Left Termination proof of /tmp/tmpNZUj4i/dependency2.pl

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

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇒, 382 ms)

↳2 Prolog

↳3 PrologToPiTRSProof (⇒, 0 ms)

↳4 PiTRS

↳5 DependencyPairsProof (⇔, 3 ms)

↳6 PiDP

↳7 DependencyGraphProof (⇔, 0 ms)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔, 0 ms)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇔, 14 ms)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔, 0 ms)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔, 0 ms)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇔, 0 ms)

        ↳20 QDP

        ↳21 QDPSizeChangeProof (⇔, 0 ms)

        ↳22 YES

(0) Obligation:

Clauses:

h(X) :- ','(f(X), g(X)).
f(c(0, X1)).
f(c(X, Y)) :- ','(no(zero(X)), ','(p(X, P), f(c(P, s(Y))))).
g(c(X2, 0)).
g(c(X, Y)) :- ','(no(zero(Y)), ','(p(Y, P), g(c(s(X), P)))).
p(0, 0).
p(s(X), X).
zero(0).
no(X) :- ','(X, ','(!, failure(a))).
no(X3).
failure(b).

Query: h(g)

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph ICLP10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: h(T1)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: h(T1), SCOPE: 1, CLAUSE: 0\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(f(T3), g(T3))\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ','(f(T3), g(T3)), SCOPE: 2, CLAUSE: 1 | ','(f(T3), g(T3)), SCOPE: 2, CLAUSE: 2\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(f(T3), g(T3)), SCOPE: 2, CLAUSE: 1\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ','(f(T3), g(T3)), SCOPE: 2, CLAUSE: 2\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: g(c(0, T8))\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: g(c(0, T8)), SCOPE: 3, CLAUSE: 3 | g(c(0, T8)), SCOPE: 3, CLAUSE: 4\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: g(c(0, T8)), SCOPE: 3, CLAUSE: 3\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: g(c(0, T8)), SCOPE: 3, CLAUSE: 4\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(no(zero(T11)), ','(p(T11, X26), g(c(s(0), X26))))\n\nT11 is ground\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(no(zero(T11)), ','(p(T11, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 8 | ','(no(zero(T11)), ','(p(T11, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nT11 is ground\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(','(call(zero(T14)), ','(!_4, failure(a))), ','(p(T14, X26), g(c(s(0), X26)))) | ','(no(zero(T14)), ','(p(T14, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nT14 is ground\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(zero(T14), ','(','(!_4, failure(a)), ','(p(T14, X26), g(c(s(0), X26))))) | ?_5 | ','(no(zero(T14)), ','(p(T14, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nT14 is ground\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: ','(zero(T14), ','(','(!_4, failure(a)), ','(p(T14, X26), g(c(s(0), X26))))), SCOPE: 6, CLAUSE: 7 | ?_6 | ?_5 | ','(no(zero(T14)), ','(p(T14, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nT14 is ground\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: ','(','(!_4, failure(a)), ','(p(0, X26), g(c(s(0), X26)))) | ?_6 | ?_5 | ','(no(zero(0)), ','(p(0, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ?_6 | ?_5 | ','(no(zero(T14)), ','(p(T14, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nT14 is ground\nX26 is free\nzero(T14) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ','(failure(a), ','(p(0, X26), g(c(s(0), X26))))\n\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(failure(a), ','(p(0, X26), g(c(s(0), X26)))), SCOPE: 7, CLAUSE: 10\n\nX26 is free", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ?_5 | ','(no(zero(T14)), ','(p(T14, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nT14 is ground\nX26 is free\nzero(T14) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(no(zero(T14)), ','(p(T14, X26), g(c(s(0), X26)))), SCOPE: 4, CLAUSE: 9\n\nT14 is ground\nX26 is free\nzero(T14) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(p(T17, X26), g(c(s(0), X26)))\n\nT17 is ground\nX26 is free\nzero(T17) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(p(T17, X26), g(c(s(0), X26))), SCOPE: 8, CLAUSE: 5 | ','(p(T17, X26), g(c(s(0), X26))), SCOPE: 8, CLAUSE: 6\n\nT17 is ground\nX26 is free\nzero(T17) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(p(T17, X26), g(c(s(0), X26))), SCOPE: 8, CLAUSE: 6\n\nT17 is ground\nX26 is free\nzero(T17) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: g(c(s(0), T20))\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: g(c(s(0), T20)), SCOPE: 9, CLAUSE: 3 | g(c(s(0), T20)), SCOPE: 9, CLAUSE: 4\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: g(c(s(0), T20)), SCOPE: 9, CLAUSE: 3\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: g(c(s(0), T20)), SCOPE: 9, CLAUSE: 4\n\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ','(no(zero(T23)), ','(p(T23, X55), g(c(s(s(0)), X55))))\n\nT23 is ground\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(no(zero(T23)), ','(p(T23, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 8 | ','(no(zero(T23)), ','(p(T23, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nT23 is ground\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(','(call(zero(T26)), ','(!_10, failure(a))), ','(p(T26, X55), g(c(s(s(0)), X55)))) | ','(no(zero(T26)), ','(p(T26, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nT26 is ground\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(zero(T26), ','(','(!_10, failure(a)), ','(p(T26, X55), g(c(s(s(0)), X55))))) | ?_11 | ','(no(zero(T26)), ','(p(T26, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nT26 is ground\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(zero(T26), ','(','(!_10, failure(a)), ','(p(T26, X55), g(c(s(s(0)), X55))))), SCOPE: 12, CLAUSE: 7 | ?_12 | ?_11 | ','(no(zero(T26)), ','(p(T26, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nT26 is ground\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(','(!_10, failure(a)), ','(p(0, X55), g(c(s(s(0)), X55)))) | ?_12 | ?_11 | ','(no(zero(0)), ','(p(0, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ?_12 | ?_11 | ','(no(zero(T26)), ','(p(T26, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nT26 is ground\nX55 is free\nzero(T26) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(failure(a), ','(p(0, X55), g(c(s(s(0)), X55))))\n\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(failure(a), ','(p(0, X55), g(c(s(s(0)), X55)))), SCOPE: 13, CLAUSE: 10\n\nX55 is free", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ?_11 | ','(no(zero(T26)), ','(p(T26, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nT26 is ground\nX55 is free\nzero(T26) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(no(zero(T26)), ','(p(T26, X55), g(c(s(s(0)), X55)))), SCOPE: 10, CLAUSE: 9\n\nT26 is ground\nX55 is free\nzero(T26) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(p(T29, X55), g(c(s(s(0)), X55)))\n\nT29 is ground\nX55 is free\nzero(T29) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(p(T29, X55), g(c(s(s(0)), X55))), SCOPE: 14, CLAUSE: 5 | ','(p(T29, X55), g(c(s(s(0)), X55))), SCOPE: 14, CLAUSE: 6\n\nT29 is ground\nX55 is free\nzero(T29) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(p(T29, X55), g(c(s(s(0)), X55))), SCOPE: 14, CLAUSE: 6\n\nT29 is ground\nX55 is free\nzero(T29) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: g(c(s(s(0)), T32))\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: g(c(s(s(0)), T32)), SCOPE: 15, CLAUSE: 3 | g(c(s(s(0)), T32)), SCOPE: 15, CLAUSE: 4\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: g(c(s(s(0)), T32)), SCOPE: 15, CLAUSE: 3\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: g(c(s(s(0)), T32)), SCOPE: 15, CLAUSE: 4\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(no(zero(T35)), ','(p(T35, X84), g(c(s(s(s(0))), X84))))\n\nT35 is ground\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(no(zero(T35)), ','(p(T35, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 8 | ','(no(zero(T35)), ','(p(T35, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nT35 is ground\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(','(call(zero(T38)), ','(!_16, failure(a))), ','(p(T38, X84), g(c(s(s(s(0))), X84)))) | ','(no(zero(T38)), ','(p(T38, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nT38 is ground\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ','(zero(T38), ','(','(!_16, failure(a)), ','(p(T38, X84), g(c(s(s(s(0))), X84))))) | ?_17 | ','(no(zero(T38)), ','(p(T38, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nT38 is ground\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(zero(T38), ','(','(!_16, failure(a)), ','(p(T38, X84), g(c(s(s(s(0))), X84))))), SCOPE: 18, CLAUSE: 7 | ?_18 | ?_17 | ','(no(zero(T38)), ','(p(T38, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nT38 is ground\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(','(!_16, failure(a)), ','(p(0, X84), g(c(s(s(s(0))), X84)))) | ?_18 | ?_17 | ','(no(zero(0)), ','(p(0, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ?_18 | ?_17 | ','(no(zero(T38)), ','(p(T38, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nT38 is ground\nX84 is free\nzero(T38) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(failure(a), ','(p(0, X84), g(c(s(s(s(0))), X84))))\n\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: ','(failure(a), ','(p(0, X84), g(c(s(s(s(0))), X84)))), SCOPE: 19, CLAUSE: 10\n\nX84 is free", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ?_17 | ','(no(zero(T38)), ','(p(T38, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nT38 is ground\nX84 is free\nzero(T38) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(no(zero(T38)), ','(p(T38, X84), g(c(s(s(s(0))), X84)))), SCOPE: 16, CLAUSE: 9\n\nT38 is ground\nX84 is free\nzero(T38) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: ','(p(T41, X84), g(c(s(s(s(0))), X84)))\n\nT41 is ground\nX84 is free\nzero(T41) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ','(p(T41, X84), g(c(s(s(s(0))), X84))), SCOPE: 20, CLAUSE: 5 | ','(p(T41, X84), g(c(s(s(s(0))), X84))), SCOPE: 20, CLAUSE: 6\n\nT41 is ground\nX84 is free\nzero(T41) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(p(T41, X84), g(c(s(s(s(0))), X84))), SCOPE: 20, CLAUSE: 6\n\nT41 is ground\nX84 is free\nzero(T41) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: g(c(s(s(s(0))), T44))\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: g(c(s(s(s(0))), T44)), SCOPE: 21, CLAUSE: 3 | g(c(s(s(s(0))), T44)), SCOPE: 21, CLAUSE: 4\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: g(c(s(s(s(0))), T44)), SCOPE: 21, CLAUSE: 3\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: g(c(s(s(s(0))), T44)), SCOPE: 21, CLAUSE: 4\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(no(zero(T47)), ','(p(T47, X113), g(c(s(s(s(s(0)))), X113))))\n\nT47 is ground\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ','(no(zero(T47)), ','(p(T47, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 8 | ','(no(zero(T47)), ','(p(T47, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nT47 is ground\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(','(call(zero(T50)), ','(!_22, failure(a))), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113)))) | ','(no(zero(T50)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nT50 is ground\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: ','(zero(T50), ','(','(!_22, failure(a)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113))))) | ?_23 | ','(no(zero(T50)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nT50 is ground\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: ','(zero(T50), ','(','(!_22, failure(a)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113))))), SCOPE: 24, CLAUSE: 7 | ?_24 | ?_23 | ','(no(zero(T50)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nT50 is ground\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(','(!_22, failure(a)), ','(p(0, X113), g(c(s(s(s(s(0)))), X113)))) | ?_24 | ?_23 | ','(no(zero(0)), ','(p(0, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ?_24 | ?_23 | ','(no(zero(T50)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nT50 is ground\nX113 is free\nzero(T50) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(failure(a), ','(p(0, X113), g(c(s(s(s(s(0)))), X113))))\n\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ','(failure(a), ','(p(0, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 25, CLAUSE: 10\n\nX113 is free", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ?_23 | ','(no(zero(T50)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nT50 is ground\nX113 is free\nzero(T50) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: ','(no(zero(T50)), ','(p(T50, X113), g(c(s(s(s(s(0)))), X113)))), SCOPE: 22, CLAUSE: 9\n\nT50 is ground\nX113 is free\nzero(T50) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: ','(p(T53, X113), g(c(s(s(s(s(0)))), X113)))\n\nT53 is ground\nX113 is free\nzero(T53) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(p(T53, X113), g(c(s(s(s(s(0)))), X113))), SCOPE: 26, CLAUSE: 5 | ','(p(T53, X113), g(c(s(s(s(s(0)))), X113))), SCOPE: 26, CLAUSE: 6\n\nT53 is ground\nX113 is free\nzero(T53) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(p(T53, X113), g(c(s(s(s(s(0)))), X113))), SCOPE: 26, CLAUSE: 6\n\nT53 is ground\nX113 is free\nzero(T53) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: g(c(s(s(s(s(0)))), T56))\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: g(c(s(s(s(s(0)))), T56)), SCOPE: 27, CLAUSE: 3 | g(c(s(s(s(s(0)))), T56)), SCOPE: 27, CLAUSE: 4\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: g(c(s(s(s(s(0)))), T56)), SCOPE: 27, CLAUSE: 3\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: g(c(s(s(s(s(0)))), T56)), SCOPE: 27, CLAUSE: 4\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: ','(no(zero(T59)), ','(p(T59, X142), g(c(s(s(s(s(s(0))))), X142))))\n\nT59 is ground\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ','(no(zero(T59)), ','(p(T59, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 8 | ','(no(zero(T59)), ','(p(T59, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nT59 is ground\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(','(call(zero(T62)), ','(!_28, failure(a))), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142)))) | ','(no(zero(T62)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nT62 is ground\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(zero(T62), ','(','(!_28, failure(a)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142))))) | ?_29 | ','(no(zero(T62)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nT62 is ground\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(zero(T62), ','(','(!_28, failure(a)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142))))), SCOPE: 30, CLAUSE: 7 | ?_30 | ?_29 | ','(no(zero(T62)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nT62 is ground\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(','(!_28, failure(a)), ','(p(0, X142), g(c(s(s(s(s(s(0))))), X142)))) | ?_30 | ?_29 | ','(no(zero(0)), ','(p(0, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ?_30 | ?_29 | ','(no(zero(T62)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nT62 is ground\nX142 is free\nzero(T62) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(failure(a), ','(p(0, X142), g(c(s(s(s(s(s(0))))), X142))))\n\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(failure(a), ','(p(0, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 31, CLAUSE: 10\n\nX142 is free", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ?_29 | ','(no(zero(T62)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nT62 is ground\nX142 is free\nzero(T62) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(no(zero(T62)), ','(p(T62, X142), g(c(s(s(s(s(s(0))))), X142)))), SCOPE: 28, CLAUSE: 9\n\nT62 is ground\nX142 is free\nzero(T62) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(p(T65, X142), g(c(s(s(s(s(s(0))))), X142)))\n\nT65 is ground\nX142 is free\nzero(T65) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(p(T65, X142), g(c(s(s(s(s(s(0))))), X142))), SCOPE: 32, CLAUSE: 5 | ','(p(T65, X142), g(c(s(s(s(s(s(0))))), X142))), SCOPE: 32, CLAUSE: 6\n\nT65 is ground\nX142 is free\nzero(T65) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: ','(p(T65, X142), g(c(s(s(s(s(s(0))))), X142))), SCOPE: 32, CLAUSE: 6\n\nT65 is ground\nX142 is free\nzero(T65) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: g(c(s(s(s(s(s(0))))), T68))\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: g(c(s(s(s(s(s(0))))), T68)), SCOPE: 33, CLAUSE: 3 | g(c(s(s(s(s(s(0))))), T68)), SCOPE: 33, CLAUSE: 4\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: g(c(s(s(s(s(s(0))))), T68)), SCOPE: 33, CLAUSE: 3\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: g(c(s(s(s(s(s(0))))), T68)), SCOPE: 33, CLAUSE: 4\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: ','(no(zero(T71)), ','(p(T71, X171), g(c(s(s(s(s(s(s(0)))))), X171))))\n\nT71 is ground\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(no(zero(T71)), ','(p(T71, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 8 | ','(no(zero(T71)), ','(p(T71, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nT71 is ground\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ','(','(call(zero(T74)), ','(!_34, failure(a))), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171)))) | ','(no(zero(T74)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nT74 is ground\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: ','(zero(T74), ','(','(!_34, failure(a)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171))))) | ?_35 | ','(no(zero(T74)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nT74 is ground\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(zero(T74), ','(','(!_34, failure(a)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171))))), SCOPE: 36, CLAUSE: 7 | ?_36 | ?_35 | ','(no(zero(T74)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nT74 is ground\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(','(!_34, failure(a)), ','(p(0, X171), g(c(s(s(s(s(s(s(0)))))), X171)))) | ?_36 | ?_35 | ','(no(zero(0)), ','(p(0, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: ?_36 | ?_35 | ','(no(zero(T74)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nT74 is ground\nX171 is free\nzero(T74) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(failure(a), ','(p(0, X171), g(c(s(s(s(s(s(s(0)))))), X171))))\n\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(failure(a), ','(p(0, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 37, CLAUSE: 10\n\nX171 is free", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: ?_35 | ','(no(zero(T74)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nT74 is ground\nX171 is free\nzero(T74) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(no(zero(T74)), ','(p(T74, X171), g(c(s(s(s(s(s(s(0)))))), X171)))), SCOPE: 34, CLAUSE: 9\n\nT74 is ground\nX171 is free\nzero(T74) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(p(T77, X171), g(c(s(s(s(s(s(s(0)))))), X171)))\n\nT77 is ground\nX171 is free\nzero(T77) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(p(T77, X171), g(c(s(s(s(s(s(s(0)))))), X171))), SCOPE: 38, CLAUSE: 5 | ','(p(T77, X171), g(c(s(s(s(s(s(s(0)))))), X171))), SCOPE: 38, CLAUSE: 6\n\nT77 is ground\nX171 is free\nzero(T77) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ','(p(T77, X171), g(c(s(s(s(s(s(s(0)))))), X171))), SCOPE: 38, CLAUSE: 6\n\nT77 is ground\nX171 is free\nzero(T77) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: g(c(s(s(s(s(s(s(0)))))), T80))\n\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: g(c(s(s(s(s(s(s(0)))))), T80)), SCOPE: 39, CLAUSE: 3 | g(c(s(s(s(s(s(s(0)))))), T80)), SCOPE: 39, CLAUSE: 4\n\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: g(c(s(s(s(s(s(s(0)))))), T80)), SCOPE: 39, CLAUSE: 3\n\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: g(c(s(s(s(s(s(s(0)))))), T80)), SCOPE: 39, CLAUSE: 4\n\nT80 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(no(zero(T83)), ','(p(T83, X200), g(c(s(s(s(s(s(s(s(0))))))), X200))))\n\nT83 is ground\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(no(zero(T83)), ','(p(T83, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 8 | ','(no(zero(T83)), ','(p(T83, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nT83 is ground\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(','(call(zero(T86)), ','(!_40, failure(a))), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))) | ','(no(zero(T86)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nT86 is ground\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: ','(zero(T86), ','(','(!_40, failure(a)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200))))) | ?_41 | ','(no(zero(T86)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nT86 is ground\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(zero(T86), ','(','(!_40, failure(a)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200))))), SCOPE: 42, CLAUSE: 7 | ?_42 | ?_41 | ','(no(zero(T86)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nT86 is ground\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: ','(','(!_40, failure(a)), ','(p(0, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))) | ?_42 | ?_41 | ','(no(zero(0)), ','(p(0, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ?_42 | ?_41 | ','(no(zero(T86)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nT86 is ground\nX200 is free\nzero(T86) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(failure(a), ','(p(0, X200), g(c(s(s(s(s(s(s(s(0))))))), X200))))\n\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(failure(a), ','(p(0, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 43, CLAUSE: 10\n\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ?_41 | ','(no(zero(T86)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nT86 is ground\nX200 is free\nzero(T86) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(no(zero(T86)), ','(p(T86, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))), SCOPE: 40, CLAUSE: 9\n\nT86 is ground\nX200 is free\nzero(T86) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(p(T89, X200), g(c(s(s(s(s(s(s(s(0))))))), X200)))\n\nT89 is ground\nX200 is free\nzero(T89) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: ','(p(T89, X200), g(c(s(s(s(s(s(s(s(0))))))), X200))), SCOPE: 44, CLAUSE: 5 | ','(p(T89, X200), g(c(s(s(s(s(s(s(s(0))))))), X200))), SCOPE: 44, CLAUSE: 6\n\nT89 is ground\nX200 is free\nzero(T89) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: ','(p(T89, X200), g(c(s(s(s(s(s(s(s(0))))))), X200))), SCOPE: 44, CLAUSE: 6\n\nT89 is ground\nX200 is free\nzero(T89) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: g(c(s(s(s(s(s(s(s(0))))))), T92))\n\nT92 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: g(c(s(s(s(s(s(s(s(0))))))), T92)), SCOPE: 45, CLAUSE: 3 | g(c(s(s(s(s(s(s(s(0))))))), T92)), SCOPE: 45, CLAUSE: 4\n\nT92 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: g(c(s(s(s(s(s(s(s(0))))))), T92)), SCOPE: 45, CLAUSE: 3\n\nT92 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: g(c(s(s(s(s(s(s(s(0))))))), T92)), SCOPE: 45, CLAUSE: 4\n\nT92 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: ','(no(zero(T95)), ','(p(T95, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229))))\n\nT95 is ground\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ','(no(zero(T95)), ','(p(T95, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 8 | ','(no(zero(T95)), ','(p(T95, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nT95 is ground\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ','(','(call(zero(T98)), ','(!_46, failure(a))), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))) | ','(no(zero(T98)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nT98 is ground\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(zero(T98), ','(','(!_46, failure(a)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229))))) | ?_47 | ','(no(zero(T98)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nT98 is ground\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: ','(zero(T98), ','(','(!_46, failure(a)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229))))), SCOPE: 48, CLAUSE: 7 | ?_48 | ?_47 | ','(no(zero(T98)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nT98 is ground\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(','(!_46, failure(a)), ','(p(0, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))) | ?_48 | ?_47 | ','(no(zero(0)), ','(p(0, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: ?_48 | ?_47 | ','(no(zero(T98)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nT98 is ground\nX229 is free\nzero(T98) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(failure(a), ','(p(0, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229))))\n\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: ','(failure(a), ','(p(0, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 49, CLAUSE: 10\n\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: ?_47 | ','(no(zero(T98)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nT98 is ground\nX229 is free\nzero(T98) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(no(zero(T98)), ','(p(T98, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))), SCOPE: 46, CLAUSE: 9\n\nT98 is ground\nX229 is free\nzero(T98) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: ','(p(T101, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229)))\n\nT101 is ground\nX229 is free\nzero(T101) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ','(p(T101, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229))), SCOPE: 50, CLAUSE: 5 | ','(p(T101, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229))), SCOPE: 50, CLAUSE: 6\n\nT101 is ground\nX229 is free\nzero(T101) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: ','(p(T101, X229), g(c(s(s(s(s(s(s(s(s(0)))))))), X229))), SCOPE: 50, CLAUSE: 6\n\nT101 is ground\nX229 is free\nzero(T101) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: g(c(s(s(s(s(s(s(s(s(0)))))))), T104))\n\nT104 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: g(c(s(T105), T104))\n\nT104 is ground\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: g(c(s(T105), T104)), SCOPE: 51, CLAUSE: 3 | g(c(s(T105), T104)), SCOPE: 51, CLAUSE: 4\n\nT104 is ground\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: g(c(s(T105), T104)), SCOPE: 51, CLAUSE: 3\n\nT104 is ground\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: g(c(s(T105), T104)), SCOPE: 51, CLAUSE: 4\n\nT104 is ground\nT105 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: ','(no(zero(T119)), ','(p(T119, X260), g(c(s(s(T118)), X260))))\n\nT118 is ground\nT119 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(no(zero(T119)), ','(p(T119, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 8 | ','(no(zero(T119)), ','(p(T119, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nT119 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(','(call(zero(T123)), ','(!_52, failure(a))), ','(p(T123, X260), g(c(s(s(T118)), X260)))) | ','(no(zero(T123)), ','(p(T123, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nT123 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: ','(zero(T123), ','(','(!_52, failure(a)), ','(p(T123, X260), g(c(s(s(T118)), X260))))) | ?_53 | ','(no(zero(T123)), ','(p(T123, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nT123 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: ','(zero(T123), ','(','(!_52, failure(a)), ','(p(T123, X260), g(c(s(s(T118)), X260))))), SCOPE: 54, CLAUSE: 7 | ?_54 | ?_53 | ','(no(zero(T123)), ','(p(T123, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nT123 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: ','(','(!_52, failure(a)), ','(p(0, X260), g(c(s(s(T118)), X260)))) | ?_54 | ?_53 | ','(no(zero(0)), ','(p(0, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: ?_54 | ?_53 | ','(no(zero(T123)), ','(p(T123, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nT123 is ground\nX260 is free\nzero(T123) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ','(failure(a), ','(p(0, X260), g(c(s(s(T118)), X260))))\n\nT118 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: ','(failure(a), ','(p(0, X260), g(c(s(s(T118)), X260)))), SCOPE: 55, CLAUSE: 10\n\nT118 is ground\nX260 is free", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: ?_53 | ','(no(zero(T123)), ','(p(T123, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nT123 is ground\nX260 is free\nzero(T123) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: ','(no(zero(T123)), ','(p(T123, X260), g(c(s(s(T118)), X260)))), SCOPE: 52, CLAUSE: 9\n\nT118 is ground\nT123 is ground\nX260 is free\nzero(T123) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: ','(p(T128, X260), g(c(s(s(T118)), X260)))\n\nT118 is ground\nT128 is ground\nX260 is free\nzero(T128) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: ','(p(T128, X260), g(c(s(s(T118)), X260))), SCOPE: 56, CLAUSE: 5 | ','(p(T128, X260), g(c(s(s(T118)), X260))), SCOPE: 56, CLAUSE: 6\n\nT118 is ground\nT128 is ground\nX260 is free\nzero(T128) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: ','(p(T128, X260), g(c(s(s(T118)), X260))), SCOPE: 56, CLAUSE: 6\n\nT118 is ground\nT128 is ground\nX260 is free\nzero(T128) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: g(c(s(s(T118)), T132))\n\nT118 is ground\nT132 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: ','(','(no(zero(T139)), ','(p(T139, X283), f(c(X283, s(T140))))), g(c(T139, T140)))\n\nT139 is ground\nT140 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: ','(','(no(zero(T139)), ','(p(T139, X283), f(c(X283, s(T140))))), g(c(T139, T140))), SCOPE: 57, CLAUSE: 8 | ','(','(no(zero(T139)), ','(p(T139, X283), f(c(X283, s(T140))))), g(c(T139, T140))), SCOPE: 57, CLAUSE: 9\n\nT139 is ground\nT140 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: ','(','(call(zero(T146)), ','(!_57, failure(a))), ','(','(p(T146, X283), f(c(X283, s(T140)))), g(c(T146, T140)))) | ','(','(no(zero(T146)), ','(p(T146, X283), f(c(X283, s(T140))))), g(c(T146, T140))), SCOPE: 57, CLAUSE: 9\n\nT140 is ground\nT146 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: ','(zero(T146), ','(','(!_57, failure(a)), ','(','(p(T146, X283), f(c(X283, s(T140)))), g(c(T146, T140))))) | ?_58 | ','(','(no(zero(T146)), ','(p(T146, X283), f(c(X283, s(T140))))), g(c(T146, T140))), SCOPE: 57, CLAUSE: 9\n\nT140 is ground\nT146 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: ','(zero(T146), ','(','(!_57, failure(a)), ','(','(p(T146, X283), f(c(X283, s(T140)))), g(c(T146, T140))))), SCOPE: 59, CLAUSE: 7 | ?_59 | ?_58 | ','(','(no(zero(T146)), ','(p(T146, X283), f(c(X283, s(T140))))), g(c(T146, T140))), SCOPE: 57, CLAUSE: 9\n\nT140 is ground\nT146 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: ','(','(!_57, failure(a)), ','(','(p(0, X283), f(c(X283, s(T140)))), g(c(0, T140)))) | ?_59 | ?_58 | ','(','(no(zero(0)), ','(p(0, X283), f(c(X283, s(T140))))), g(c(0, T140))), SCOPE: 57, CLAUSE: 9\n\nT140 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: ?_59 | ?_58 | ','(','(no(zero(T146)), ','(p(T146, X283), f(c(X283, s(T140))))), g(c(T146, T140))), SCOPE: 57, CLAUSE: 9\n\nT140 is ground\nT146 is ground\nX283 is free\nzero(T146) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: ','(failure(a), ','(','(p(0, X283), f(c(X283, s(T140)))), g(c(0, T140))))\n\nT140 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: ','(failure(a), ','(','(p(0, X283), f(c(X283, s(T140)))), g(c(0, T140)))), SCOPE: 60, CLAUSE: 10\n\nT140 is ground\nX283 is free", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: ?_58 | ','(','(no(zero(T146)), ','(p(T146, X283), f(c(X283, s(T140))))), g(c(T146, T140))), SCOPE: 57, CLAUSE: 9\n\nT140 is ground\nT146 is ground\nX283 is free\nzero(T146) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: ','(','(no(zero(T146)), ','(p(T146, X283), f(c(X283, s(T140))))), g(c(T146, T140))), SCOPE: 57, CLAUSE: 9\n\nT140 is ground\nT146 is ground\nX283 is free\nzero(T146) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: ','(','(p(T153, X283), f(c(X283, s(T140)))), g(c(T153, T140)))\n\nT140 is ground\nT153 is ground\nX283 is free\nzero(T153) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: ','(','(p(T153, X283), f(c(X283, s(T140)))), g(c(T153, T140))), SCOPE: 61, CLAUSE: 5 | ','(','(p(T153, X283), f(c(X283, s(T140)))), g(c(T153, T140))), SCOPE: 61, CLAUSE: 6\n\nT140 is ground\nT153 is ground\nX283 is free\nzero(T153) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: ','(','(p(T153, X283), f(c(X283, s(T140)))), g(c(T153, T140))), SCOPE: 61, CLAUSE: 6\n\nT140 is ground\nT153 is ground\nX283 is free\nzero(T153) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: ','(f(c(T159, s(T140))), g(c(s(T159), T140)))\n\nT140 is ground\nT159 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: f(c(T159, s(T140)))\n\nT140 is ground\nT159 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: g(c(s(T159), T140))\n\nT140 is ground\nT159 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: f(c(T159, s(T140))), SCOPE: 62, CLAUSE: 1 | f(c(T159, s(T140))), SCOPE: 62, CLAUSE: 2\n\nT140 is ground\nT159 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: f(c(T159, s(T140))), SCOPE: 62, CLAUSE: 1\n\nT140 is ground\nT159 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: f(c(T159, s(T140))), SCOPE: 62, CLAUSE: 2\n\nT140 is ground\nT159 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: ','(no(zero(T174)), ','(p(T174, X322), f(c(X322, s(s(T175))))))\n\nT174 is ground\nT175 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: ','(no(zero(T174)), ','(p(T174, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 8 | ','(no(zero(T174)), ','(p(T174, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT174 is ground\nT175 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: ','(','(call(zero(T179)), ','(!_63, failure(a))), ','(p(T179, X322), f(c(X322, s(s(T175)))))) | ','(no(zero(T179)), ','(p(T179, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT175 is ground\nT179 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: ','(zero(T179), ','(','(!_63, failure(a)), ','(p(T179, X322), f(c(X322, s(s(T175))))))) | ?_64 | ','(no(zero(T179)), ','(p(T179, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT175 is ground\nT179 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: ','(zero(T179), ','(','(!_63, failure(a)), ','(p(T179, X322), f(c(X322, s(s(T175))))))), SCOPE: 65, CLAUSE: 7 | ?_65 | ?_64 | ','(no(zero(T179)), ','(p(T179, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT175 is ground\nT179 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: ','(','(!_63, failure(a)), ','(p(0, X322), f(c(X322, s(s(T175)))))) | ?_65 | ?_64 | ','(no(zero(0)), ','(p(0, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT175 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: ?_65 | ?_64 | ','(no(zero(T179)), ','(p(T179, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT175 is ground\nT179 is ground\nX322 is free\nzero(T179) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: ','(failure(a), ','(p(0, X322), f(c(X322, s(s(T175))))))\n\nT175 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: ','(failure(a), ','(p(0, X322), f(c(X322, s(s(T175)))))), SCOPE: 66, CLAUSE: 10\n\nT175 is ground\nX322 is free", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: ?_64 | ','(no(zero(T179)), ','(p(T179, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT175 is ground\nT179 is ground\nX322 is free\nzero(T179) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: ','(no(zero(T179)), ','(p(T179, X322), f(c(X322, s(s(T175)))))), SCOPE: 63, CLAUSE: 9\n\nT175 is ground\nT179 is ground\nX322 is free\nzero(T179) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: ','(p(T184, X322), f(c(X322, s(s(T175)))))\n\nT175 is ground\nT184 is ground\nX322 is free\nzero(T184) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: ','(p(T184, X322), f(c(X322, s(s(T175))))), SCOPE: 67, CLAUSE: 5 | ','(p(T184, X322), f(c(X322, s(s(T175))))), SCOPE: 67, CLAUSE: 6\n\nT175 is ground\nT184 is ground\nX322 is free\nzero(T184) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: ','(p(T184, X322), f(c(X322, s(s(T175))))), SCOPE: 67, CLAUSE: 6\n\nT175 is ground\nT184 is ground\nX322 is free\nzero(T184) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: f(c(T188, s(s(T175))))\n\nT175 is ground\nT188 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 260 [arrowhead = none ];
260 -> 2;

261 [label="ONLY EVAL with clause\nh(X5) :- ','(f(X5), g(X5)).\nand substitutionT1 -> T3,\nX5 -> T3", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 261 [arrowhead = none ];
261 -> 3;

262 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 262 [arrowhead = none ];
262 -> 4;

263 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 263 [arrowhead = none ];
263 -> 5;

264 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 264 [arrowhead = none ];
264 -> 6;

265 [label="EVAL with clause\nf(c(0, X10)).\nand substitutionX10 -> T8,\nT3 -> c(0, T8)", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 265 [arrowhead = none ];
265 -> 7;

266 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 266 [arrowhead = none ];
266 -> 8;

267 [label="EVAL with clause\nf(c(X281, X282)) :- ','(no(zero(X281)), ','(p(X281, X283), f(c(X283, s(X282))))).\nand substitutionX281 -> T139,\nX282 -> T140,\nT3 -> c(T139, T140)", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 267 [arrowhead = none ];
267 -> 217;

268 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 268 [arrowhead = none ];
268 -> 218;

269 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 269 [arrowhead = none ];
269 -> 9;

270 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
9 -> 270 [arrowhead = none ];
270 -> 10;

271 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
9 -> 271 [arrowhead = none ];
271 -> 11;

272 [label="EVAL with clause\ng(c(X17, 0)).\nand substitutionX17 -> 0,\nT8 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 272 [arrowhead = none ];
272 -> 12;

273 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 273 [arrowhead = none ];
273 -> 13;

274 [label="ONLY EVAL with clause\ng(c(X24, X25)) :- ','(no(zero(X25)), ','(p(X25, X26), g(c(s(X24), X26)))).\nand substitutionX24 -> 0,\nT8 -> T11,\nX25 -> T11", fontsize=14, style = filled, fillcolor = lightblue];
11 -> 274 [arrowhead = none ];
274 -> 15;

275 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 275 [arrowhead = none ];
275 -> 14;

276 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 276 [arrowhead = none ];
276 -> 16;

277 [label="ONLY EVAL with clause\nno(X30) :- ','(call(X30), ','(!_4, failure(a))).\nand substitutionT11 -> T14,\nX30 -> zero(T14)", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 277 [arrowhead = none ];
277 -> 17;

278 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
17 -> 278 [arrowhead = none ];
278 -> 18;

279 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
18 -> 279 [arrowhead = none ];
279 -> 19;

280 [label="EVAL with clause\nzero(0).\nand substitutionT14 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 280 [arrowhead = none ];
280 -> 20;

281 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 281 [arrowhead = none ];
281 -> 21;

282 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 282 [arrowhead = none ];
282 -> 22;

283 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 283 [arrowhead = none ];
283 -> 25;

284 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 284 [arrowhead = none ];
284 -> 23;

285 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 285 [arrowhead = none ];
285 -> 24;

286 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 286 [arrowhead = none ];
286 -> 26;

287 [label="ONLY EVAL with clause\nno(X35).\nand substitutionT14 -> T17,\nX35 -> zero(T17)", fontsize=14, style = filled, fillcolor = lightblue];
26 -> 287 [arrowhead = none ];
287 -> 27;

288 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
27 -> 288 [arrowhead = none ];
288 -> 28;

289 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T17), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 289 [arrowhead = none ];
289 -> 29;

290 [label="EVAL with clause\np(s(X39), X39).\nand substitutionX39 -> T20,\nT17 -> s(T20),\nX26 -> T20", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 290 [arrowhead = none ];
290 -> 30;

291 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 291 [arrowhead = none ];
291 -> 31;

292 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
30 -> 292 [arrowhead = none ];
292 -> 32;

293 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
32 -> 293 [arrowhead = none ];
293 -> 33;

294 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
32 -> 294 [arrowhead = none ];
294 -> 34;

295 [label="EVAL with clause\ng(c(X46, 0)).\nand substitutionX46 -> s(0),\nT20 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 295 [arrowhead = none ];
295 -> 35;

296 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 296 [arrowhead = none ];
296 -> 36;

297 [label="ONLY EVAL with clause\ng(c(X53, X54)) :- ','(no(zero(X54)), ','(p(X54, X55), g(c(s(X53), X55)))).\nand substitutionX53 -> s(0),\nT20 -> T23,\nX54 -> T23", fontsize=14, style = filled, fillcolor = lightblue];
34 -> 297 [arrowhead = none ];
297 -> 38;

298 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 298 [arrowhead = none ];
298 -> 37;

299 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
38 -> 299 [arrowhead = none ];
299 -> 39;

300 [label="ONLY EVAL with clause\nno(X59) :- ','(call(X59), ','(!_10, failure(a))).\nand substitutionT23 -> T26,\nX59 -> zero(T26)", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 300 [arrowhead = none ];
300 -> 40;

301 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
40 -> 301 [arrowhead = none ];
301 -> 41;

302 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
41 -> 302 [arrowhead = none ];
302 -> 42;

303 [label="EVAL with clause\nzero(0).\nand substitutionT26 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
42 -> 303 [arrowhead = none ];
303 -> 43;

304 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 304 [arrowhead = none ];
304 -> 44;

305 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
43 -> 305 [arrowhead = none ];
305 -> 45;

306 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
44 -> 306 [arrowhead = none ];
306 -> 48;

307 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
45 -> 307 [arrowhead = none ];
307 -> 46;

308 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 308 [arrowhead = none ];
308 -> 47;

309 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
48 -> 309 [arrowhead = none ];
309 -> 49;

310 [label="ONLY EVAL with clause\nno(X64).\nand substitutionT26 -> T29,\nX64 -> zero(T29)", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 310 [arrowhead = none ];
310 -> 50;

311 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
50 -> 311 [arrowhead = none ];
311 -> 51;

312 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T29), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 312 [arrowhead = none ];
312 -> 52;

313 [label="EVAL with clause\np(s(X68), X68).\nand substitutionX68 -> T32,\nT29 -> s(T32),\nX55 -> T32", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 313 [arrowhead = none ];
313 -> 53;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 314 [arrowhead = none ];
314 -> 54;

315 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
53 -> 315 [arrowhead = none ];
315 -> 55;

316 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 316 [arrowhead = none ];
316 -> 56;

317 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 317 [arrowhead = none ];
317 -> 57;

318 [label="EVAL with clause\ng(c(X75, 0)).\nand substitutionX75 -> s(s(0)),\nT32 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 318 [arrowhead = none ];
318 -> 58;

319 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 319 [arrowhead = none ];
319 -> 59;

320 [label="ONLY EVAL with clause\ng(c(X82, X83)) :- ','(no(zero(X83)), ','(p(X83, X84), g(c(s(X82), X84)))).\nand substitutionX82 -> s(s(0)),\nT32 -> T35,\nX83 -> T35", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 320 [arrowhead = none ];
320 -> 61;

321 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
58 -> 321 [arrowhead = none ];
321 -> 60;

322 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
61 -> 322 [arrowhead = none ];
322 -> 62;

323 [label="ONLY EVAL with clause\nno(X88) :- ','(call(X88), ','(!_16, failure(a))).\nand substitutionT35 -> T38,\nX88 -> zero(T38)", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 323 [arrowhead = none ];
323 -> 63;

324 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
63 -> 324 [arrowhead = none ];
324 -> 64;

325 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
64 -> 325 [arrowhead = none ];
325 -> 65;

326 [label="EVAL with clause\nzero(0).\nand substitutionT38 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 326 [arrowhead = none ];
326 -> 66;

327 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 327 [arrowhead = none ];
327 -> 67;

328 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
66 -> 328 [arrowhead = none ];
328 -> 68;

329 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 329 [arrowhead = none ];
329 -> 71;

330 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 330 [arrowhead = none ];
330 -> 69;

331 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 331 [arrowhead = none ];
331 -> 70;

332 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 332 [arrowhead = none ];
332 -> 72;

333 [label="ONLY EVAL with clause\nno(X93).\nand substitutionT38 -> T41,\nX93 -> zero(T41)", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 333 [arrowhead = none ];
333 -> 73;

334 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
73 -> 334 [arrowhead = none ];
334 -> 74;

335 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T41), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
74 -> 335 [arrowhead = none ];
335 -> 75;

336 [label="EVAL with clause\np(s(X97), X97).\nand substitutionX97 -> T44,\nT41 -> s(T44),\nX84 -> T44", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 336 [arrowhead = none ];
336 -> 76;

337 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
75 -> 337 [arrowhead = none ];
337 -> 77;

338 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
76 -> 338 [arrowhead = none ];
338 -> 78;

339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
78 -> 339 [arrowhead = none ];
339 -> 79;

340 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
78 -> 340 [arrowhead = none ];
340 -> 80;

341 [label="EVAL with clause\ng(c(X104, 0)).\nand substitutionX104 -> s(s(s(0))),\nT44 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
79 -> 341 [arrowhead = none ];
341 -> 81;

342 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 342 [arrowhead = none ];
342 -> 82;

343 [label="ONLY EVAL with clause\ng(c(X111, X112)) :- ','(no(zero(X112)), ','(p(X112, X113), g(c(s(X111), X113)))).\nand substitutionX111 -> s(s(s(0))),\nT44 -> T47,\nX112 -> T47", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 343 [arrowhead = none ];
343 -> 84;

344 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 344 [arrowhead = none ];
344 -> 83;

345 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
84 -> 345 [arrowhead = none ];
345 -> 85;

346 [label="ONLY EVAL with clause\nno(X117) :- ','(call(X117), ','(!_22, failure(a))).\nand substitutionT47 -> T50,\nX117 -> zero(T50)", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 346 [arrowhead = none ];
346 -> 86;

347 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
86 -> 347 [arrowhead = none ];
347 -> 87;

348 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
87 -> 348 [arrowhead = none ];
348 -> 88;

349 [label="EVAL with clause\nzero(0).\nand substitutionT50 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 349 [arrowhead = none ];
349 -> 89;

350 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 350 [arrowhead = none ];
350 -> 90;

351 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 351 [arrowhead = none ];
351 -> 91;

352 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 352 [arrowhead = none ];
352 -> 94;

353 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 353 [arrowhead = none ];
353 -> 92;

354 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
92 -> 354 [arrowhead = none ];
354 -> 93;

355 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
94 -> 355 [arrowhead = none ];
355 -> 95;

356 [label="ONLY EVAL with clause\nno(X122).\nand substitutionT50 -> T53,\nX122 -> zero(T53)", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 356 [arrowhead = none ];
356 -> 96;

357 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
96 -> 357 [arrowhead = none ];
357 -> 97;

358 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T53), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 358 [arrowhead = none ];
358 -> 98;

359 [label="EVAL with clause\np(s(X126), X126).\nand substitutionX126 -> T56,\nT53 -> s(T56),\nX113 -> T56", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 359 [arrowhead = none ];
359 -> 99;

360 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 360 [arrowhead = none ];
360 -> 100;

361 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
99 -> 361 [arrowhead = none ];
361 -> 101;

362 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 362 [arrowhead = none ];
362 -> 102;

363 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 363 [arrowhead = none ];
363 -> 103;

364 [label="EVAL with clause\ng(c(X133, 0)).\nand substitutionX133 -> s(s(s(s(0)))),\nT56 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
102 -> 364 [arrowhead = none ];
364 -> 104;

365 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 365 [arrowhead = none ];
365 -> 105;

366 [label="ONLY EVAL with clause\ng(c(X140, X141)) :- ','(no(zero(X141)), ','(p(X141, X142), g(c(s(X140), X142)))).\nand substitutionX140 -> s(s(s(s(0)))),\nT56 -> T59,\nX141 -> T59", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 366 [arrowhead = none ];
366 -> 107;

367 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
104 -> 367 [arrowhead = none ];
367 -> 106;

368 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
107 -> 368 [arrowhead = none ];
368 -> 108;

369 [label="ONLY EVAL with clause\nno(X146) :- ','(call(X146), ','(!_28, failure(a))).\nand substitutionT59 -> T62,\nX146 -> zero(T62)", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 369 [arrowhead = none ];
369 -> 109;

370 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
109 -> 370 [arrowhead = none ];
370 -> 110;

371 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
110 -> 371 [arrowhead = none ];
371 -> 111;

372 [label="EVAL with clause\nzero(0).\nand substitutionT62 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 372 [arrowhead = none ];
372 -> 112;

373 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
111 -> 373 [arrowhead = none ];
373 -> 113;

374 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 374 [arrowhead = none ];
374 -> 114;

375 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 375 [arrowhead = none ];
375 -> 117;

376 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
114 -> 376 [arrowhead = none ];
376 -> 115;

377 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
115 -> 377 [arrowhead = none ];
377 -> 116;

378 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
117 -> 378 [arrowhead = none ];
378 -> 118;

379 [label="ONLY EVAL with clause\nno(X151).\nand substitutionT62 -> T65,\nX151 -> zero(T65)", fontsize=14, style = filled, fillcolor = lightblue];
118 -> 379 [arrowhead = none ];
379 -> 119;

380 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
119 -> 380 [arrowhead = none ];
380 -> 120;

381 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T65), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 381 [arrowhead = none ];
381 -> 121;

382 [label="EVAL with clause\np(s(X155), X155).\nand substitutionX155 -> T68,\nT65 -> s(T68),\nX142 -> T68", fontsize=14, style = filled, fillcolor = lightblue];
121 -> 382 [arrowhead = none ];
382 -> 122;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
121 -> 383 [arrowhead = none ];
383 -> 123;

384 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
122 -> 384 [arrowhead = none ];
384 -> 124;

385 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 385 [arrowhead = none ];
385 -> 125;

386 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 386 [arrowhead = none ];
386 -> 126;

387 [label="EVAL with clause\ng(c(X162, 0)).\nand substitutionX162 -> s(s(s(s(s(0))))),\nT68 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 387 [arrowhead = none ];
387 -> 127;

388 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 388 [arrowhead = none ];
388 -> 128;

389 [label="ONLY EVAL with clause\ng(c(X169, X170)) :- ','(no(zero(X170)), ','(p(X170, X171), g(c(s(X169), X171)))).\nand substitutionX169 -> s(s(s(s(s(0))))),\nT68 -> T71,\nX170 -> T71", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 389 [arrowhead = none ];
389 -> 130;

390 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
127 -> 390 [arrowhead = none ];
390 -> 129;

391 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
130 -> 391 [arrowhead = none ];
391 -> 131;

392 [label="ONLY EVAL with clause\nno(X175) :- ','(call(X175), ','(!_34, failure(a))).\nand substitutionT71 -> T74,\nX175 -> zero(T74)", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 392 [arrowhead = none ];
392 -> 132;

393 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
132 -> 393 [arrowhead = none ];
393 -> 133;

394 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 394 [arrowhead = none ];
394 -> 134;

395 [label="EVAL with clause\nzero(0).\nand substitutionT74 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
134 -> 395 [arrowhead = none ];
395 -> 135;

396 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 396 [arrowhead = none ];
396 -> 136;

397 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
135 -> 397 [arrowhead = none ];
397 -> 137;

398 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 398 [arrowhead = none ];
398 -> 140;

399 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
137 -> 399 [arrowhead = none ];
399 -> 138;

400 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
138 -> 400 [arrowhead = none ];
400 -> 139;

401 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 401 [arrowhead = none ];
401 -> 141;

402 [label="ONLY EVAL with clause\nno(X180).\nand substitutionT74 -> T77,\nX180 -> zero(T77)", fontsize=14, style = filled, fillcolor = lightblue];
141 -> 402 [arrowhead = none ];
402 -> 142;

403 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
142 -> 403 [arrowhead = none ];
403 -> 143;

404 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T77), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
143 -> 404 [arrowhead = none ];
404 -> 144;

405 [label="EVAL with clause\np(s(X184), X184).\nand substitutionX184 -> T80,\nT77 -> s(T80),\nX171 -> T80", fontsize=14, style = filled, fillcolor = lightblue];
144 -> 405 [arrowhead = none ];
405 -> 145;

406 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 406 [arrowhead = none ];
406 -> 146;

407 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
145 -> 407 [arrowhead = none ];
407 -> 147;

408 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 408 [arrowhead = none ];
408 -> 148;

409 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
147 -> 409 [arrowhead = none ];
409 -> 149;

410 [label="EVAL with clause\ng(c(X191, 0)).\nand substitutionX191 -> s(s(s(s(s(s(0)))))),\nT80 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 410 [arrowhead = none ];
410 -> 150;

411 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
148 -> 411 [arrowhead = none ];
411 -> 151;

412 [label="ONLY EVAL with clause\ng(c(X198, X199)) :- ','(no(zero(X199)), ','(p(X199, X200), g(c(s(X198), X200)))).\nand substitutionX198 -> s(s(s(s(s(s(0)))))),\nT80 -> T83,\nX199 -> T83", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 412 [arrowhead = none ];
412 -> 153;

413 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
150 -> 413 [arrowhead = none ];
413 -> 152;

414 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
153 -> 414 [arrowhead = none ];
414 -> 154;

415 [label="ONLY EVAL with clause\nno(X204) :- ','(call(X204), ','(!_40, failure(a))).\nand substitutionT83 -> T86,\nX204 -> zero(T86)", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 415 [arrowhead = none ];
415 -> 155;

416 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
155 -> 416 [arrowhead = none ];
416 -> 156;

417 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
156 -> 417 [arrowhead = none ];
417 -> 157;

418 [label="EVAL with clause\nzero(0).\nand substitutionT86 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 418 [arrowhead = none ];
418 -> 158;

419 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 419 [arrowhead = none ];
419 -> 159;

420 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 420 [arrowhead = none ];
420 -> 160;

421 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
159 -> 421 [arrowhead = none ];
421 -> 163;

422 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
160 -> 422 [arrowhead = none ];
422 -> 161;

423 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
161 -> 423 [arrowhead = none ];
423 -> 162;

424 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
163 -> 424 [arrowhead = none ];
424 -> 164;

425 [label="ONLY EVAL with clause\nno(X209).\nand substitutionT86 -> T89,\nX209 -> zero(T89)", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 425 [arrowhead = none ];
425 -> 165;

426 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
165 -> 426 [arrowhead = none ];
426 -> 166;

427 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T89), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 427 [arrowhead = none ];
427 -> 167;

428 [label="EVAL with clause\np(s(X213), X213).\nand substitutionX213 -> T92,\nT89 -> s(T92),\nX200 -> T92", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 428 [arrowhead = none ];
428 -> 168;

429 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 429 [arrowhead = none ];
429 -> 169;

430 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
168 -> 430 [arrowhead = none ];
430 -> 170;

431 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 431 [arrowhead = none ];
431 -> 171;

432 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
170 -> 432 [arrowhead = none ];
432 -> 172;

433 [label="EVAL with clause\ng(c(X220, 0)).\nand substitutionX220 -> s(s(s(s(s(s(s(0))))))),\nT92 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 433 [arrowhead = none ];
433 -> 173;

434 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 434 [arrowhead = none ];
434 -> 174;

435 [label="ONLY EVAL with clause\ng(c(X227, X228)) :- ','(no(zero(X228)), ','(p(X228, X229), g(c(s(X227), X229)))).\nand substitutionX227 -> s(s(s(s(s(s(s(0))))))),\nT92 -> T95,\nX228 -> T95", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 435 [arrowhead = none ];
435 -> 176;

436 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 436 [arrowhead = none ];
436 -> 175;

437 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
176 -> 437 [arrowhead = none ];
437 -> 177;

438 [label="ONLY EVAL with clause\nno(X233) :- ','(call(X233), ','(!_46, failure(a))).\nand substitutionT95 -> T98,\nX233 -> zero(T98)", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 438 [arrowhead = none ];
438 -> 178;

439 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
178 -> 439 [arrowhead = none ];
439 -> 179;

440 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
179 -> 440 [arrowhead = none ];
440 -> 180;

441 [label="EVAL with clause\nzero(0).\nand substitutionT98 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 441 [arrowhead = none ];
441 -> 181;

442 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
180 -> 442 [arrowhead = none ];
442 -> 182;

443 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 443 [arrowhead = none ];
443 -> 183;

444 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
182 -> 444 [arrowhead = none ];
444 -> 186;

445 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
183 -> 445 [arrowhead = none ];
445 -> 184;

446 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
184 -> 446 [arrowhead = none ];
446 -> 185;

447 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
186 -> 447 [arrowhead = none ];
447 -> 187;

448 [label="ONLY EVAL with clause\nno(X238).\nand substitutionT98 -> T101,\nX238 -> zero(T101)", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 448 [arrowhead = none ];
448 -> 188;

449 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
188 -> 449 [arrowhead = none ];
449 -> 189;

450 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T101), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 450 [arrowhead = none ];
450 -> 190;

451 [label="EVAL with clause\np(s(X242), X242).\nand substitutionX242 -> T104,\nT101 -> s(T104),\nX229 -> T104", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 451 [arrowhead = none ];
451 -> 191;

452 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
190 -> 452 [arrowhead = none ];
452 -> 192;

453 [label="GENERALIZATION\nT105 <-- s(s(s(s(s(s(s(0)))))))\n\nNew Knowledge:\nT105 is ground", fontsize=14, style = filled, fillcolor = violet];
191 -> 453 [arrowhead = none ];
453 -> 193;

454 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
193 -> 454 [arrowhead = none ];
454 -> 194;

455 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
194 -> 455 [arrowhead = none ];
455 -> 195;

456 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
194 -> 456 [arrowhead = none ];
456 -> 196;

457 [label="EVAL with clause\ng(c(X251, 0)).\nand substitutionT105 -> T112,\nX251 -> s(T112),\nT104 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
195 -> 457 [arrowhead = none ];
457 -> 197;

458 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 458 [arrowhead = none ];
458 -> 198;

459 [label="ONLY EVAL with clause\ng(c(X258, X259)) :- ','(no(zero(X259)), ','(p(X259, X260), g(c(s(X258), X260)))).\nand substitutionT105 -> T118,\nX258 -> s(T118),\nT104 -> T119,\nX259 -> T119", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 459 [arrowhead = none ];
459 -> 200;

460 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
197 -> 460 [arrowhead = none ];
460 -> 199;

461 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
200 -> 461 [arrowhead = none ];
461 -> 201;

462 [label="ONLY EVAL with clause\nno(X264) :- ','(call(X264), ','(!_52, failure(a))).\nand substitutionT119 -> T123,\nX264 -> zero(T123)", fontsize=14, style = filled, fillcolor = lightblue];
201 -> 462 [arrowhead = none ];
462 -> 202;

463 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
202 -> 463 [arrowhead = none ];
463 -> 203;

464 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
203 -> 464 [arrowhead = none ];
464 -> 204;

465 [label="EVAL with clause\nzero(0).\nand substitutionT123 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 465 [arrowhead = none ];
465 -> 205;

466 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
204 -> 466 [arrowhead = none ];
466 -> 206;

467 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
205 -> 467 [arrowhead = none ];
467 -> 207;

468 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
206 -> 468 [arrowhead = none ];
468 -> 210;

469 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
207 -> 469 [arrowhead = none ];
469 -> 208;

470 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 470 [arrowhead = none ];
470 -> 209;

471 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 471 [arrowhead = none ];
471 -> 211;

472 [label="ONLY EVAL with clause\nno(X269).\nand substitutionT123 -> T128,\nX269 -> zero(T128)", fontsize=14, style = filled, fillcolor = lightblue];
211 -> 472 [arrowhead = none ];
472 -> 212;

473 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
212 -> 473 [arrowhead = none ];
473 -> 213;

474 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T128), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
213 -> 474 [arrowhead = none ];
474 -> 214;

475 [label="EVAL with clause\np(s(X273), X273).\nand substitutionX273 -> T132,\nT128 -> s(T132),\nX260 -> T132", fontsize=14, style = filled, fillcolor = lightblue];
214 -> 475 [arrowhead = none ];
475 -> 215;

476 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
214 -> 476 [arrowhead = none ];
476 -> 216;

477 [label="INSTANCE with matching:\nT105 -> s(T118)\nT104 -> T132", fontsize=14, style = filled, fillcolor = lightgrey];
215 -> 477 [arrowhead = none , style=dashed];
477 -> 193[style=dashed];

478 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
217 -> 478 [arrowhead = none ];
478 -> 219;

479 [label="ONLY EVAL with clause\nno(X289) :- ','(call(X289), ','(!_57, failure(a))).\nand substitutionT139 -> T146,\nX289 -> zero(T146)", fontsize=14, style = filled, fillcolor = lightblue];
219 -> 479 [arrowhead = none ];
479 -> 220;

480 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
220 -> 480 [arrowhead = none ];
480 -> 221;

481 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
221 -> 481 [arrowhead = none ];
481 -> 222;

482 [label="EVAL with clause\nzero(0).\nand substitutionT146 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
222 -> 482 [arrowhead = none ];
482 -> 223;

483 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
222 -> 483 [arrowhead = none ];
483 -> 224;

484 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
223 -> 484 [arrowhead = none ];
484 -> 225;

485 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
224 -> 485 [arrowhead = none ];
485 -> 228;

486 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
225 -> 486 [arrowhead = none ];
486 -> 226;

487 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
226 -> 487 [arrowhead = none ];
487 -> 227;

488 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
228 -> 488 [arrowhead = none ];
488 -> 229;

489 [label="ONLY EVAL with clause\nno(X298).\nand substitutionT146 -> T153,\nX298 -> zero(T153)", fontsize=14, style = filled, fillcolor = lightblue];
229 -> 489 [arrowhead = none ];
489 -> 230;

490 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
230 -> 490 [arrowhead = none ];
490 -> 231;

491 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T153), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
231 -> 491 [arrowhead = none ];
491 -> 232;

492 [label="EVAL with clause\np(s(X304), X304).\nand substitutionX304 -> T159,\nT153 -> s(T159),\nX283 -> T159", fontsize=14, style = filled, fillcolor = lightblue];
232 -> 492 [arrowhead = none ];
492 -> 233;

493 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
232 -> 493 [arrowhead = none ];
493 -> 234;

494 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
233 -> 494 [arrowhead = none ];
494 -> 235;

495 [label="SPLIT 2\nnew knowledge:\nT159 is ground\nT140 is ground", fontsize=14, style = filled, fillcolor = violet];
233 -> 495 [arrowhead = none ];
495 -> 236;

496 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
235 -> 496 [arrowhead = none ];
496 -> 237;

497 [label="INSTANCE with matching:\nT105 -> T159\nT104 -> T140", fontsize=14, style = filled, fillcolor = lightgrey];
236 -> 497 [arrowhead = none , style=dashed];
497 -> 193[style=dashed];

498 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
237 -> 498 [arrowhead = none ];
498 -> 238;

499 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
237 -> 499 [arrowhead = none ];
499 -> 239;

500 [label="EVAL with clause\nf(c(0, X313)).\nand substitutionT159 -> 0,\nT140 -> T168,\nX313 -> s(T168)", fontsize=14, style = filled, fillcolor = lightblue];
238 -> 500 [arrowhead = none ];
500 -> 240;

501 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
238 -> 501 [arrowhead = none ];
501 -> 241;

502 [label="ONLY EVAL with clause\nf(c(X320, X321)) :- ','(no(zero(X320)), ','(p(X320, X322), f(c(X322, s(X321))))).\nand substitutionT159 -> T174,\nX320 -> T174,\nT140 -> T175,\nX321 -> s(T175)", fontsize=14, style = filled, fillcolor = lightblue];
239 -> 502 [arrowhead = none ];
502 -> 243;

503 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
240 -> 503 [arrowhead = none ];
503 -> 242;

504 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
243 -> 504 [arrowhead = none ];
504 -> 244;

505 [label="ONLY EVAL with clause\nno(X326) :- ','(call(X326), ','(!_63, failure(a))).\nand substitutionT174 -> T179,\nX326 -> zero(T179)", fontsize=14, style = filled, fillcolor = lightblue];
244 -> 505 [arrowhead = none ];
505 -> 245;

506 [label="CALL", fontsize=14, style = filled, fillcolor = lightcyan];
245 -> 506 [arrowhead = none ];
506 -> 246;

507 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
246 -> 507 [arrowhead = none ];
507 -> 247;

508 [label="EVAL with clause\nzero(0).\nand substitutionT179 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
247 -> 508 [arrowhead = none ];
508 -> 248;

509 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
247 -> 509 [arrowhead = none ];
509 -> 249;

510 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
248 -> 510 [arrowhead = none ];
510 -> 250;

511 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
249 -> 511 [arrowhead = none ];
511 -> 253;

512 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
250 -> 512 [arrowhead = none ];
512 -> 251;

513 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
251 -> 513 [arrowhead = none ];
513 -> 252;

514 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
253 -> 514 [arrowhead = none ];
514 -> 254;

515 [label="ONLY EVAL with clause\nno(X331).\nand substitutionT179 -> T184,\nX331 -> zero(T184)", fontsize=14, style = filled, fillcolor = lightblue];
254 -> 515 [arrowhead = none ];
515 -> 255;

516 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
255 -> 516 [arrowhead = none ];
516 -> 256;

517 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (zero(T184), zero(0))", fontsize=14, style = filled, fillcolor = lightgreen];
256 -> 517 [arrowhead = none ];
517 -> 257;

518 [label="EVAL with clause\np(s(X335), X335).\nand substitutionX335 -> T188,\nT184 -> s(T188),\nX322 -> T188", fontsize=14, style = filled, fillcolor = lightblue];
257 -> 518 [arrowhead = none ];
518 -> 258;

519 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
257 -> 519 [arrowhead = none ];
519 -> 259;

520 [label="INSTANCE with matching:\nT159 -> T188\nT140 -> s(T175)", fontsize=14, style = filled, fillcolor = lightgrey];
258 -> 520 [arrowhead = none , style=dashed];
520 -> 235[style=dashed];

}

(2) Obligation:

Clauses:

gA(T112, 0).
gA(T118, s(T132)) :- gA(s(T118), T132).
fB(0, T168).
fB(s(T188), T175) :- fB(T188, s(T175)).
hC(c(0, 0)).
hC(c(0, s(0))).
hC(c(0, s(s(0)))).
hC(c(0, s(s(s(0))))).
hC(c(0, s(s(s(s(0)))))).
hC(c(0, s(s(s(s(s(0))))))).
hC(c(0, s(s(s(s(s(s(0)))))))).
hC(c(0, s(s(s(s(s(s(s(0))))))))).
hC(c(0, s(s(s(s(s(s(s(s(T104)))))))))) :- gA(s(s(s(s(s(s(s(0))))))), T104).
hC(c(s(T159), T140)) :- fB(T159, T140).
hC(c(s(T159), T140)) :- ','(fB(T159, T140), gA(T159, T140)).

Query: hC(g)

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
hC_in: (b)
gA_in: (b,b)
fB_in: (b,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

hC_in_g(c(0, 0)) → hC_out_g(c(0, 0))
hC_in_g(c(0, s(0))) → hC_out_g(c(0, s(0)))
hC_in_g(c(0, s(s(0)))) → hC_out_g(c(0, s(s(0))))
hC_in_g(c(0, s(s(s(0))))) → hC_out_g(c(0, s(s(s(0)))))
hC_in_g(c(0, s(s(s(s(0)))))) → hC_out_g(c(0, s(s(s(s(0))))))
hC_in_g(c(0, s(s(s(s(s(0))))))) → hC_out_g(c(0, s(s(s(s(s(0)))))))
hC_in_g(c(0, s(s(s(s(s(s(0)))))))) → hC_out_g(c(0, s(s(s(s(s(s(0))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(0))))))))) → hC_out_g(c(0, s(s(s(s(s(s(s(0)))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_g(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
gA_in_gg(T112, 0) → gA_out_gg(T112, 0)
gA_in_gg(T118, s(T132)) → U1_gg(T118, T132, gA_in_gg(s(T118), T132))
U1_gg(T118, T132, gA_out_gg(s(T118), T132)) → gA_out_gg(T118, s(T132))
U3_g(T104, gA_out_gg(s(s(s(s(s(s(s(0))))))), T104)) → hC_out_g(c(0, s(s(s(s(s(s(s(s(T104))))))))))
hC_in_g(c(s(T159), T140)) → U4_g(T159, T140, fB_in_gg(T159, T140))
fB_in_gg(0, T168) → fB_out_gg(0, T168)
fB_in_gg(s(T188), T175) → U2_gg(T188, T175, fB_in_gg(T188, s(T175)))
U2_gg(T188, T175, fB_out_gg(T188, s(T175))) → fB_out_gg(s(T188), T175)
U4_g(T159, T140, fB_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))
U4_g(T159, T140, fB_out_gg(T159, T140)) → U5_g(T159, T140, gA_in_gg(T159, T140))
U5_g(T159, T140, gA_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

hC_in_g(c(0, 0)) → hC_out_g(c(0, 0))
hC_in_g(c(0, s(0))) → hC_out_g(c(0, s(0)))
hC_in_g(c(0, s(s(0)))) → hC_out_g(c(0, s(s(0))))
hC_in_g(c(0, s(s(s(0))))) → hC_out_g(c(0, s(s(s(0)))))
hC_in_g(c(0, s(s(s(s(0)))))) → hC_out_g(c(0, s(s(s(s(0))))))
hC_in_g(c(0, s(s(s(s(s(0))))))) → hC_out_g(c(0, s(s(s(s(s(0)))))))
hC_in_g(c(0, s(s(s(s(s(s(0)))))))) → hC_out_g(c(0, s(s(s(s(s(s(0))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(0))))))))) → hC_out_g(c(0, s(s(s(s(s(s(s(0)))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_g(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
gA_in_gg(T112, 0) → gA_out_gg(T112, 0)
gA_in_gg(T118, s(T132)) → U1_gg(T118, T132, gA_in_gg(s(T118), T132))
U1_gg(T118, T132, gA_out_gg(s(T118), T132)) → gA_out_gg(T118, s(T132))
U3_g(T104, gA_out_gg(s(s(s(s(s(s(s(0))))))), T104)) → hC_out_g(c(0, s(s(s(s(s(s(s(s(T104))))))))))
hC_in_g(c(s(T159), T140)) → U4_g(T159, T140, fB_in_gg(T159, T140))
fB_in_gg(0, T168) → fB_out_gg(0, T168)
fB_in_gg(s(T188), T175) → U2_gg(T188, T175, fB_in_gg(T188, s(T175)))
U2_gg(T188, T175, fB_out_gg(T188, s(T175))) → fB_out_gg(s(T188), T175)
U4_g(T159, T140, fB_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))
U4_g(T159, T140, fB_out_gg(T159, T140)) → U5_g(T159, T140, gA_in_gg(T159, T140))
U5_g(T159, T140, gA_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))

(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:

HC_IN_G(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_G(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
HC_IN_G(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → GA_IN_GG(s(s(s(s(s(s(s(0))))))), T104)
GA_IN_GG(T118, s(T132)) → U1_GG(T118, T132, gA_in_gg(s(T118), T132))
GA_IN_GG(T118, s(T132)) → GA_IN_GG(s(T118), T132)
HC_IN_G(c(s(T159), T140)) → U4_G(T159, T140, fB_in_gg(T159, T140))
HC_IN_G(c(s(T159), T140)) → FB_IN_GG(T159, T140)
FB_IN_GG(s(T188), T175) → U2_GG(T188, T175, fB_in_gg(T188, s(T175)))
FB_IN_GG(s(T188), T175) → FB_IN_GG(T188, s(T175))
U4_G(T159, T140, fB_out_gg(T159, T140)) → U5_G(T159, T140, gA_in_gg(T159, T140))
U4_G(T159, T140, fB_out_gg(T159, T140)) → GA_IN_GG(T159, T140)

The TRS R consists of the following rules:

hC_in_g(c(0, 0)) → hC_out_g(c(0, 0))
hC_in_g(c(0, s(0))) → hC_out_g(c(0, s(0)))
hC_in_g(c(0, s(s(0)))) → hC_out_g(c(0, s(s(0))))
hC_in_g(c(0, s(s(s(0))))) → hC_out_g(c(0, s(s(s(0)))))
hC_in_g(c(0, s(s(s(s(0)))))) → hC_out_g(c(0, s(s(s(s(0))))))
hC_in_g(c(0, s(s(s(s(s(0))))))) → hC_out_g(c(0, s(s(s(s(s(0)))))))
hC_in_g(c(0, s(s(s(s(s(s(0)))))))) → hC_out_g(c(0, s(s(s(s(s(s(0))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(0))))))))) → hC_out_g(c(0, s(s(s(s(s(s(s(0)))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_g(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
gA_in_gg(T112, 0) → gA_out_gg(T112, 0)
gA_in_gg(T118, s(T132)) → U1_gg(T118, T132, gA_in_gg(s(T118), T132))
U1_gg(T118, T132, gA_out_gg(s(T118), T132)) → gA_out_gg(T118, s(T132))
U3_g(T104, gA_out_gg(s(s(s(s(s(s(s(0))))))), T104)) → hC_out_g(c(0, s(s(s(s(s(s(s(s(T104))))))))))
hC_in_g(c(s(T159), T140)) → U4_g(T159, T140, fB_in_gg(T159, T140))
fB_in_gg(0, T168) → fB_out_gg(0, T168)
fB_in_gg(s(T188), T175) → U2_gg(T188, T175, fB_in_gg(T188, s(T175)))
U2_gg(T188, T175, fB_out_gg(T188, s(T175))) → fB_out_gg(s(T188), T175)
U4_g(T159, T140, fB_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))
U4_g(T159, T140, fB_out_gg(T159, T140)) → U5_g(T159, T140, gA_in_gg(T159, T140))
U5_g(T159, T140, gA_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))

The argument filtering Pi contains the following mapping:
hC_in_g(x1) = hC_in_g(x1)
c(x1, x2) = c(x1, x2)
0 = 0
hC_out_g(x1) = hC_out_g
s(x1) = s(x1)
U3_g(x1, x2) = U3_g(x2)
gA_in_gg(x1, x2) = gA_in_gg(x1, x2)
gA_out_gg(x1, x2) = gA_out_gg
U1_gg(x1, x2, x3) = U1_gg(x3)
U4_g(x1, x2, x3) = U4_g(x1, x2, x3)
fB_in_gg(x1, x2) = fB_in_gg(x1, x2)
fB_out_gg(x1, x2) = fB_out_gg
U2_gg(x1, x2, x3) = U2_gg(x3)
U5_g(x1, x2, x3) = U5_g(x3)
HC_IN_G(x1) = HC_IN_G(x1)
U3_G(x1, x2) = U3_G(x2)
GA_IN_GG(x1, x2) = GA_IN_GG(x1, x2)
U1_GG(x1, x2, x3) = U1_GG(x3)
U4_G(x1, x2, x3) = U4_G(x1, x2, x3)
FB_IN_GG(x1, x2) = FB_IN_GG(x1, x2)
U2_GG(x1, x2, x3) = U2_GG(x3)
U5_G(x1, x2, x3) = U5_G(x3)

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

(6) Obligation:

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

HC_IN_G(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_G(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
HC_IN_G(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → GA_IN_GG(s(s(s(s(s(s(s(0))))))), T104)
GA_IN_GG(T118, s(T132)) → U1_GG(T118, T132, gA_in_gg(s(T118), T132))
GA_IN_GG(T118, s(T132)) → GA_IN_GG(s(T118), T132)
HC_IN_G(c(s(T159), T140)) → U4_G(T159, T140, fB_in_gg(T159, T140))
HC_IN_G(c(s(T159), T140)) → FB_IN_GG(T159, T140)
FB_IN_GG(s(T188), T175) → U2_GG(T188, T175, fB_in_gg(T188, s(T175)))
FB_IN_GG(s(T188), T175) → FB_IN_GG(T188, s(T175))
U4_G(T159, T140, fB_out_gg(T159, T140)) → U5_G(T159, T140, gA_in_gg(T159, T140))
U4_G(T159, T140, fB_out_gg(T159, T140)) → GA_IN_GG(T159, T140)

The TRS R consists of the following rules:

hC_in_g(c(0, 0)) → hC_out_g(c(0, 0))
hC_in_g(c(0, s(0))) → hC_out_g(c(0, s(0)))
hC_in_g(c(0, s(s(0)))) → hC_out_g(c(0, s(s(0))))
hC_in_g(c(0, s(s(s(0))))) → hC_out_g(c(0, s(s(s(0)))))
hC_in_g(c(0, s(s(s(s(0)))))) → hC_out_g(c(0, s(s(s(s(0))))))
hC_in_g(c(0, s(s(s(s(s(0))))))) → hC_out_g(c(0, s(s(s(s(s(0)))))))
hC_in_g(c(0, s(s(s(s(s(s(0)))))))) → hC_out_g(c(0, s(s(s(s(s(s(0))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(0))))))))) → hC_out_g(c(0, s(s(s(s(s(s(s(0)))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_g(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
gA_in_gg(T112, 0) → gA_out_gg(T112, 0)
gA_in_gg(T118, s(T132)) → U1_gg(T118, T132, gA_in_gg(s(T118), T132))
U1_gg(T118, T132, gA_out_gg(s(T118), T132)) → gA_out_gg(T118, s(T132))
U3_g(T104, gA_out_gg(s(s(s(s(s(s(s(0))))))), T104)) → hC_out_g(c(0, s(s(s(s(s(s(s(s(T104))))))))))
hC_in_g(c(s(T159), T140)) → U4_g(T159, T140, fB_in_gg(T159, T140))
fB_in_gg(0, T168) → fB_out_gg(0, T168)
fB_in_gg(s(T188), T175) → U2_gg(T188, T175, fB_in_gg(T188, s(T175)))
U2_gg(T188, T175, fB_out_gg(T188, s(T175))) → fB_out_gg(s(T188), T175)
U4_g(T159, T140, fB_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))
U4_g(T159, T140, fB_out_gg(T159, T140)) → U5_g(T159, T140, gA_in_gg(T159, T140))
U5_g(T159, T140, gA_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 8 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

FB_IN_GG(s(T188), T175) → FB_IN_GG(T188, s(T175))

The TRS R consists of the following rules:

hC_in_g(c(0, 0)) → hC_out_g(c(0, 0))
hC_in_g(c(0, s(0))) → hC_out_g(c(0, s(0)))
hC_in_g(c(0, s(s(0)))) → hC_out_g(c(0, s(s(0))))
hC_in_g(c(0, s(s(s(0))))) → hC_out_g(c(0, s(s(s(0)))))
hC_in_g(c(0, s(s(s(s(0)))))) → hC_out_g(c(0, s(s(s(s(0))))))
hC_in_g(c(0, s(s(s(s(s(0))))))) → hC_out_g(c(0, s(s(s(s(s(0)))))))
hC_in_g(c(0, s(s(s(s(s(s(0)))))))) → hC_out_g(c(0, s(s(s(s(s(s(0))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(0))))))))) → hC_out_g(c(0, s(s(s(s(s(s(s(0)))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_g(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
gA_in_gg(T112, 0) → gA_out_gg(T112, 0)
gA_in_gg(T118, s(T132)) → U1_gg(T118, T132, gA_in_gg(s(T118), T132))
U1_gg(T118, T132, gA_out_gg(s(T118), T132)) → gA_out_gg(T118, s(T132))
U3_g(T104, gA_out_gg(s(s(s(s(s(s(s(0))))))), T104)) → hC_out_g(c(0, s(s(s(s(s(s(s(s(T104))))))))))
hC_in_g(c(s(T159), T140)) → U4_g(T159, T140, fB_in_gg(T159, T140))
fB_in_gg(0, T168) → fB_out_gg(0, T168)
fB_in_gg(s(T188), T175) → U2_gg(T188, T175, fB_in_gg(T188, s(T175)))
U2_gg(T188, T175, fB_out_gg(T188, s(T175))) → fB_out_gg(s(T188), T175)
U4_g(T159, T140, fB_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))
U4_g(T159, T140, fB_out_gg(T159, T140)) → U5_g(T159, T140, gA_in_gg(T159, T140))
U5_g(T159, T140, gA_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))

The argument filtering Pi contains the following mapping:
hC_in_g(x1) = hC_in_g(x1)
c(x1, x2) = c(x1, x2)
0 = 0
hC_out_g(x1) = hC_out_g
s(x1) = s(x1)
U3_g(x1, x2) = U3_g(x2)
gA_in_gg(x1, x2) = gA_in_gg(x1, x2)
gA_out_gg(x1, x2) = gA_out_gg
U1_gg(x1, x2, x3) = U1_gg(x3)
U4_g(x1, x2, x3) = U4_g(x1, x2, x3)
fB_in_gg(x1, x2) = fB_in_gg(x1, x2)
fB_out_gg(x1, x2) = fB_out_gg
U2_gg(x1, x2, x3) = U2_gg(x3)
U5_g(x1, x2, x3) = U5_g(x3)
FB_IN_GG(x1, x2) = FB_IN_GG(x1, x2)

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:

FB_IN_GG(s(T188), T175) → FB_IN_GG(T188, s(T175))

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:

FB_IN_GG(s(T188), T175) → FB_IN_GG(T188, s(T175))

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:

FB_IN_GG(s(T188), T175) → FB_IN_GG(T188, s(T175))
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

GA_IN_GG(T118, s(T132)) → GA_IN_GG(s(T118), T132)

The TRS R consists of the following rules:

hC_in_g(c(0, 0)) → hC_out_g(c(0, 0))
hC_in_g(c(0, s(0))) → hC_out_g(c(0, s(0)))
hC_in_g(c(0, s(s(0)))) → hC_out_g(c(0, s(s(0))))
hC_in_g(c(0, s(s(s(0))))) → hC_out_g(c(0, s(s(s(0)))))
hC_in_g(c(0, s(s(s(s(0)))))) → hC_out_g(c(0, s(s(s(s(0))))))
hC_in_g(c(0, s(s(s(s(s(0))))))) → hC_out_g(c(0, s(s(s(s(s(0)))))))
hC_in_g(c(0, s(s(s(s(s(s(0)))))))) → hC_out_g(c(0, s(s(s(s(s(s(0))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(0))))))))) → hC_out_g(c(0, s(s(s(s(s(s(s(0)))))))))
hC_in_g(c(0, s(s(s(s(s(s(s(s(T104)))))))))) → U3_g(T104, gA_in_gg(s(s(s(s(s(s(s(0))))))), T104))
gA_in_gg(T112, 0) → gA_out_gg(T112, 0)
gA_in_gg(T118, s(T132)) → U1_gg(T118, T132, gA_in_gg(s(T118), T132))
U1_gg(T118, T132, gA_out_gg(s(T118), T132)) → gA_out_gg(T118, s(T132))
U3_g(T104, gA_out_gg(s(s(s(s(s(s(s(0))))))), T104)) → hC_out_g(c(0, s(s(s(s(s(s(s(s(T104))))))))))
hC_in_g(c(s(T159), T140)) → U4_g(T159, T140, fB_in_gg(T159, T140))
fB_in_gg(0, T168) → fB_out_gg(0, T168)
fB_in_gg(s(T188), T175) → U2_gg(T188, T175, fB_in_gg(T188, s(T175)))
U2_gg(T188, T175, fB_out_gg(T188, s(T175))) → fB_out_gg(s(T188), T175)
U4_g(T159, T140, fB_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))
U4_g(T159, T140, fB_out_gg(T159, T140)) → U5_g(T159, T140, gA_in_gg(T159, T140))
U5_g(T159, T140, gA_out_gg(T159, T140)) → hC_out_g(c(s(T159), T140))

The argument filtering Pi contains the following mapping:
hC_in_g(x1) = hC_in_g(x1)
c(x1, x2) = c(x1, x2)
0 = 0
hC_out_g(x1) = hC_out_g
s(x1) = s(x1)
U3_g(x1, x2) = U3_g(x2)
gA_in_gg(x1, x2) = gA_in_gg(x1, x2)
gA_out_gg(x1, x2) = gA_out_gg
U1_gg(x1, x2, x3) = U1_gg(x3)
U4_g(x1, x2, x3) = U4_g(x1, x2, x3)
fB_in_gg(x1, x2) = fB_in_gg(x1, x2)
fB_out_gg(x1, x2) = fB_out_gg
U2_gg(x1, x2, x3) = U2_gg(x3)
U5_g(x1, x2, x3) = U5_g(x3)
GA_IN_GG(x1, x2) = GA_IN_GG(x1, 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:

GA_IN_GG(T118, s(T132)) → GA_IN_GG(s(T118), T132)

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

(19) PiDPToQDPProof (EQUIVALENT 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:

GA_IN_GG(T118, s(T132)) → GA_IN_GG(s(T118), T132)

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:

GA_IN_GG(T118, s(T132)) → GA_IN_GG(s(T118), T132)
The graph contains the following edges 2 > 2

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (EQUIVALENT transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (EQUIVALENT transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES