, T355, T353) → U23_aag(T354, T355, T353, addC147_in_aag(T354, T355, T353))
addC147_in_aag(zero(T374), zero(T375), one(T373)) → U13_aag(T374, T375, T373, addz77_in_aag(T374, T375, T373))
U13_aag(T374, T375, T373, addz77_out_aag(T374, T375, T373)) → addC147_out_aag(zero(T374), zero(T375), one(T373))
addC147_in_aag(zero(zero(T401)), one(b), zero(one(T401))) → U14_aag(T401, binaryZ43_in_g(T401))
U14_aag(T401, binaryZ43_out_g(T401)) → addC147_out_aag(zero(zero(T401)), one(b), zero(one(T401)))
addC147_in_aag(zero(one(T413)), one(b), zero(zero(T412))) → U15_aag(T413, T412, succ129_in_ag(T413, T412))
U15_aag(T413, T412, succ129_out_ag(T413, T412)) → addC147_out_aag(zero(one(T413)), one(b), zero(zero(T412)))
addC147_in_aag(zero(T428), one(T429), zero(T427)) → U16_aag(T428, T429, T427, addC147_in_aag(T428, T429, T427))
addC147_in_aag(one(b), zero(zero(T455)), zero(one(T455))) → U17_aag(T455, binaryZ43_in_g(T455))
U17_aag(T455, binaryZ43_out_g(T455)) → addC147_out_aag(one(b), zero(zero(T455)), zero(one(T455)))
addC147_in_aag(one(b), zero(one(T467)), zero(zero(T466))) → U18_aag(T467, T466, succ129_in_ag(T467, T466))
U18_aag(T467, T466, succ129_out_ag(T467, T466)) → addC147_out_aag(one(b), zero(one(T467)), zero(zero(T466)))
addC147_in_aag(one(T482), zero(T483), zero(T481)) → U19_aag(T482, T483, T481, addC147_in_aag(T482, T483, T481))
addC147_in_aag(one(T496), one(T497), one(T495)) → U20_aag(T496, T497, T495, addc112_in_aag(T496, T497, T495))
U20_aag(T496, T497, T495, addc112_out_aag(T496, T497, T495)) → addC147_out_aag(one(T496), one(T497), one(T495))
U19_aag(T482, T483, T481, addC147_out_aag(T482, T483, T481)) → addC147_out_aag(one(T482), zero(T483), zero(T481))
U16_aag(T428, T429, T427, addC147_out_aag(T428, T429, T427)) → addC147_out_aag(zero(T428), one(T429), zero(T427))
U23_aag(T354, T355, T353, addC147_out_aag(T354, T355, T353)) → addc112_out_aag(T354, T355, T353)
U8_aag(T288, T289, T287, addc112_out_aag(T288, T289, T287)) → addz77_out_aag(one(T288), one(T289), zero(T287))
U29_aag(T274, T275, T273, addz77_out_aag(T274, T275, T273)) → addy100_out_aag(T274, T275, T273)
U7_aag(T246, T247, T245, addy100_out_aag(T246, T247, T245)) → addz77_out_aag(one(T246), zero(T247), one(T245))
U26_aag(T226, T227, T225, addz77_out_aag(T226, T227, T225)) → addx86_out_aag(T226, T227, T225)
U6_aag(T198, T199, T197, addx86_out_aag(T198, T199, T197)) → addz77_out_aag(zero(T198), one(T199), one(T197))
U5_aag(T178, T179, T177, addz77_out_aag(T178, T179, T177)) → addz77_out_aag(zero(T178), zero(T179), zero(T177))
U30_aag(T158, T159, T157, addz77_out_aag(T158, T159, T157)) → addz73_out_aag(zero(T158), zero(T159), zero(T157))
addz73_in_aag(zero(T513), one(T514), one(T512)) → U31_aag(T513, T514, T512, addx86_in_aag(T513, T514, T512))
U31_aag(T513, T514, T512, addx86_out_aag(T513, T514, T512)) → addz73_out_aag(zero(T513), one(T514), one(T512))
addz73_in_aag(one(T531), zero(T532), one(T530)) → U32_aag(T531, T532, T530, addy100_in_aag(T531, T532, T530))
U32_aag(T531, T532, T530, addy100_out_aag(T531, T532, T530)) → addz73_out_aag(one(T531), zero(T532), one(T530))
addz73_in_aag(one(T543), one(T544), zero(T542)) → U33_aag(T543, T544, T542, addc112_in_aag(T543, T544, T542))
U33_aag(T543, T544, T542, addc112_out_aag(T543, T544, T542)) → addz73_out_aag(one(T543), one(T544), zero(T542))
U37_aag(T138, T139, T137, addz73_out_aag(T138, T139, T137)) → add1_out_aag(T138, T139, T137)
add1_in_aag(b, zero(T551), zero(T551)) → U38_aag(T551, binaryZ43_in_g(T551))
U38_aag(T551, binaryZ43_out_g(T551)) → add1_out_aag(b, zero(T551), zero(T551))
add1_in_aag(b, one(T557), one(T557)) → U39_aag(T557, binary50_in_g(T557))
U39_aag(T557, binary50_out_g(T557)) → add1_out_aag(b, one(T557), one(T557))
add1_in_aag(T572, T573, T571) → U40_aag(T572, T573, T571, addz73_in_aag(T572, T573, T571))
U40_aag(T572, T573, T571, addz73_out_aag(T572, T573, T571)) → add1_out_aag(T572, T573, T571)
add1_in_aag(zero(T600), zero(T601), zero(T599)) → U41_aag(T600, T601, T599, addz77_in_aag(T600, T601, T599))
U41_aag(T600, T601, T599, addz77_out_aag(T600, T601, T599)) → add1_out_aag(zero(T600), zero(T601), zero(T599))
add1_in_aag(zero(T620), one(T621), one(T619)) → U42_aag(T620, T621, T619, addx86_in_aag(T620, T621, T619))
U42_aag(T620, T621, T619, addx86_out_aag(T620, T621, T619)) → add1_out_aag(zero(T620), one(T621), one(T619))
add1_in_aag(one(T638), zero(T639), one(T637)) → U43_aag(T638, T639, T637, addy100_in_aag(T638, T639, T637))
U43_aag(T638, T639, T637, addy100_out_aag(T638, T639, T637)) → add1_out_aag(one(T638), zero(T639), one(T637))
add1_in_aag(one(T650), one(T651), zero(T649)) → U44_aag(T650, T651, T649, addc112_in_aag(T650, T651, T649))
U44_aag(T650, T651, T649, addc112_out_aag(T650, T651, T649)) → add1_out_aag(one(T650), one(T651), zero(T649))

The argument filtering Pi contains the following mapping:
add1_in_aag(x1, x2, x3)  =  add1_in_aag(x3)
b  =  b
add1_out_aag(x1, x2, x3)  =  add1_out_aag(x1, x2, x3)
zero(x1)  =  zero(x1)
U34_aag(x1, x2)  =  U34_aag(x1, x2)
binaryZ43_in_g(x1)  =  binaryZ43_in_g(x1)
U1_g(x1, x2)  =  U1_g(x1, x2)
one(x1)  =  one(x1)
U2_g(x1, x2)  =  U2_g(x1, x2)
binary50_in_g(x1)  =  binary50_in_g(x1)
binary50_out_g(x1)  =  binary50_out_g(x1)
U3_g(x1, x2)  =  U3_g(x1, x2)
binaryZ43_out_g(x1)  =  binaryZ43_out_g(x1)
U4_g(x1, x2)  =  U4_g(x1, 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(x3, x4)
addz73_in_aag(x1, x2, x3)  =  addz73_in_aag(x3)
U30_aag(x1, x2, x3, x4)  =  U30_aag(x3, x4)
addz77_in_aag(x1, x2, x3)  =  addz77_in_aag(x3)
U5_aag(x1, x2, x3, x4)  =  U5_aag(x3, x4)
U6_aag(x1, x2, x3, x4)  =  U6_aag(x3, x4)
addx86_in_aag(x1, x2, x3)  =  addx86_in_aag(x3)
U24_aag(x1, x2)  =  U24_aag(x1, x2)
addx86_out_aag(x1, x2, x3)  =  addx86_out_aag(x1, x2, x3)
U25_aag(x1, x2)  =  U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x3, x4)
U7_aag(x1, x2, x3, x4)  =  U7_aag(x3, x4)
addy100_in_aag(x1, x2, x3)  =  addy100_in_aag(x3)
U27_aag(x1, x2)  =  U27_aag(x1, x2)
addy100_out_aag(x1, x2, x3)  =  addy100_out_aag(x1, x2, x3)
U28_aag(x1, x2)  =  U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4)  =  U29_aag(x3, x4)
U8_aag(x1, x2, x3, x4)  =  U8_aag(x3, x4)
addc112_in_aag(x1, x2, x3)  =  addc112_in_aag(x3)
addc112_out_aag(x1, x2, x3)  =  addc112_out_aag(x1, x2, x3)
U21_aag(x1, x2, x3)  =  U21_aag(x2, x3)
succZ122_in_ag(x1, x2)  =  succZ122_in_ag(x2)
U11_ag(x1, x2)  =  U11_ag(x1, x2)
succZ122_out_ag(x1, x2)  =  succZ122_out_ag(x1, x2)
U12_ag(x1, x2, x3)  =  U12_ag(x2, x3)
succ129_in_ag(x1, x2)  =  succ129_in_ag(x2)
succ129_out_ag(x1, x2)  =  succ129_out_ag(x1, x2)
U9_ag(x1, x2)  =  U9_ag(x1, x2)
U10_ag(x1, x2, x3)  =  U10_ag(x2, x3)
U22_aag(x1, x2, x3)  =  U22_aag(x2, x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x3, x4)
addC147_in_aag(x1, x2, x3)  =  addC147_in_aag(x3)
U13_aag(x1, x2, x3, x4)  =  U13_aag(x3, x4)
addz77_out_aag(x1, x2, x3)  =  addz77_out_aag(x1, x2, x3)
addC147_out_aag(x1, x2, x3)  =  addC147_out_aag(x1, x2, x3)
U14_aag(x1, x2)  =  U14_aag(x1, x2)
U15_aag(x1, x2, x3)  =  U15_aag(x2, x3)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x3, x4)
U17_aag(x1, x2)  =  U17_aag(x1, x2)
U18_aag(x1, x2, x3)  =  U18_aag(x2, x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x3, x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x3, x4)
addz73_out_aag(x1, x2, x3)  =  addz73_out_aag(x1, x2, x3)
U31_aag(x1, x2, x3, x4)  =  U31_aag(x3, x4)
U32_aag(x1, x2, x3, x4)  =  U32_aag(x3, x4)
U33_aag(x1, x2, x3, x4)  =  U33_aag(x3, 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(x3, x4)
U41_aag(x1, x2, x3, x4)  =  U41_aag(x3, x4)
U42_aag(x1, x2, x3, x4)  =  U42_aag(x3, x4)
U43_aag(x1, x2, x3, x4)  =  U43_aag(x3, x4)
U44_aag(x1, x2, x3, x4)  =  U44_aag(x3, x4)
SUCC129_IN_AG(x1, x2)  =  SUCC129_IN_AG(x2)

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

(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:

SUCC129_IN_AG(one(T327), zero(T326)) → SUCC129_IN_AG(T327, T326)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1)  =  zero(x1)
one(x1)  =  one(x1)
SUCC129_IN_AG(x1, x2)  =  SUCC129_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:

SUCC129_IN_AG(zero(T326)) → SUCC129_IN_AG(T326)

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:

• SUCC129_IN_AG(zero(T326)) → SUCC129_IN_AG(T326)
  The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

ADDX86_IN_AAG(T226, T227, T225) → ADDZ77_IN_AAG(T226, T227, T225)
ADDZ77_IN_AAG(zero(T178), zero(T179), zero(T177)) → ADDZ77_IN_AAG(T178, T179, T177)
ADDZ77_IN_AAG(zero(T198), one(T199), one(T197)) → ADDX86_IN_AAG(T198, T199, T197)
ADDZ77_IN_AAG(one(T246), zero(T247), one(T245)) → ADDY100_IN_AAG(T246, T247, T245)
ADDY100_IN_AAG(T274, T275, T273) → ADDZ77_IN_AAG(T274, T275, T273)
ADDZ77_IN_AAG(one(T288), one(T289), zero(T287)) → ADDC112_IN_AAG(T288, T289, T287)
ADDC112_IN_AAG(T354, T355, T353) → ADDC147_IN_AAG(T354, T355, T353)
ADDC147_IN_AAG(zero(T374), zero(T375), one(T373)) → ADDZ77_IN_AAG(T374, T375, T373)
ADDC147_IN_AAG(zero(T428), one(T429), zero(T427)) → ADDC147_IN_AAG(T428, T429, T427)
ADDC147_IN_AAG(one(T482), zero(T483), zero(T481)) → ADDC147_IN_AAG(T482, T483, T481)
ADDC147_IN_AAG(one(T496), one(T497), one(T495)) → ADDC112_IN_AAG(T496, T497, T495)

The TRS R consists of the following rules:

add1_in_aag(b, b, b) → add1_out_aag(b, b, b)
add1_in_aag(zero(T93), b, zero(T93)) → U34_aag(T93, binaryZ43_in_g(T93))
binaryZ43_in_g(zero(T99)) → U1_g(T99, binaryZ43_in_g(T99))
binaryZ43_in_g(one(T103)) → U2_g(T103, binary50_in_g(T103))
binary50_in_g(b) → binary50_out_g(b)
binary50_in_g(zero(T108)) → U3_g(T108, binaryZ43_in_g(T108))
U3_g(T108, binaryZ43_out_g(T108)) → binary50_out_g(zero(T108))
binary50_in_g(one(T112)) → U4_g(T112, binary50_in_g(T112))
U4_g(T112, binary50_out_g(T112)) → binary50_out_g(one(T112))
U2_g(T103, binary50_out_g(T103)) → binaryZ43_out_g(one(T103))
U1_g(T99, binaryZ43_out_g(T99)) → binaryZ43_out_g(zero(T99))
U34_aag(T93, binaryZ43_out_g(T93)) → add1_out_aag(zero(T93), b, zero(T93))
add1_in_aag(one(T117), b, one(T117)) → U35_aag(T117, binary50_in_g(T117))
U35_aag(T117, binary50_out_g(T117)) → add1_out_aag(one(T117), b, one(T117))
add1_in_aag(b, T122, T122) → U36_aag(T122, binaryZ43_in_g(T122))
U36_aag(T122, binaryZ43_out_g(T122)) → add1_out_aag(b, T122, T122)
add1_in_aag(T138, T139, T137) → U37_aag(T138, T139, T137, addz73_in_aag(T138, T139, T137))
addz73_in_aag(zero(T158), zero(T159), zero(T157)) → U30_aag(T158, T159, T157, addz77_in_aag(T158, T159, T157))
addz77_in_aag(zero(T178), zero(T179), zero(T177)) → U5_aag(T178, T179, T177, addz77_in_aag(T178, T179, T177))
addz77_in_aag(zero(T198), one(T199), one(T197)) → U6_aag(T198, T199, T197, addx86_in_aag(T198, T199, T197))
addx86_in_aag(one(T205), b, one(T205)) → U24_aag(T205, binary50_in_g(T205))
U24_aag(T205, binary50_out_g(T205)) → addx86_out_aag(one(T205), b, one(T205))
addx86_in_aag(zero(T210), b, zero(T210)) → U25_aag(T210, binaryZ43_in_g(T210))
U25_aag(T210, binaryZ43_out_g(T210)) → addx86_out_aag(zero(T210), b, zero(T210))
addx86_in_aag(T226, T227, T225) → U26_aag(T226, T227, T225, addz77_in_aag(T226, T227, T225))
addz77_in_aag(one(T246), zero(T247), one(T245)) → U7_aag(T246, T247, T245, addy100_in_aag(T246, T247, T245))
addy100_in_aag(b, one(T253), one(T253)) → U27_aag(T253, binary50_in_g(T253))
U27_aag(T253, binary50_out_g(T253)) → addy100_out_aag(b, one(T253), one(T253))
addy100_in_aag(b, zero(T258), zero(T258)) → U28_aag(T258, binaryZ43_in_g(T258))
U28_aag(T258, binaryZ43_out_g(T258)) → addy100_out_aag(b, zero(T258), zero(T258))
addy100_in_aag(T274, T275, T273) → U29_aag(T274, T275, T273, addz77_in_aag(T274, T275, T273))
addz77_in_aag(one(T288), one(T289), zero(T287)) → U8_aag(T288, T289, T287, addc112_in_aag(T288, T289, T287))
addc112_in_aag(b, b, one(b)) → addc112_out_aag(b, b, one(b))
addc112_in_aag(T300, b, T299) → U21_aag(T300, T299, succZ122_in_ag(T300, T299))
succZ122_in_ag(zero(T306), one(T306)) → U11_ag(T306, binaryZ43_in_g(T306))
U11_ag(T306, binaryZ43_out_g(T306)) → succZ122_out_ag(zero(T306), one(T306))
succZ122_in_ag(one(T314), zero(T313)) → U12_ag(T314, T313, succ129_in_ag(T314, T313))
succ129_in_ag(b, one(b)) → succ129_out_ag(b, one(b))
succ129_in_ag(zero(T319), one(T319)) → U9_ag(T319, binaryZ43_in_g(T319))
U9_ag(T319, binaryZ43_out_g(T319)) → succ129_out_ag(zero(T319), one(T319))
succ129_in_ag(one(T327), zero(T326)) → U10_ag(T327, T326, succ129_in_ag(T327, T326))
U10_ag(T327, T326, succ129_out_ag(T327, T326)) → succ129_out_ag(one(T327), zero(T326))
U12_ag(T314, T313, succ129_out_ag(T314, T313)) → succZ122_out_ag(one(T314), zero(T313))
U21_aag(T300, T299, succZ122_out_ag(T300, T299)) → addc112_out_aag(T300, b, T299)
addc112_in_aag(b, T338, T337) → U22_aag(T338, T337, succZ122_in_ag(T338, T337))
U22_aag(T338, T337, succZ122_out_ag(T338, T337)) → addc112_out_aag(b, T338, T337)
addc112_in_aag(T354, T355, T353) → U23_aag(T354, T355, T353, addC147_in_aag(T354, T355, T353))
addC147_in_aag(zero(T374), zero(T375), one(T373)) → U13_aag(T374, T375, T373, addz77_in_aag(T374, T375, T373))
U13_aag(T374, T375, T373, addz77_out_aag(T374, T375, T373)) → addC147_out_aag(zero(T374), zero(T375), one(T373))
addC147_in_aag(zero(zero(T401)), one(b), zero(one(T401))) → U14_aag(T401, binaryZ43_in_g(T401))
U14_aag(T401, binaryZ43_out_g(T401)) → addC147_out_aag(zero(zero(T401)), one(b), zero(one(T401)))
addC147_in_aag(zero(one(T413)), one(b), zero(zero(T412))) → U15_aag(T413, T412, succ129_in_ag(T413, T412))
U15_aag(T413, T412, succ129_out_ag(T413, T412)) → addC147_out_aag(zero(one(T413)), one(b), zero(zero(T412)))
addC147_in_aag(zero(T428), one(T429), zero(T427)) → U16_aag(T428, T429, T427, addC147_in_aag(T428, T429, T427))
addC147_in_aag(one(b), zero(zero(T455)), zero(one(T455))) → U17_aag(T455, binaryZ43_in_g(T455))
U17_aag(T455, binaryZ43_out_g(T455)) → addC147_out_aag(one(b), zero(zero(T455)), zero(one(T455)))
addC147_in_aag(one(b), zero(one(T467)), zero(zero(T466))) → U18_aag(T467, T466, succ129_in_ag(T467, T466))
U18_aag(T467, T466, succ129_out_ag(T467, T466)) → addC147_out_aag(one(b), zero(one(T467)), zero(zero(T466)))
addC147_in_aag(one(T482), zero(T483), zero(T481)) → U19_aag(T482, T483, T481, addC147_in_aag(T482, T483, T481))
addC147_in_aag(one(T496), one(T497), one(T495)) → U20_aag(T496, T497, T495, addc112_in_aag(T496, T497, T495))
U20_aag(T496, T497, T495, addc112_out_aag(T496, T497, T495)) → addC147_out_aag(one(T496), one(T497), one(T495))
U19_aag(T482, T483, T481, addC147_out_aag(T482, T483, T481)) → addC147_out_aag(one(T482), zero(T483), zero(T481))
U16_aag(T428, T429, T427, addC147_out_aag(T428, T429, T427)) → addC147_out_aag(zero(T428), one(T429), zero(T427))
U23_aag(T354, T355, T353, addC147_out_aag(T354, T355, T353)) → addc112_out_aag(T354, T355, T353)
U8_aag(T288, T289, T287, addc112_out_aag(T288, T289, T287)) → addz77_out_aag(one(T288), one(T289), zero(T287))
U29_aag(T274, T275, T273, addz77_out_aag(T274, T275, T273)) → addy100_out_aag(T274, T275, T273)
U7_aag(T246, T247, T245, addy100_out_aag(T246, T247, T245)) → addz77_out_aag(one(T246), zero(T247), one(T245))
U26_aag(T226, T227, T225, addz77_out_aag(T226, T227, T225)) → addx86_out_aag(T226, T227, T225)
U6_aag(T198, T199, T197, addx86_out_aag(T198, T199, T197)) → addz77_out_aag(zero(T198), one(T199), one(T197))
U5_aag(T178, T179, T177, addz77_out_aag(T178, T179, T177)) → addz77_out_aag(zero(T178), zero(T179), zero(T177))
U30_aag(T158, T159, T157, addz77_out_aag(T158, T159, T157)) → addz73_out_aag(zero(T158), zero(T159), zero(T157))
addz73_in_aag(zero(T513), one(T514), one(T512)) → U31_aag(T513, T514, T512, addx86_in_aag(T513, T514, T512))
U31_aag(T513, T514, T512, addx86_out_aag(T513, T514, T512)) → addz73_out_aag(zero(T513), one(T514), one(T512))
addz73_in_aag(one(T531), zero(T532), one(T530)) → U32_aag(T531, T532, T530, addy100_in_aag(T531, T532, T530))
U32_aag(T531, T532, T530, addy100_out_aag(T531, T532, T530)) → addz73_out_aag(one(T531), zero(T532), one(T530))
addz73_in_aag(one(T543), one(T544), zero(T542)) → U33_aag(T543, T544, T542, addc112_in_aag(T543, T544, T542))
U33_aag(T543, T544, T542, addc112_out_aag(T543, T544, T542)) → addz73_out_aag(one(T543), one(T544), zero(T542))
U37_aag(T138, T139, T137, addz73_out_aag(T138, T139, T137)) → add1_out_aag(T138, T139, T137)
add1_in_aag(b, zero(T551), zero(T551)) → U38_aag(T551, binaryZ43_in_g(T551))
U38_aag(T551, binaryZ43_out_g(T551)) → add1_out_aag(b, zero(T551), zero(T551))
add1_in_aag(b, one(T557), one(T557)) → U39_aag(T557, binary50_in_g(T557))
U39_aag(T557, binary50_out_g(T557)) → add1_out_aag(b, one(T557), one(T557))
add1_in_aag(T572, T573, T571) → U40_aag(T572, T573, T571, addz73_in_aag(T572, T573, T571))
U40_aag(T572, T573, T571, addz73_out_aag(T572, T573, T571)) → add1_out_aag(T572, T573, T571)
add1_in_aag(zero(T600), zero(T601), zero(T599)) → U41_aag(T600, T601, T599, addz77_in_aag(T600, T601, T599))
U41_aag(T600, T601, T599, addz77_out_aag(T600, T601, T599)) → add1_out_aag(zero(T600), zero(T601), zero(T599))
add1_in_aag(zero(T620), one(T621), one(T619)) → U42_aag(T620, T621, T619, addx86_in_aag(T620, T621, T619))
U42_aag(T620, T621, T619, addx86_out_aag(T620, T621, T619)) → add1_out_aag(zero(T620), one(T621), one(T619))
add1_in_aag(one(T638), zero(T639), one(T637)) → U43_aag(T638, T639, T637, addy100_in_aag(T638, T639, T637))
U43_aag(T638, T639, T637, addy100_out_aag(T638, T639, T637)) → add1_out_aag(one(T638), zero(T639), one(T637))
add1_in_aag(one(T650), one(T651), zero(T649)) → U44_aag(T650, T651, T649, addc112_in_aag(T650, T651, T649))
U44_aag(T650, T651, T649, addc112_out_aag(T650, T651, T649)) → add1_out_aag(one(T650), one(T651), zero(T649))

The argument filtering Pi contains the following mapping:
add1_in_aag(x1, x2, x3)  =  add1_in_aag(x3)
b  =  b
add1_out_aag(x1, x2, x3)  =  add1_out_aag(x1, x2, x3)
zero(x1)  =  zero(x1)
U34_aag(x1, x2)  =  U34_aag(x1, x2)
binaryZ43_in_g(x1)  =  binaryZ43_in_g(x1)
U1_g(x1, x2)  =  U1_g(x1, x2)
one(x1)  =  one(x1)
U2_g(x1, x2)  =  U2_g(x1, x2)
binary50_in_g(x1)  =  binary50_in_g(x1)
binary50_out_g(x1)  =  binary50_out_g(x1)
U3_g(x1, x2)  =  U3_g(x1, x2)
binaryZ43_out_g(x1)  =  binaryZ43_out_g(x1)
U4_g(x1, x2)  =  U4_g(x1, 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(x3, x4)
addz73_in_aag(x1, x2, x3)  =  addz73_in_aag(x3)
U30_aag(x1, x2, x3, x4)  =  U30_aag(x3, x4)
addz77_in_aag(x1, x2, x3)  =  addz77_in_aag(x3)
U5_aag(x1, x2, x3, x4)  =  U5_aag(x3, x4)
U6_aag(x1, x2, x3, x4)  =  U6_aag(x3, x4)
addx86_in_aag(x1, x2, x3)  =  addx86_in_aag(x3)
U24_aag(x1, x2)  =  U24_aag(x1, x2)
addx86_out_aag(x1, x2, x3)  =  addx86_out_aag(x1, x2, x3)
U25_aag(x1, x2)  =  U25_aag(x1, x2)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x3, x4)
U7_aag(x1, x2, x3, x4)  =  U7_aag(x3, x4)
addy100_in_aag(x1, x2, x3)  =  addy100_in_aag(x3)
U27_aag(x1, x2)  =  U27_aag(x1, x2)
addy100_out_aag(x1, x2, x3)  =  addy100_out_aag(x1, x2, x3)
U28_aag(x1, x2)  =  U28_aag(x1, x2)
U29_aag(x1, x2, x3, x4)  =  U29_aag(x3, x4)
U8_aag(x1, x2, x3, x4)  =  U8_aag(x3, x4)
addc112_in_aag(x1, x2, x3)  =  addc112_in_aag(x3)
addc112_out_aag(x1, x2, x3)  =  addc112_out_aag(x1, x2, x3)
U21_aag(x1, x2, x3)  =  U21_aag(x2, x3)
succZ122_in_ag(x1, x2)  =  succZ122_in_ag(x2)
U11_ag(x1, x2)  =  U11_ag(x1, x2)
succZ122_out_ag(x1, x2)  =  succZ122_out_ag(x1, x2)
U12_ag(x1, x2, x3)  =  U12_ag(x2, x3)
succ129_in_ag(x1, x2)  =  succ129_in_ag(x2)
succ129_out_ag(x1, x2)  =  succ129_out_ag(x1, x2)
U9_ag(x1, x2)  =  U9_ag(x1, x2)
U10_ag(x1, x2, x3)  =  U10_ag(x2, x3)
U22_aag(x1, x2, x3)  =  U22_aag(x2, x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x3, x4)
addC147_in_aag(x1, x2, x3)  =  addC147_in_aag(x3)
U13_aag(x1, x2, x3, x4)  =  U13_aag(x3, x4)
addz77_out_aag(x1, x2, x3)  =  addz77_out_aag(x1, x2, x3)
addC147_out_aag(x1, x2, x3)  =  addC147_out_aag(x1, x2, x3)
U14_aag(x1, x2)  =  U14_aag(x1, x2)
U15_aag(x1, x2, x3)  =  U15_aag(x2, x3)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x3, x4)
U17_aag(x1, x2)  =  U17_aag(x1, x2)
U18_aag(x1, x2, x3)  =  U18_aag(x2, x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x3, x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x3, x4)
addz73_out_aag(x1, x2, x3)  =  addz73_out_aag(x1, x2, x3)
U31_aag(x1, x2, x3, x4)  =  U31_aag(x3, x4)
U32_aag(x1, x2, x3, x4)  =  U32_aag(x3, x4)
U33_aag(x1, x2, x3, x4)  =  U33_aag(x3, 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(x3, x4)
U41_aag(x1, x2, x3, x4)  =  U41_aag(x3, x4)
U42_aag(x1, x2, x3, x4)  =  U42_aag(x3, x4)
U43_aag(x1, x2, x3, x4)  =  U43_aag(x3, x4)
U44_aag(x1, x2, x3, x4)  =  U44_aag(x3, x4)
ADDZ77_IN_AAG(x1, x2, x3)  =  ADDZ77_IN_AAG(x3)
ADDX86_IN_AAG(x1, x2, x3)  =  ADDX86_IN_AAG(x3)
ADDY100_IN_AAG(x1, x2, x3)  =  ADDY100_IN_AAG(x3)
ADDC112_IN_AAG(x1, x2, x3)  =  ADDC112_IN_AAG(x3)
ADDC147_IN_AAG(x1, x2, x3)  =  ADDC147_IN_AAG(x3)

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

(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:

ADDX86_IN_AAG(T226, T227, T225) → ADDZ77_IN_AAG(T226, T227, T225)
ADDZ77_IN_AAG(zero(T178), zero(T179), zero(T177)) → ADDZ77_IN_AAG(T178, T179, T177)
ADDZ77_IN_AAG(zero(T198), one(T199), one(T197)) → ADDX86_IN_AAG(T198, T199, T197)
ADDZ77_IN_AAG(one(T246), zero(T247), one(T245)) → ADDY100_IN_AAG(T246, T247, T245)
ADDY100_IN_AAG(T274, T275, T273) → ADDZ77_IN_AAG(T274, T275, T273)
ADDZ77_IN_AAG(one(T288), one(T289), zero(T287)) → ADDC112_IN_AAG(T288, T289, T287)
ADDC112_IN_AAG(T354, T355, T353) → ADDC147_IN_AAG(T354, T355, T353)
ADDC147_IN_AAG(zero(T374), zero(T375), one(T373)) → ADDZ77_IN_AAG(T374, T375, T373)
ADDC147_IN_AAG(zero(T428), one(T429), zero(T427)) → ADDC147_IN_AAG(T428, T429, T427)
ADDC147_IN_AAG(one(T482), zero(T483), zero(T481)) → ADDC147_IN_AAG(T482, T483, T481)
ADDC147_IN_AAG(one(T496), one(T497), one(T495)) → ADDC112_IN_AAG(T496, T497, T495)

R is empty.
The argument filtering Pi contains the following mapping:
zero(x1)  =  zero(x1)
one(x1)  =  one(x1)
ADDZ77_IN_AAG(x1, x2, x3)  =  ADDZ77_IN_AAG(x3)
ADDX86_IN_AAG(x1, x2, x3)  =  ADDX86_IN_AAG(x3)
ADDY100_IN_AAG(x1, x2, x3)  =  ADDY100_IN_AAG(x3)
ADDC112_IN_AAG(x1, x2, x3)  =  ADDC112_IN_AAG(x3)
ADDC147_IN_AAG(x1, x2, x3)  =  ADDC147_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:

ADDX86_IN_AAG(T225) → ADDZ77_IN_AAG(T225)
ADDZ77_IN_AAG(zero(T177)) → ADDZ77_IN_AAG(T177)
ADDZ77_IN_AAG(one(T197)) → ADDX86_IN_AAG(T197)
ADDZ77_IN_AAG(one(T245)) → ADDY100_IN_AAG(T245)
ADDY100_IN_AAG(T273) → ADDZ77_IN_AAG(T273)
ADDZ77_IN_AAG(zero(T287)) → ADDC112_IN_AAG(T287)
ADDC112_IN_AAG(T353) → ADDC147_IN_AAG(T353)
ADDC147_IN_AAG(one(T373)) → ADDZ77_IN_AAG(T373)
ADDC147_IN_AAG(zero(T427)) → ADDC147_IN_AAG(T427)
ADDC147_IN_AAG(one(T495)) → ADDC112_IN_AAG(T495)

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:

• ADDZ77_IN_AAG(one(T197)) → ADDX86_IN_AAG(T197)
  The graph contains the following edges 1 > 1

• ADDZ77_IN_AAG(zero(T177)) → ADDZ77_IN_AAG(T177)
  The graph contains the following edges 1 > 1

• ADDX86_IN_AAG(T225) → ADDZ77_IN_AAG(T225)
  The graph contains the following edges 1 >= 1

• ADDY100_IN_AAG(T273) → ADDZ77_IN_AAG(T273)
  The graph contains the following edges 1 >= 1

• ADDC147_IN_AAG(one(T373)) → ADDZ77_IN_AAG(T373)
  The graph contains the following edges 1 > 1

• ADDZ77_IN_AAG(one(T245)) → ADDY100_IN_AAG(T245)
  The graph contains the following edges 1 > 1

• ADDZ77_IN_AAG(zero(T287)) → ADDC112_IN_AAG(T287)
  The graph contains the following edges 1 > 1

• ADDC112_IN_AAG(T353) → ADDC147_IN_AAG(T353)
  The graph contains the following edges 1 >= 1

• ADDC147_IN_AAG(one(T495)) → ADDC112_IN_AAG(T495)
  The graph contains the following edges 1 > 1

• ADDC147_IN_AAG(zero(T427)) → ADDC147_IN_AAG(T427)
  The graph contains the following edges 1 > 1

(29) YES