Left Termination proof of /tmp/tmpKjBFtT/quot.pl

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

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇒, 1177 ms)

↳2 Prolog

↳3 PrologToPiTRSProof (⇒, 71 ms)

↳4 PiTRS

↳5 DependencyPairsProof (⇔, 394 ms)

↳6 PiDP

↳7 DependencyGraphProof (⇔, 19 ms)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔, 0 ms)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇒, 0 ms)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔, 0 ms)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔, 0 ms)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇒, 0 ms)

        ↳20 QDP

        ↳21 QDPSizeChangeProof (⇔, 0 ms)

        ↳22 YES

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔, 0 ms)

        ↳25 PiDP

        ↳26 PiDPToQDPProof (⇒, 0 ms)

        ↳27 QDP

        ↳28 QDPSizeChangeProof (⇔, 0 ms)

        ↳29 YES

    ↳30 PiDP

        ↳31 UsableRulesProof (⇔, 0 ms)

        ↳32 PiDP

        ↳33 PiDPToQDPProof (⇒, 0 ms)

        ↳34 QDP

        ↳35 QDPSizeChangeProof (⇔, 0 ms)

        ↳36 YES

    ↳37 PiDP

        ↳38 UsableRulesProof (⇔, 0 ms)

        ↳39 PiDP

        ↳40 PiDPToQDPProof (⇒, 0 ms)

        ↳41 QDP

        ↳42 QDPSizeChangeProof (⇔, 0 ms)

        ↳43 YES

    ↳44 PiDP

        ↳45 UsableRulesProof (⇔, 0 ms)

        ↳46 PiDP

        ↳47 PiDPToQDPProof (⇒, 0 ms)

        ↳48 QDP

        ↳49 QDPSizeChangeProof (⇔, 0 ms)

        ↳50 YES

    ↳51 PiDP

        ↳52 UsableRulesProof (⇔, 0 ms)

        ↳53 PiDP

        ↳54 PiDPToQDPProof (⇒, 0 ms)

        ↳55 QDP

        ↳56 QDPSizeChangeProof (⇔, 0 ms)

        ↳57 YES

    ↳58 PiDP

        ↳59 UsableRulesProof (⇔, 0 ms)

        ↳60 PiDP

        ↳61 PiDPToQDPProof (⇒, 0 ms)

        ↳62 QDP

        ↳63 QDPSizeChangeProof (⇔, 0 ms)

        ↳64 YES

(0) Obligation:

Clauses:

div(X, Y, Z) :- quot(X, Y, Y, Z).
quot(0, s(Y), s(Z), 0).
quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U).
quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U).

Query: div(g,g,a)

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph ICLP10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: div(T1, T2, T3)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: div(T1, T2, T3), SCOPE: 1, CLAUSE: 0\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: quot(T7, T8, T8, T10)\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 1 | quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 2 | quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 1\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 2 | quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 2\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: quot(T7, T8, T8, T10), SCOPE: 2, CLAUSE: 3\n\nT7 is ground\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: quot(T28, T29, s(T29), T31)\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 1 | quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 2 | quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 1\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 2 | quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 2\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: quot(T28, T29, s(T29), T31), SCOPE: 3, CLAUSE: 3\n\nT28 is ground\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: quot(T51, T52, s(s(T52)), T54)\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 1 | quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 2 | quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 1\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 2 | quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 2\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: quot(T51, T52, s(s(T52)), T54), SCOPE: 4, CLAUSE: 3\n\nT51 is ground\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: quot(T74, T75, s(s(s(T75))), T77)\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 1 | quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 2 | quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 3\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 1\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 2 | quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 3\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 2\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: quot(T74, T75, s(s(s(T75))), T77), SCOPE: 5, CLAUSE: 3\n\nT74 is ground\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: quot(T97, T98, s(s(s(s(T98)))), T100)\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 1 | quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 2 | quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 3\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 1\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 2 | quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 3\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 2\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: quot(T97, T98, s(s(s(s(T98)))), T100), SCOPE: 6, CLAUSE: 3\n\nT97 is ground\nT98 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: quot(T120, T121, s(s(s(s(s(T121))))), T123)\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 1 | quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 2 | quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 3\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 1\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 2 | quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 3\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 2\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: quot(T120, T121, s(s(s(s(s(T121))))), T123), SCOPE: 7, CLAUSE: 3\n\nT120 is ground\nT121 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146)\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 1 | quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 2 | quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 3\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 1\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 2 | quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 3\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 2\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: quot(T143, T144, s(s(s(s(s(s(T144)))))), T146), SCOPE: 8, CLAUSE: 3\n\nT143 is ground\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169)\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 1 | quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 2 | quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 3\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 1\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 2 | quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 3\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 2\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: quot(T166, T167, s(s(s(s(s(s(s(T167))))))), T169), SCOPE: 9, CLAUSE: 3\n\nT166 is ground\nT167 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: quot(T189, T190, s(s(s(s(s(s(s(s(T190)))))))), T192)\n\nT189 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: quot(T189, T190, s(T195), T192)\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 1 | quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 2 | quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 3\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 1\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 2 | quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 3\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 2\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: quot(T189, T190, s(T195), T192), SCOPE: 10, CLAUSE: 3\n\nT189 is ground\nT190 is ground\nT195 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: quot(T226, T227, s(T228), T230)\n\nT226 is ground\nT227 is ground\nT228 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: quot(T241, s(T242), s(T242), T244)\n\nT241 is ground\nT242 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253)\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 1 | quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 2 | quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 3\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 1\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 2 | quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 3\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 2\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: quot(T251, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T253), SCOPE: 11, CLAUSE: 3\n\nT251 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264)\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 1 | quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 2 | quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 3\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 1\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 2 | quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 3\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 2\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: quot(T262, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(0))))))), T264), SCOPE: 12, CLAUSE: 3\n\nT262 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275)\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 1 | quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 2 | quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 3\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 1\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 2 | quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 3\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 2\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: quot(T273, s(s(s(s(s(0))))), s(s(s(s(s(s(s(0))))))), T275), SCOPE: 13, CLAUSE: 3\n\nT273 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286)\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 1 | quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 2 | quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 3\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 1\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 2 | quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 3\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 2\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: quot(T284, s(s(s(s(0)))), s(s(s(s(s(s(s(0))))))), T286), SCOPE: 14, CLAUSE: 3\n\nT284 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297)\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 1 | quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 2 | quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 3\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 1\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 2 | quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 3\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 2\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: quot(T295, s(s(s(0))), s(s(s(s(s(s(s(0))))))), T297), SCOPE: 15, CLAUSE: 3\n\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308)\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 1 | quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 2 | quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 3\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 1\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 2 | quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 3\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 2\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: quot(T306, s(s(0)), s(s(s(s(s(s(s(0))))))), T308), SCOPE: 16, CLAUSE: 3\n\nT306 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319)\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 1 | quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 2 | quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 3\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 1\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 2 | quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 3\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 2\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: quot(T317, s(0), s(s(s(s(s(s(s(0))))))), T319), SCOPE: 17, CLAUSE: 3\n\nT317 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330)\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 1 | quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 2 | quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 3\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 2 | quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 3\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: quot(T328, 0, s(s(s(s(s(s(s(0))))))), T330), SCOPE: 18, CLAUSE: 3\n\nT328 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: quot(T336, s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(0))))))), T338)\n\nT336 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: \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: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352)\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 1 | quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 2 | quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 3\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 1\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 2 | quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 3\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 2\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: quot(T350, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T352), SCOPE: 19, CLAUSE: 3\n\nT350 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363)\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 1 | quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 2 | quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 3\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 1\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 2 | quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 3\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 2\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: quot(T361, s(s(s(s(s(0))))), s(s(s(s(s(s(0)))))), T363), SCOPE: 20, CLAUSE: 3\n\nT361 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374)\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 1 | quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 2 | quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 3\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 1\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 2 | quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 3\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 2\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: quot(T372, s(s(s(s(0)))), s(s(s(s(s(s(0)))))), T374), SCOPE: 21, CLAUSE: 3\n\nT372 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385)\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 1 | quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 2 | quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 3\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 1\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 2 | quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 3\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 2\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: quot(T383, s(s(s(0))), s(s(s(s(s(s(0)))))), T385), SCOPE: 22, CLAUSE: 3\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396)\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 1 | quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 2 | quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 3\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 1\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 2 | quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 3\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 2\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: quot(T394, s(s(0)), s(s(s(s(s(s(0)))))), T396), SCOPE: 23, CLAUSE: 3\n\nT394 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407)\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 1 | quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 2 | quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 3\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 1\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 2 | quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 3\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 2\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: quot(T405, s(0), s(s(s(s(s(s(0)))))), T407), SCOPE: 24, CLAUSE: 3\n\nT405 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: quot(T416, 0, s(s(s(s(s(s(0)))))), T418)\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 1 | quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 2 | quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 3\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 2 | quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 3\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: quot(T416, 0, s(s(s(s(s(s(0)))))), T418), SCOPE: 25, CLAUSE: 3\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: quot(T424, s(s(s(s(s(s(0)))))), s(s(s(s(s(s(0)))))), T426)\n\nT424 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439)\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 1 | quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 2 | quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 3\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 1\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 2 | quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 3\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 2\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: quot(T437, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T439), SCOPE: 26, CLAUSE: 3\n\nT437 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450)\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 1 | quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 2 | quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 3\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 1\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 2 | quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 3\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 2\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: quot(T448, s(s(s(s(0)))), s(s(s(s(s(0))))), T450), SCOPE: 27, CLAUSE: 3\n\nT448 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461)\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 1 | quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 2 | quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 1\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 2 | quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 2\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: quot(T459, s(s(s(0))), s(s(s(s(s(0))))), T461), SCOPE: 28, CLAUSE: 3\n\nT459 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472)\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 1 | quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 2 | quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 3\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 1\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 2 | quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 3\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 2\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: quot(T470, s(s(0)), s(s(s(s(s(0))))), T472), SCOPE: 29, CLAUSE: 3\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: quot(T481, s(0), s(s(s(s(s(0))))), T483)\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 1 | quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 2 | quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 3\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 1\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 2 | quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 3\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 2\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: quot(T481, s(0), s(s(s(s(s(0))))), T483), SCOPE: 30, CLAUSE: 3\n\nT481 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: quot(T492, 0, s(s(s(s(s(0))))), T494)\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 1 | quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 2 | quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 2 | quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: quot(T492, 0, s(s(s(s(s(0))))), T494), SCOPE: 31, CLAUSE: 3\n\nT492 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: quot(T500, s(s(s(s(s(0))))), s(s(s(s(s(0))))), T502)\n\nT500 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="312: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514)\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 1 | quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 2 | quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 3\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 1\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 2 | quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 3\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 2\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: quot(T512, s(s(s(s(0)))), s(s(s(s(0)))), T514), SCOPE: 32, CLAUSE: 3\n\nT512 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
326 [label="326: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525)\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 1 | quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 2 | quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 3\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 1\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 2 | quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 3\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 2\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="335: quot(T523, s(s(s(0))), s(s(s(s(0)))), T525), SCOPE: 33, CLAUSE: 3\n\nT523 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="336: quot(T534, s(s(0)), s(s(s(s(0)))), T536)\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
337 [label="337: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 1 | quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 2 | quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 3\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 1\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 2 | quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 3\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 2\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
345 [label="345: quot(T534, s(s(0)), s(s(s(s(0)))), T536), SCOPE: 34, CLAUSE: 3\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
346 [label="346: quot(T545, s(0), s(s(s(s(0)))), T547)\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
347 [label="347: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 1 | quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 2 | quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 3\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 1\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="350: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 2 | quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 3\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
351 [label="351: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
353 [label="353: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
354 [label="354: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 2\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: quot(T545, s(0), s(s(s(s(0)))), T547), SCOPE: 35, CLAUSE: 3\n\nT545 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
356 [label="356: quot(T556, 0, s(s(s(s(0)))), T558)\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 1 | quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 2 | quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 3\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="359: quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 2 | quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 3\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
360 [label="360: quot(T556, 0, s(s(s(s(0)))), T558), SCOPE: 36, CLAUSE: 3\n\nT556 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: quot(T564, s(s(s(s(0)))), s(s(s(s(0)))), T566)\n\nT564 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="362: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
363 [label="363: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
364 [label="364: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
365 [label="365: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="366: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
367 [label="367: quot(T575, s(s(s(0))), s(s(s(0))), T577)\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
368 [label="368: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
369 [label="369: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 1 | quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 2 | quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 3\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
370 [label="370: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 1\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 2 | quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 3\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
373 [label="373: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
374 [label="374: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
375 [label="375: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 2\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
376 [label="376: quot(T575, s(s(s(0))), s(s(s(0))), T577), SCOPE: 37, CLAUSE: 3\n\nT575 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
377 [label="377: quot(T586, s(s(0)), s(s(s(0))), T588)\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
378 [label="378: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
379 [label="379: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 1 | quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 2 | quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 3\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
380 [label="380: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 1\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 2 | quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 3\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
383 [label="383: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
384 [label="384: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
385 [label="385: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 2\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
386 [label="386: quot(T586, s(s(0)), s(s(s(0))), T588), SCOPE: 38, CLAUSE: 3\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: quot(T597, s(0), s(s(s(0))), T599)\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="389: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 1 | quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 2 | quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 3\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 1\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 2 | quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 3\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
392 [label="392: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
393 [label="393: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
394 [label="394: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
395 [label="395: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 2\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
396 [label="396: quot(T597, s(0), s(s(s(0))), T599), SCOPE: 39, CLAUSE: 3\n\nT597 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
397 [label="397: quot(T608, 0, s(s(s(0))), T610)\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
398 [label="398: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
399 [label="399: quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 1 | quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 2 | quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 3\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
400 [label="400: quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 2 | quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 3\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
401 [label="401: quot(T608, 0, s(s(s(0))), T610), SCOPE: 40, CLAUSE: 3\n\nT608 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
402 [label="402: quot(T616, s(s(s(0))), s(s(s(0))), T618)\n\nT616 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
403 [label="403: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
404 [label="404: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
405 [label="405: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
406 [label="406: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
407 [label="407: quot(T626, s(s(0)), s(s(0)), T628)\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
408 [label="408: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
409 [label="409: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 1 | quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 2 | quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 3\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
410 [label="410: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 1\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
411 [label="411: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 2 | quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 3\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
412 [label="412: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 2\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: quot(T626, s(s(0)), s(s(0)), T628), SCOPE: 41, CLAUSE: 3\n\nT626 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: quot(T637, s(0), s(s(0)), T639)\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
419 [label="419: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 1 | quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 2 | quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 3\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
420 [label="420: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 1\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
421 [label="421: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 2 | quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 3\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
423 [label="423: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="424: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
425 [label="425: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 2\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
426 [label="426: quot(T637, s(0), s(s(0)), T639), SCOPE: 42, CLAUSE: 3\n\nT637 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
427 [label="427: quot(T648, 0, s(s(0)), T650)\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
428 [label="428: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
429 [label="429: quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 1 | quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 2 | quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 3\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="430: quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 2 | quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 3\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
431 [label="431: quot(T648, 0, s(s(0)), T650), SCOPE: 43, CLAUSE: 3\n\nT648 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
432 [label="432: quot(T656, s(s(0)), s(s(0)), T658)\n\nT656 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
433 [label="433: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
434 [label="434: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
435 [label="435: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
436 [label="436: quot(T665, s(0), s(0), T667)\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
437 [label="437: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
438 [label="438: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 1 | quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 2 | quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 3\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 1\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
440 [label="440: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 2 | quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 3\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
441 [label="441: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
442 [label="442: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
443 [label="443: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
444 [label="444: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 2\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
445 [label="445: quot(T665, s(0), s(0), T667), SCOPE: 44, CLAUSE: 3\n\nT665 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="446: quot(T676, 0, s(0), T678)\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
447 [label="447: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 1 | quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 2 | quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 3\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
449 [label="449: quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 2 | quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 3\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
450 [label="450: quot(T676, 0, s(0), T678), SCOPE: 45, CLAUSE: 3\n\nT676 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
451 [label="451: quot(T684, s(0), s(0), T686)\n\nT684 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
452 [label="452: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
453 [label="453: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
454 [label="454: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
455 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 455 [arrowhead = none ];
455 -> 2;

456 [label="ONLY EVAL with clause\ndiv(X4, X5, X6) :- quot(X4, X5, X5, X6).\nand substitutionT1 -> T7,\nX4 -> T7,\nT2 -> T8,\nX5 -> T8,\nT3 -> T10,\nX6 -> T10,\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 456 [arrowhead = none ];
456 -> 3;

457 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 457 [arrowhead = none ];
457 -> 4;

458 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 458 [arrowhead = none ];
458 -> 5;

459 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 459 [arrowhead = none ];
459 -> 6;

460 [label="EVAL with clause\nquot(0, s(X15), s(X16), 0).\nand substitutionT7 -> 0,\nX15 -> T15,\nT8 -> s(T15),\nX16 -> T15,\nT10 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 460 [arrowhead = none ];
460 -> 7;

461 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 461 [arrowhead = none ];
461 -> 8;

462 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
6 -> 462 [arrowhead = none ];
462 -> 10;

463 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
6 -> 463 [arrowhead = none ];
463 -> 11;

464 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 464 [arrowhead = none ];
464 -> 9;

465 [label="EVAL with clause\nquot(s(X33), s(X34), X35, X36) :- quot(X33, X34, X35, X36).\nand substitutionX33 -> T28,\nT7 -> s(T28),\nX34 -> T29,\nT8 -> s(T29),\nX35 -> s(T29),\nT10 -> T31,\nX36 -> T31,\nT30 -> T31", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 465 [arrowhead = none ];
465 -> 12;

466 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 466 [arrowhead = none ];
466 -> 13;

467 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 467 [arrowhead = none ];
467 -> 454;

468 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
12 -> 468 [arrowhead = none ];
468 -> 14;

469 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 469 [arrowhead = none ];
469 -> 15;

470 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 470 [arrowhead = none ];
470 -> 16;

471 [label="EVAL with clause\nquot(0, s(X49), s(X50), 0).\nand substitutionT28 -> 0,\nX49 -> T38,\nT29 -> s(T38),\nX50 -> s(T38),\nT31 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 471 [arrowhead = none ];
471 -> 17;

472 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 472 [arrowhead = none ];
472 -> 18;

473 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 473 [arrowhead = none ];
473 -> 20;

474 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 474 [arrowhead = none ];
474 -> 21;

475 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 475 [arrowhead = none ];
475 -> 19;

476 [label="EVAL with clause\nquot(s(X67), s(X68), X69, X70) :- quot(X67, X68, X69, X70).\nand substitutionX67 -> T51,\nT28 -> s(T51),\nX68 -> T52,\nT29 -> s(T52),\nX69 -> s(s(T52)),\nT31 -> T54,\nX70 -> T54,\nT53 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 476 [arrowhead = none ];
476 -> 22;

477 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 477 [arrowhead = none ];
477 -> 23;

478 [label="EVAL with clause\nquot(X1527, 0, s(X1528), s(X1529)) :- quot(X1527, s(X1528), s(X1528), X1529).\nand substitutionT28 -> T665,\nX1527 -> T665,\nT29 -> 0,\nX1528 -> 0,\nX1529 -> T667,\nT31 -> s(T667),\nT666 -> T667", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 478 [arrowhead = none ];
478 -> 436;

479 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 479 [arrowhead = none ];
479 -> 437;

480 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 480 [arrowhead = none ];
480 -> 24;

481 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 481 [arrowhead = none ];
481 -> 25;

482 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 482 [arrowhead = none ];
482 -> 26;

483 [label="EVAL with clause\nquot(0, s(X83), s(X84), 0).\nand substitutionT51 -> 0,\nX83 -> T61,\nT52 -> s(T61),\nX84 -> s(s(T61)),\nT54 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 483 [arrowhead = none ];
483 -> 27;

484 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 484 [arrowhead = none ];
484 -> 28;

485 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 485 [arrowhead = none ];
485 -> 30;

486 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 486 [arrowhead = none ];
486 -> 31;

487 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 487 [arrowhead = none ];
487 -> 29;

488 [label="EVAL with clause\nquot(s(X101), s(X102), X103, X104) :- quot(X101, X102, X103, X104).\nand substitutionX101 -> T74,\nT51 -> s(T74),\nX102 -> T75,\nT52 -> s(T75),\nX103 -> s(s(s(T75))),\nT54 -> T77,\nX104 -> T77,\nT76 -> T77", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 488 [arrowhead = none ];
488 -> 32;

489 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 489 [arrowhead = none ];
489 -> 33;

490 [label="EVAL with clause\nquot(X1421, 0, s(X1422), s(X1423)) :- quot(X1421, s(X1422), s(X1422), X1423).\nand substitutionT51 -> T626,\nX1421 -> T626,\nT52 -> 0,\nX1422 -> s(0),\nX1423 -> T628,\nT54 -> s(T628),\nT627 -> T628", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 490 [arrowhead = none ];
490 -> 407;

491 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 491 [arrowhead = none ];
491 -> 408;

492 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
32 -> 492 [arrowhead = none ];
492 -> 34;

493 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
34 -> 493 [arrowhead = none ];
493 -> 35;

494 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
34 -> 494 [arrowhead = none ];
494 -> 36;

495 [label="EVAL with clause\nquot(0, s(X117), s(X118), 0).\nand substitutionT74 -> 0,\nX117 -> T84,\nT75 -> s(T84),\nX118 -> s(s(s(T84))),\nT77 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 495 [arrowhead = none ];
495 -> 37;

496 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 496 [arrowhead = none ];
496 -> 38;

497 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 497 [arrowhead = none ];
497 -> 40;

498 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 498 [arrowhead = none ];
498 -> 41;

499 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 499 [arrowhead = none ];
499 -> 39;

500 [label="EVAL with clause\nquot(s(X135), s(X136), X137, X138) :- quot(X135, X136, X137, X138).\nand substitutionX135 -> T97,\nT74 -> s(T97),\nX136 -> T98,\nT75 -> s(T98),\nX137 -> s(s(s(s(T98)))),\nT77 -> T100,\nX138 -> T100,\nT99 -> T100", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 500 [arrowhead = none ];
500 -> 42;

501 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
40 -> 501 [arrowhead = none ];
501 -> 43;

502 [label="EVAL with clause\nquot(X1278, 0, s(X1279), s(X1280)) :- quot(X1278, s(X1279), s(X1279), X1280).\nand substitutionT74 -> T575,\nX1278 -> T575,\nT75 -> 0,\nX1279 -> s(s(0)),\nX1280 -> T577,\nT77 -> s(T577),\nT576 -> T577", fontsize=14, style = filled, fillcolor = lightblue];
41 -> 502 [arrowhead = none ];
502 -> 367;

503 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 503 [arrowhead = none ];
503 -> 368;

504 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
42 -> 504 [arrowhead = none ];
504 -> 44;

505 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
44 -> 505 [arrowhead = none ];
505 -> 45;

506 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
44 -> 506 [arrowhead = none ];
506 -> 46;

507 [label="EVAL with clause\nquot(0, s(X151), s(X152), 0).\nand substitutionT97 -> 0,\nX151 -> T107,\nT98 -> s(T107),\nX152 -> s(s(s(s(T107)))),\nT100 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 507 [arrowhead = none ];
507 -> 47;

508 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
45 -> 508 [arrowhead = none ];
508 -> 48;

509 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
46 -> 509 [arrowhead = none ];
509 -> 50;

510 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
46 -> 510 [arrowhead = none ];
510 -> 51;

511 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 511 [arrowhead = none ];
511 -> 49;

512 [label="EVAL with clause\nquot(s(X169), s(X170), X171, X172) :- quot(X169, X170, X171, X172).\nand substitutionX169 -> T120,\nT97 -> s(T120),\nX170 -> T121,\nT98 -> s(T121),\nX171 -> s(s(s(s(s(T121))))),\nT100 -> T123,\nX172 -> T123,\nT122 -> T123", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 512 [arrowhead = none ];
512 -> 52;

513 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
50 -> 513 [arrowhead = none ];
513 -> 53;

514 [label="EVAL with clause\nquot(X1098, 0, s(X1099), s(X1100)) :- quot(X1098, s(X1099), s(X1099), X1100).\nand substitutionT97 -> T512,\nX1098 -> T512,\nT98 -> 0,\nX1099 -> s(s(s(0))),\nX1100 -> T514,\nT100 -> s(T514),\nT513 -> T514", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 514 [arrowhead = none ];
514 -> 316;

515 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 515 [arrowhead = none ];
515 -> 317;

516 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
52 -> 516 [arrowhead = none ];
516 -> 54;

517 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 517 [arrowhead = none ];
517 -> 55;

518 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
54 -> 518 [arrowhead = none ];
518 -> 56;

519 [label="EVAL with clause\nquot(0, s(X185), s(X186), 0).\nand substitutionT120 -> 0,\nX185 -> T130,\nT121 -> s(T130),\nX186 -> s(s(s(s(s(T130))))),\nT123 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 519 [arrowhead = none ];
519 -> 57;

520 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 520 [arrowhead = none ];
520 -> 58;

521 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 521 [arrowhead = none ];
521 -> 60;

522 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 522 [arrowhead = none ];
522 -> 61;

523 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
57 -> 523 [arrowhead = none ];
523 -> 59;

524 [label="EVAL with clause\nquot(s(X203), s(X204), X205, X206) :- quot(X203, X204, X205, X206).\nand substitutionX203 -> T143,\nT120 -> s(T143),\nX204 -> T144,\nT121 -> s(T144),\nX205 -> s(s(s(s(s(s(T144)))))),\nT123 -> T146,\nX206 -> T146,\nT145 -> T146", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 524 [arrowhead = none ];
524 -> 62;

525 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
60 -> 525 [arrowhead = none ];
525 -> 63;

526 [label="EVAL with clause\nquot(X881, 0, s(X882), s(X883)) :- quot(X881, s(X882), s(X882), X883).\nand substitutionT120 -> T437,\nX881 -> T437,\nT121 -> 0,\nX882 -> s(s(s(s(0)))),\nX883 -> T439,\nT123 -> s(T439),\nT438 -> T439", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 526 [arrowhead = none ];
526 -> 254;

527 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 527 [arrowhead = none ];
527 -> 255;

528 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
62 -> 528 [arrowhead = none ];
528 -> 64;

529 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
64 -> 529 [arrowhead = none ];
529 -> 65;

530 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
64 -> 530 [arrowhead = none ];
530 -> 66;

531 [label="EVAL with clause\nquot(0, s(X219), s(X220), 0).\nand substitutionT143 -> 0,\nX219 -> T153,\nT144 -> s(T153),\nX220 -> s(s(s(s(s(s(T153)))))),\nT146 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 531 [arrowhead = none ];
531 -> 67;

532 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 532 [arrowhead = none ];
532 -> 68;

533 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 533 [arrowhead = none ];
533 -> 70;

534 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 534 [arrowhead = none ];
534 -> 71;

535 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 535 [arrowhead = none ];
535 -> 69;

536 [label="EVAL with clause\nquot(s(X237), s(X238), X239, X240) :- quot(X237, X238, X239, X240).\nand substitutionX237 -> T166,\nT143 -> s(T166),\nX238 -> T167,\nT144 -> s(T167),\nX239 -> s(s(s(s(s(s(s(T167))))))),\nT146 -> T169,\nX240 -> T169,\nT168 -> T169", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 536 [arrowhead = none ];
536 -> 72;

537 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
70 -> 537 [arrowhead = none ];
537 -> 73;

538 [label="EVAL with clause\nquot(X627, 0, s(X628), s(X629)) :- quot(X627, s(X628), s(X628), X629).\nand substitutionT143 -> T350,\nX627 -> T350,\nT144 -> 0,\nX628 -> s(s(s(s(s(0))))),\nX629 -> T352,\nT146 -> s(T352),\nT351 -> T352", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 538 [arrowhead = none ];
538 -> 181;

539 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 539 [arrowhead = none ];
539 -> 182;

540 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
72 -> 540 [arrowhead = none ];
540 -> 74;

541 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 541 [arrowhead = none ];
541 -> 75;

542 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 542 [arrowhead = none ];
542 -> 76;

543 [label="EVAL with clause\nquot(0, s(X253), s(X254), 0).\nand substitutionT166 -> 0,\nX253 -> T176,\nT167 -> s(T176),\nX254 -> s(s(s(s(s(s(s(T176))))))),\nT169 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 543 [arrowhead = none ];
543 -> 77;

544 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
75 -> 544 [arrowhead = none ];
544 -> 78;

545 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 545 [arrowhead = none ];
545 -> 80;

546 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
76 -> 546 [arrowhead = none ];
546 -> 81;

547 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
77 -> 547 [arrowhead = none ];
547 -> 79;

548 [label="EVAL with clause\nquot(s(X271), s(X272), X273, X274) :- quot(X271, X272, X273, X274).\nand substitutionX271 -> T189,\nT166 -> s(T189),\nX272 -> T190,\nT167 -> s(T190),\nX273 -> s(s(s(s(s(s(s(s(T190)))))))),\nT169 -> T192,\nX274 -> T192,\nT191 -> T192", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 548 [arrowhead = none ];
548 -> 82;

549 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 549 [arrowhead = none ];
549 -> 83;

550 [label="EVAL with clause\nquot(X336, 0, s(X337), s(X338)) :- quot(X336, s(X337), s(X337), X338).\nand substitutionT166 -> T251,\nX336 -> T251,\nT167 -> 0,\nX337 -> s(s(s(s(s(s(0)))))),\nX338 -> T253,\nT169 -> s(T253),\nT252 -> T253", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 550 [arrowhead = none ];
550 -> 97;

551 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 551 [arrowhead = none ];
551 -> 98;

552 [label="GENERALIZATION\nT195 <-- s(s(s(s(s(s(s(T190)))))))\n\nNew Knowledge:\nT195 is ground", fontsize=14, style = filled, fillcolor = violet];
82 -> 552 [arrowhead = none ];
552 -> 84;

553 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
84 -> 553 [arrowhead = none ];
553 -> 85;

554 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
85 -> 554 [arrowhead = none ];
554 -> 86;

555 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
85 -> 555 [arrowhead = none ];
555 -> 87;

556 [label="EVAL with clause\nquot(0, s(X291), s(X292), 0).\nand substitutionT189 -> 0,\nX291 -> T208,\nT190 -> s(T208),\nT195 -> T209,\nX292 -> T209,\nT192 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 556 [arrowhead = none ];
556 -> 88;

557 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
86 -> 557 [arrowhead = none ];
557 -> 89;

558 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 558 [arrowhead = none ];
558 -> 91;

559 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 559 [arrowhead = none ];
559 -> 92;

560 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 560 [arrowhead = none ];
560 -> 90;

561 [label="EVAL with clause\nquot(s(X309), s(X310), X311, X312) :- quot(X309, X310, X311, X312).\nand substitutionX309 -> T226,\nT189 -> s(T226),\nX310 -> T227,\nT190 -> s(T227),\nT195 -> T228,\nX311 -> s(T228),\nT192 -> T230,\nX312 -> T230,\nT229 -> T230", fontsize=14, style = filled, fillcolor = lightblue];
91 -> 561 [arrowhead = none ];
561 -> 93;

562 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
91 -> 562 [arrowhead = none ];
562 -> 94;

563 [label="EVAL with clause\nquot(X323, 0, s(X324), s(X325)) :- quot(X323, s(X324), s(X324), X325).\nand substitutionT189 -> T241,\nX323 -> T241,\nT190 -> 0,\nT195 -> T242,\nX324 -> T242,\nX325 -> T244,\nT192 -> s(T244),\nT243 -> T244", fontsize=14, style = filled, fillcolor = lightblue];
92 -> 563 [arrowhead = none ];
563 -> 95;

564 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
92 -> 564 [arrowhead = none ];
564 -> 96;

565 [label="INSTANCE with matching:\nT189 -> T226\nT190 -> T227\nT195 -> T228\nT192 -> T230", fontsize=14, style = filled, fillcolor = lightgrey];
93 -> 565 [arrowhead = none , style=dashed];
565 -> 84[style=dashed];

566 [label="INSTANCE with matching:\nT7 -> T241\nT8 -> s(T242)\nT10 -> T244", fontsize=14, style = filled, fillcolor = lightgrey];
95 -> 566 [arrowhead = none , style=dashed];
566 -> 3[style=dashed];

567 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
97 -> 567 [arrowhead = none ];
567 -> 99;

568 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 568 [arrowhead = none ];
568 -> 100;

569 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 569 [arrowhead = none ];
569 -> 101;

570 [label="EVAL with clause\nquot(0, s(X351), s(X352), 0).\nand substitutionT251 -> 0,\nX351 -> s(s(s(s(s(s(0)))))),\nX352 -> s(s(s(s(s(s(0)))))),\nT253 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 570 [arrowhead = none ];
570 -> 102;

571 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
100 -> 571 [arrowhead = none ];
571 -> 103;

572 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 572 [arrowhead = none ];
572 -> 105;

573 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
101 -> 573 [arrowhead = none ];
573 -> 106;

574 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 574 [arrowhead = none ];
574 -> 104;

575 [label="EVAL with clause\nquot(s(X369), s(X370), X371, X372) :- quot(X369, X370, X371, X372).\nand substitutionX369 -> T262,\nT251 -> s(T262),\nX370 -> s(s(s(s(s(s(0)))))),\nX371 -> s(s(s(s(s(s(s(0))))))),\nT253 -> T264,\nX372 -> T264,\nT263 -> T264", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 575 [arrowhead = none ];
575 -> 107;

576 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 576 [arrowhead = none ];
576 -> 108;

577 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
106 -> 577 [arrowhead = none ];
577 -> 180;

578 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
107 -> 578 [arrowhead = none ];
578 -> 109;

579 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
109 -> 579 [arrowhead = none ];
579 -> 110;

580 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
109 -> 580 [arrowhead = none ];
580 -> 111;

581 [label="EVAL with clause\nquot(0, s(X385), s(X386), 0).\nand substitutionT262 -> 0,\nX385 -> s(s(s(s(s(0))))),\nX386 -> s(s(s(s(s(s(0)))))),\nT264 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 581 [arrowhead = none ];
581 -> 112;

582 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 582 [arrowhead = none ];
582 -> 113;

583 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 583 [arrowhead = none ];
583 -> 115;

584 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 584 [arrowhead = none ];
584 -> 116;

585 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 585 [arrowhead = none ];
585 -> 114;

586 [label="EVAL with clause\nquot(s(X403), s(X404), X405, X406) :- quot(X403, X404, X405, X406).\nand substitutionX403 -> T273,\nT262 -> s(T273),\nX404 -> s(s(s(s(s(0))))),\nX405 -> s(s(s(s(s(s(s(0))))))),\nT264 -> T275,\nX406 -> T275,\nT274 -> T275", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 586 [arrowhead = none ];
586 -> 117;

587 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
115 -> 587 [arrowhead = none ];
587 -> 118;

588 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
116 -> 588 [arrowhead = none ];
588 -> 179;

589 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
117 -> 589 [arrowhead = none ];
589 -> 119;

590 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
119 -> 590 [arrowhead = none ];
590 -> 120;

591 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
119 -> 591 [arrowhead = none ];
591 -> 121;

592 [label="EVAL with clause\nquot(0, s(X419), s(X420), 0).\nand substitutionT273 -> 0,\nX419 -> s(s(s(s(0)))),\nX420 -> s(s(s(s(s(s(0)))))),\nT275 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 592 [arrowhead = none ];
592 -> 122;

593 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 593 [arrowhead = none ];
593 -> 123;

594 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 594 [arrowhead = none ];
594 -> 125;

595 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 595 [arrowhead = none ];
595 -> 126;

596 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 596 [arrowhead = none ];
596 -> 124;

597 [label="EVAL with clause\nquot(s(X437), s(X438), X439, X440) :- quot(X437, X438, X439, X440).\nand substitutionX437 -> T284,\nT273 -> s(T284),\nX438 -> s(s(s(s(0)))),\nX439 -> s(s(s(s(s(s(s(0))))))),\nT275 -> T286,\nX440 -> T286,\nT285 -> T286", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 597 [arrowhead = none ];
597 -> 127;

598 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 598 [arrowhead = none ];
598 -> 128;

599 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
126 -> 599 [arrowhead = none ];
599 -> 178;

600 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 600 [arrowhead = none ];
600 -> 129;

601 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 601 [arrowhead = none ];
601 -> 130;

602 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 602 [arrowhead = none ];
602 -> 131;

603 [label="EVAL with clause\nquot(0, s(X453), s(X454), 0).\nand substitutionT284 -> 0,\nX453 -> s(s(s(0))),\nX454 -> s(s(s(s(s(s(0)))))),\nT286 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
130 -> 603 [arrowhead = none ];
603 -> 132;

604 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
130 -> 604 [arrowhead = none ];
604 -> 133;

605 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 605 [arrowhead = none ];
605 -> 135;

606 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
131 -> 606 [arrowhead = none ];
606 -> 136;

607 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
132 -> 607 [arrowhead = none ];
607 -> 134;

608 [label="EVAL with clause\nquot(s(X471), s(X472), X473, X474) :- quot(X471, X472, X473, X474).\nand substitutionX471 -> T295,\nT284 -> s(T295),\nX472 -> s(s(s(0))),\nX473 -> s(s(s(s(s(s(s(0))))))),\nT286 -> T297,\nX474 -> T297,\nT296 -> T297", fontsize=14, style = filled, fillcolor = lightblue];
135 -> 608 [arrowhead = none ];
608 -> 137;

609 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
135 -> 609 [arrowhead = none ];
609 -> 138;

610 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 610 [arrowhead = none ];
610 -> 177;

611 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
137 -> 611 [arrowhead = none ];
611 -> 139;

612 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
139 -> 612 [arrowhead = none ];
612 -> 140;

613 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
139 -> 613 [arrowhead = none ];
613 -> 141;

614 [label="EVAL with clause\nquot(0, s(X487), s(X488), 0).\nand substitutionT295 -> 0,\nX487 -> s(s(0)),\nX488 -> s(s(s(s(s(s(0)))))),\nT297 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 614 [arrowhead = none ];
614 -> 142;

615 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 615 [arrowhead = none ];
615 -> 143;

616 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
141 -> 616 [arrowhead = none ];
616 -> 145;

617 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
141 -> 617 [arrowhead = none ];
617 -> 146;

618 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 618 [arrowhead = none ];
618 -> 144;

619 [label="EVAL with clause\nquot(s(X505), s(X506), X507, X508) :- quot(X505, X506, X507, X508).\nand substitutionX505 -> T306,\nT295 -> s(T306),\nX506 -> s(s(0)),\nX507 -> s(s(s(s(s(s(s(0))))))),\nT297 -> T308,\nX508 -> T308,\nT307 -> T308", fontsize=14, style = filled, fillcolor = lightblue];
145 -> 619 [arrowhead = none ];
619 -> 147;

620 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
145 -> 620 [arrowhead = none ];
620 -> 148;

621 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
146 -> 621 [arrowhead = none ];
621 -> 176;

622 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
147 -> 622 [arrowhead = none ];
622 -> 149;

623 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 623 [arrowhead = none ];
623 -> 150;

624 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 624 [arrowhead = none ];
624 -> 151;

625 [label="EVAL with clause\nquot(0, s(X521), s(X522), 0).\nand substitutionT306 -> 0,\nX521 -> s(0),\nX522 -> s(s(s(s(s(s(0)))))),\nT308 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 625 [arrowhead = none ];
625 -> 152;

626 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
150 -> 626 [arrowhead = none ];
626 -> 153;

627 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
151 -> 627 [arrowhead = none ];
627 -> 155;

628 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
151 -> 628 [arrowhead = none ];
628 -> 156;

629 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
152 -> 629 [arrowhead = none ];
629 -> 154;

630 [label="EVAL with clause\nquot(s(X539), s(X540), X541, X542) :- quot(X539, X540, X541, X542).\nand substitutionX539 -> T317,\nT306 -> s(T317),\nX540 -> s(0),\nX541 -> s(s(s(s(s(s(s(0))))))),\nT308 -> T319,\nX542 -> T319,\nT318 -> T319", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 630 [arrowhead = none ];
630 -> 157;

631 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 631 [arrowhead = none ];
631 -> 158;

632 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 632 [arrowhead = none ];
632 -> 175;

633 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
157 -> 633 [arrowhead = none ];
633 -> 159;

634 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
159 -> 634 [arrowhead = none ];
634 -> 160;

635 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
159 -> 635 [arrowhead = none ];
635 -> 161;

636 [label="EVAL with clause\nquot(0, s(X555), s(X556), 0).\nand substitutionT317 -> 0,\nX555 -> 0,\nX556 -> s(s(s(s(s(s(0)))))),\nT319 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 636 [arrowhead = none ];
636 -> 162;

637 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
160 -> 637 [arrowhead = none ];
637 -> 163;

638 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
161 -> 638 [arrowhead = none ];
638 -> 165;

639 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
161 -> 639 [arrowhead = none ];
639 -> 166;

640 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
162 -> 640 [arrowhead = none ];
640 -> 164;

641 [label="EVAL with clause\nquot(s(X573), s(X574), X575, X576) :- quot(X573, X574, X575, X576).\nand substitutionX573 -> T328,\nT317 -> s(T328),\nX574 -> 0,\nX575 -> s(s(s(s(s(s(s(0))))))),\nT319 -> T330,\nX576 -> T330,\nT329 -> T330", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 641 [arrowhead = none ];
641 -> 167;

642 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
165 -> 642 [arrowhead = none ];
642 -> 168;

643 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 643 [arrowhead = none ];
643 -> 174;

644 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
167 -> 644 [arrowhead = none ];
644 -> 169;

645 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 645 [arrowhead = none ];
645 -> 170;

646 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
170 -> 646 [arrowhead = none ];
646 -> 171;

647 [label="EVAL with clause\nquot(X593, 0, s(X594), s(X595)) :- quot(X593, s(X594), s(X594), X595).\nand substitutionT328 -> T336,\nX593 -> T336,\nX594 -> s(s(s(s(s(s(0)))))),\nX595 -> T338,\nT330 -> s(T338),\nT337 -> T338", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 647 [arrowhead = none ];
647 -> 172;

648 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 648 [arrowhead = none ];
648 -> 173;

649 [label="INSTANCE with matching:\nT251 -> T336\nT253 -> T338", fontsize=14, style = filled, fillcolor = lightgrey];
172 -> 649 [arrowhead = none , style=dashed];
649 -> 97[style=dashed];

650 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
181 -> 650 [arrowhead = none ];
650 -> 183;

651 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
183 -> 651 [arrowhead = none ];
651 -> 184;

652 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
183 -> 652 [arrowhead = none ];
652 -> 185;

653 [label="EVAL with clause\nquot(0, s(X642), s(X643), 0).\nand substitutionT350 -> 0,\nX642 -> s(s(s(s(s(0))))),\nX643 -> s(s(s(s(s(0))))),\nT352 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 653 [arrowhead = none ];
653 -> 186;

654 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
184 -> 654 [arrowhead = none ];
654 -> 187;

655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
185 -> 655 [arrowhead = none ];
655 -> 189;

656 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
185 -> 656 [arrowhead = none ];
656 -> 190;

657 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
186 -> 657 [arrowhead = none ];
657 -> 188;

658 [label="EVAL with clause\nquot(s(X660), s(X661), X662, X663) :- quot(X660, X661, X662, X663).\nand substitutionX660 -> T361,\nT350 -> s(T361),\nX661 -> s(s(s(s(s(0))))),\nX662 -> s(s(s(s(s(s(0)))))),\nT352 -> T363,\nX663 -> T363,\nT362 -> T363", fontsize=14, style = filled, fillcolor = lightblue];
189 -> 658 [arrowhead = none ];
658 -> 191;

659 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
189 -> 659 [arrowhead = none ];
659 -> 192;

660 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
190 -> 660 [arrowhead = none ];
660 -> 253;

661 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
191 -> 661 [arrowhead = none ];
661 -> 193;

662 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 662 [arrowhead = none ];
662 -> 194;

663 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 663 [arrowhead = none ];
663 -> 195;

664 [label="EVAL with clause\nquot(0, s(X676), s(X677), 0).\nand substitutionT361 -> 0,\nX676 -> s(s(s(s(0)))),\nX677 -> s(s(s(s(s(0))))),\nT363 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
194 -> 664 [arrowhead = none ];
664 -> 196;

665 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
194 -> 665 [arrowhead = none ];
665 -> 197;

666 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
195 -> 666 [arrowhead = none ];
666 -> 199;

667 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
195 -> 667 [arrowhead = none ];
667 -> 200;

668 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 668 [arrowhead = none ];
668 -> 198;

669 [label="EVAL with clause\nquot(s(X694), s(X695), X696, X697) :- quot(X694, X695, X696, X697).\nand substitutionX694 -> T372,\nT361 -> s(T372),\nX695 -> s(s(s(s(0)))),\nX696 -> s(s(s(s(s(s(0)))))),\nT363 -> T374,\nX697 -> T374,\nT373 -> T374", fontsize=14, style = filled, fillcolor = lightblue];
199 -> 669 [arrowhead = none ];
669 -> 201;

670 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 670 [arrowhead = none ];
670 -> 202;

671 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 671 [arrowhead = none ];
671 -> 252;

672 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
201 -> 672 [arrowhead = none ];
672 -> 203;

673 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
203 -> 673 [arrowhead = none ];
673 -> 204;

674 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
203 -> 674 [arrowhead = none ];
674 -> 205;

675 [label="EVAL with clause\nquot(0, s(X710), s(X711), 0).\nand substitutionT372 -> 0,\nX710 -> s(s(s(0))),\nX711 -> s(s(s(s(s(0))))),\nT374 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
204 -> 675 [arrowhead = none ];
675 -> 206;

676 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
204 -> 676 [arrowhead = none ];
676 -> 207;

677 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 677 [arrowhead = none ];
677 -> 209;

678 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 678 [arrowhead = none ];
678 -> 210;

679 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
206 -> 679 [arrowhead = none ];
679 -> 208;

680 [label="EVAL with clause\nquot(s(X728), s(X729), X730, X731) :- quot(X728, X729, X730, X731).\nand substitutionX728 -> T383,\nT372 -> s(T383),\nX729 -> s(s(s(0))),\nX730 -> s(s(s(s(s(s(0)))))),\nT374 -> T385,\nX731 -> T385,\nT384 -> T385", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 680 [arrowhead = none ];
680 -> 211;

681 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
209 -> 681 [arrowhead = none ];
681 -> 212;

682 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 682 [arrowhead = none ];
682 -> 251;

683 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
211 -> 683 [arrowhead = none ];
683 -> 213;

684 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
213 -> 684 [arrowhead = none ];
684 -> 214;

685 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
213 -> 685 [arrowhead = none ];
685 -> 215;

686 [label="EVAL with clause\nquot(0, s(X744), s(X745), 0).\nand substitutionT383 -> 0,\nX744 -> s(s(0)),\nX745 -> s(s(s(s(s(0))))),\nT385 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
214 -> 686 [arrowhead = none ];
686 -> 216;

687 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
214 -> 687 [arrowhead = none ];
687 -> 217;

688 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
215 -> 688 [arrowhead = none ];
688 -> 219;

689 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
215 -> 689 [arrowhead = none ];
689 -> 220;

690 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
216 -> 690 [arrowhead = none ];
690 -> 218;

691 [label="EVAL with clause\nquot(s(X762), s(X763), X764, X765) :- quot(X762, X763, X764, X765).\nand substitutionX762 -> T394,\nT383 -> s(T394),\nX763 -> s(s(0)),\nX764 -> s(s(s(s(s(s(0)))))),\nT385 -> T396,\nX765 -> T396,\nT395 -> T396", fontsize=14, style = filled, fillcolor = lightblue];
219 -> 691 [arrowhead = none ];
691 -> 221;

692 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
219 -> 692 [arrowhead = none ];
692 -> 222;

693 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 693 [arrowhead = none ];
693 -> 250;

694 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
221 -> 694 [arrowhead = none ];
694 -> 223;

695 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
223 -> 695 [arrowhead = none ];
695 -> 224;

696 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
223 -> 696 [arrowhead = none ];
696 -> 225;

697 [label="EVAL with clause\nquot(0, s(X778), s(X779), 0).\nand substitutionT394 -> 0,\nX778 -> s(0),\nX779 -> s(s(s(s(s(0))))),\nT396 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
224 -> 697 [arrowhead = none ];
697 -> 226;

698 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
224 -> 698 [arrowhead = none ];
698 -> 227;

699 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
225 -> 699 [arrowhead = none ];
699 -> 229;

700 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
225 -> 700 [arrowhead = none ];
700 -> 230;

701 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
226 -> 701 [arrowhead = none ];
701 -> 228;

702 [label="EVAL with clause\nquot(s(X796), s(X797), X798, X799) :- quot(X796, X797, X798, X799).\nand substitutionX796 -> T405,\nT394 -> s(T405),\nX797 -> s(0),\nX798 -> s(s(s(s(s(s(0)))))),\nT396 -> T407,\nX799 -> T407,\nT406 -> T407", fontsize=14, style = filled, fillcolor = lightblue];
229 -> 702 [arrowhead = none ];
702 -> 231;

703 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
229 -> 703 [arrowhead = none ];
703 -> 232;

704 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
230 -> 704 [arrowhead = none ];
704 -> 249;

705 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
231 -> 705 [arrowhead = none ];
705 -> 233;

706 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
233 -> 706 [arrowhead = none ];
706 -> 234;

707 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
233 -> 707 [arrowhead = none ];
707 -> 235;

708 [label="EVAL with clause\nquot(0, s(X812), s(X813), 0).\nand substitutionT405 -> 0,\nX812 -> 0,\nX813 -> s(s(s(s(s(0))))),\nT407 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
234 -> 708 [arrowhead = none ];
708 -> 236;

709 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
234 -> 709 [arrowhead = none ];
709 -> 237;

710 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
235 -> 710 [arrowhead = none ];
710 -> 239;

711 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
235 -> 711 [arrowhead = none ];
711 -> 240;

712 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
236 -> 712 [arrowhead = none ];
712 -> 238;

713 [label="EVAL with clause\nquot(s(X830), s(X831), X832, X833) :- quot(X830, X831, X832, X833).\nand substitutionX830 -> T416,\nT405 -> s(T416),\nX831 -> 0,\nX832 -> s(s(s(s(s(s(0)))))),\nT407 -> T418,\nX833 -> T418,\nT417 -> T418", fontsize=14, style = filled, fillcolor = lightblue];
239 -> 713 [arrowhead = none ];
713 -> 241;

714 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
239 -> 714 [arrowhead = none ];
714 -> 242;

715 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
240 -> 715 [arrowhead = none ];
715 -> 248;

716 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
241 -> 716 [arrowhead = none ];
716 -> 243;

717 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
243 -> 717 [arrowhead = none ];
717 -> 244;

718 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
244 -> 718 [arrowhead = none ];
718 -> 245;

719 [label="EVAL with clause\nquot(X850, 0, s(X851), s(X852)) :- quot(X850, s(X851), s(X851), X852).\nand substitutionT416 -> T424,\nX850 -> T424,\nX851 -> s(s(s(s(s(0))))),\nX852 -> T426,\nT418 -> s(T426),\nT425 -> T426", fontsize=14, style = filled, fillcolor = lightblue];
245 -> 719 [arrowhead = none ];
719 -> 246;

720 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
245 -> 720 [arrowhead = none ];
720 -> 247;

721 [label="INSTANCE with matching:\nT350 -> T424\nT352 -> T426", fontsize=14, style = filled, fillcolor = lightgrey];
246 -> 721 [arrowhead = none , style=dashed];
721 -> 181[style=dashed];

722 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
254 -> 722 [arrowhead = none ];
722 -> 256;

723 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
256 -> 723 [arrowhead = none ];
723 -> 257;

724 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
256 -> 724 [arrowhead = none ];
724 -> 258;

725 [label="EVAL with clause\nquot(0, s(X896), s(X897), 0).\nand substitutionT437 -> 0,\nX896 -> s(s(s(s(0)))),\nX897 -> s(s(s(s(0)))),\nT439 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
257 -> 725 [arrowhead = none ];
725 -> 259;

726 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
257 -> 726 [arrowhead = none ];
726 -> 260;

727 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
258 -> 727 [arrowhead = none ];
727 -> 262;

728 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
258 -> 728 [arrowhead = none ];
728 -> 263;

729 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
259 -> 729 [arrowhead = none ];
729 -> 261;

730 [label="EVAL with clause\nquot(s(X914), s(X915), X916, X917) :- quot(X914, X915, X916, X917).\nand substitutionX914 -> T448,\nT437 -> s(T448),\nX915 -> s(s(s(s(0)))),\nX916 -> s(s(s(s(s(0))))),\nT439 -> T450,\nX917 -> T450,\nT449 -> T450", fontsize=14, style = filled, fillcolor = lightblue];
262 -> 730 [arrowhead = none ];
730 -> 264;

731 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
262 -> 731 [arrowhead = none ];
731 -> 265;

732 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 732 [arrowhead = none ];
732 -> 315;

733 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
264 -> 733 [arrowhead = none ];
733 -> 266;

734 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
266 -> 734 [arrowhead = none ];
734 -> 267;

735 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
266 -> 735 [arrowhead = none ];
735 -> 268;

736 [label="EVAL with clause\nquot(0, s(X930), s(X931), 0).\nand substitutionT448 -> 0,\nX930 -> s(s(s(0))),\nX931 -> s(s(s(s(0)))),\nT450 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
267 -> 736 [arrowhead = none ];
736 -> 269;

737 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
267 -> 737 [arrowhead = none ];
737 -> 270;

738 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
268 -> 738 [arrowhead = none ];
738 -> 272;

739 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
268 -> 739 [arrowhead = none ];
739 -> 273;

740 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
269 -> 740 [arrowhead = none ];
740 -> 271;

741 [label="EVAL with clause\nquot(s(X948), s(X949), X950, X951) :- quot(X948, X949, X950, X951).\nand substitutionX948 -> T459,\nT448 -> s(T459),\nX949 -> s(s(s(0))),\nX950 -> s(s(s(s(s(0))))),\nT450 -> T461,\nX951 -> T461,\nT460 -> T461", fontsize=14, style = filled, fillcolor = lightblue];
272 -> 741 [arrowhead = none ];
741 -> 274;

742 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
272 -> 742 [arrowhead = none ];
742 -> 275;

743 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
273 -> 743 [arrowhead = none ];
743 -> 314;

744 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
274 -> 744 [arrowhead = none ];
744 -> 276;

745 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 745 [arrowhead = none ];
745 -> 277;

746 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 746 [arrowhead = none ];
746 -> 278;

747 [label="EVAL with clause\nquot(0, s(X964), s(X965), 0).\nand substitutionT459 -> 0,\nX964 -> s(s(0)),\nX965 -> s(s(s(s(0)))),\nT461 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
277 -> 747 [arrowhead = none ];
747 -> 279;

748 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
277 -> 748 [arrowhead = none ];
748 -> 280;

749 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 749 [arrowhead = none ];
749 -> 282;

750 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
278 -> 750 [arrowhead = none ];
750 -> 283;

751 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
279 -> 751 [arrowhead = none ];
751 -> 281;

752 [label="EVAL with clause\nquot(s(X982), s(X983), X984, X985) :- quot(X982, X983, X984, X985).\nand substitutionX982 -> T470,\nT459 -> s(T470),\nX983 -> s(s(0)),\nX984 -> s(s(s(s(s(0))))),\nT461 -> T472,\nX985 -> T472,\nT471 -> T472", fontsize=14, style = filled, fillcolor = lightblue];
282 -> 752 [arrowhead = none ];
752 -> 284;

753 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
282 -> 753 [arrowhead = none ];
753 -> 285;

754 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
283 -> 754 [arrowhead = none ];
754 -> 313;

755 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
284 -> 755 [arrowhead = none ];
755 -> 286;

756 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
286 -> 756 [arrowhead = none ];
756 -> 287;

757 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
286 -> 757 [arrowhead = none ];
757 -> 288;

758 [label="EVAL with clause\nquot(0, s(X998), s(X999), 0).\nand substitutionT470 -> 0,\nX998 -> s(0),\nX999 -> s(s(s(s(0)))),\nT472 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
287 -> 758 [arrowhead = none ];
758 -> 289;

759 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
287 -> 759 [arrowhead = none ];
759 -> 290;

760 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
288 -> 760 [arrowhead = none ];
760 -> 292;

761 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
288 -> 761 [arrowhead = none ];
761 -> 293;

762 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
289 -> 762 [arrowhead = none ];
762 -> 291;

763 [label="EVAL with clause\nquot(s(X1016), s(X1017), X1018, X1019) :- quot(X1016, X1017, X1018, X1019).\nand substitutionX1016 -> T481,\nT470 -> s(T481),\nX1017 -> s(0),\nX1018 -> s(s(s(s(s(0))))),\nT472 -> T483,\nX1019 -> T483,\nT482 -> T483", fontsize=14, style = filled, fillcolor = lightblue];
292 -> 763 [arrowhead = none ];
763 -> 294;

764 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
292 -> 764 [arrowhead = none ];
764 -> 295;

765 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
293 -> 765 [arrowhead = none ];
765 -> 312;

766 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
294 -> 766 [arrowhead = none ];
766 -> 296;

767 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
296 -> 767 [arrowhead = none ];
767 -> 297;

768 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
296 -> 768 [arrowhead = none ];
768 -> 298;

769 [label="EVAL with clause\nquot(0, s(X1032), s(X1033), 0).\nand substitutionT481 -> 0,\nX1032 -> 0,\nX1033 -> s(s(s(s(0)))),\nT483 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
297 -> 769 [arrowhead = none ];
769 -> 299;

770 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
297 -> 770 [arrowhead = none ];
770 -> 300;

771 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
298 -> 771 [arrowhead = none ];
771 -> 302;

772 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
298 -> 772 [arrowhead = none ];
772 -> 303;

773 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
299 -> 773 [arrowhead = none ];
773 -> 301;

774 [label="EVAL with clause\nquot(s(X1050), s(X1051), X1052, X1053) :- quot(X1050, X1051, X1052, X1053).\nand substitutionX1050 -> T492,\nT481 -> s(T492),\nX1051 -> 0,\nX1052 -> s(s(s(s(s(0))))),\nT483 -> T494,\nX1053 -> T494,\nT493 -> T494", fontsize=14, style = filled, fillcolor = lightblue];
302 -> 774 [arrowhead = none ];
774 -> 304;

775 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
302 -> 775 [arrowhead = none ];
775 -> 305;

776 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
303 -> 776 [arrowhead = none ];
776 -> 311;

777 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
304 -> 777 [arrowhead = none ];
777 -> 306;

778 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
306 -> 778 [arrowhead = none ];
778 -> 307;

779 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
307 -> 779 [arrowhead = none ];
779 -> 308;

780 [label="EVAL with clause\nquot(X1070, 0, s(X1071), s(X1072)) :- quot(X1070, s(X1071), s(X1071), X1072).\nand substitutionT492 -> T500,\nX1070 -> T500,\nX1071 -> s(s(s(s(0)))),\nX1072 -> T502,\nT494 -> s(T502),\nT501 -> T502", fontsize=14, style = filled, fillcolor = lightblue];
308 -> 780 [arrowhead = none ];
780 -> 309;

781 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
308 -> 781 [arrowhead = none ];
781 -> 310;

782 [label="INSTANCE with matching:\nT437 -> T500\nT439 -> T502", fontsize=14, style = filled, fillcolor = lightgrey];
309 -> 782 [arrowhead = none , style=dashed];
782 -> 254[style=dashed];

783 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
316 -> 783 [arrowhead = none ];
783 -> 318;

784 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
318 -> 784 [arrowhead = none ];
784 -> 319;

785 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
318 -> 785 [arrowhead = none ];
785 -> 320;

786 [label="EVAL with clause\nquot(0, s(X1113), s(X1114), 0).\nand substitutionT512 -> 0,\nX1113 -> s(s(s(0))),\nX1114 -> s(s(s(0))),\nT514 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
319 -> 786 [arrowhead = none ];
786 -> 321;

787 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
319 -> 787 [arrowhead = none ];
787 -> 322;

788 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
320 -> 788 [arrowhead = none ];
788 -> 324;

789 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
320 -> 789 [arrowhead = none ];
789 -> 325;

790 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
321 -> 790 [arrowhead = none ];
790 -> 323;

791 [label="EVAL with clause\nquot(s(X1131), s(X1132), X1133, X1134) :- quot(X1131, X1132, X1133, X1134).\nand substitutionX1131 -> T523,\nT512 -> s(T523),\nX1132 -> s(s(s(0))),\nX1133 -> s(s(s(s(0)))),\nT514 -> T525,\nX1134 -> T525,\nT524 -> T525", fontsize=14, style = filled, fillcolor = lightblue];
324 -> 791 [arrowhead = none ];
791 -> 326;

792 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
324 -> 792 [arrowhead = none ];
792 -> 327;

793 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
325 -> 793 [arrowhead = none ];
793 -> 366;

794 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
326 -> 794 [arrowhead = none ];
794 -> 328;

795 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 795 [arrowhead = none ];
795 -> 329;

796 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
328 -> 796 [arrowhead = none ];
796 -> 330;

797 [label="EVAL with clause\nquot(0, s(X1147), s(X1148), 0).\nand substitutionT523 -> 0,\nX1147 -> s(s(0)),\nX1148 -> s(s(s(0))),\nT525 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
329 -> 797 [arrowhead = none ];
797 -> 331;

798 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
329 -> 798 [arrowhead = none ];
798 -> 332;

799 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
330 -> 799 [arrowhead = none ];
799 -> 334;

800 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
330 -> 800 [arrowhead = none ];
800 -> 335;

801 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
331 -> 801 [arrowhead = none ];
801 -> 333;

802 [label="EVAL with clause\nquot(s(X1165), s(X1166), X1167, X1168) :- quot(X1165, X1166, X1167, X1168).\nand substitutionX1165 -> T534,\nT523 -> s(T534),\nX1166 -> s(s(0)),\nX1167 -> s(s(s(s(0)))),\nT525 -> T536,\nX1168 -> T536,\nT535 -> T536", fontsize=14, style = filled, fillcolor = lightblue];
334 -> 802 [arrowhead = none ];
802 -> 336;

803 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
334 -> 803 [arrowhead = none ];
803 -> 337;

804 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
335 -> 804 [arrowhead = none ];
804 -> 365;

805 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
336 -> 805 [arrowhead = none ];
805 -> 338;

806 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
338 -> 806 [arrowhead = none ];
806 -> 339;

807 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
338 -> 807 [arrowhead = none ];
807 -> 340;

808 [label="EVAL with clause\nquot(0, s(X1181), s(X1182), 0).\nand substitutionT534 -> 0,\nX1181 -> s(0),\nX1182 -> s(s(s(0))),\nT536 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
339 -> 808 [arrowhead = none ];
808 -> 341;

809 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
339 -> 809 [arrowhead = none ];
809 -> 342;

810 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
340 -> 810 [arrowhead = none ];
810 -> 344;

811 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
340 -> 811 [arrowhead = none ];
811 -> 345;

812 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
341 -> 812 [arrowhead = none ];
812 -> 343;

813 [label="EVAL with clause\nquot(s(X1199), s(X1200), X1201, X1202) :- quot(X1199, X1200, X1201, X1202).\nand substitutionX1199 -> T545,\nT534 -> s(T545),\nX1200 -> s(0),\nX1201 -> s(s(s(s(0)))),\nT536 -> T547,\nX1202 -> T547,\nT546 -> T547", fontsize=14, style = filled, fillcolor = lightblue];
344 -> 813 [arrowhead = none ];
813 -> 346;

814 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
344 -> 814 [arrowhead = none ];
814 -> 347;

815 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
345 -> 815 [arrowhead = none ];
815 -> 364;

816 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
346 -> 816 [arrowhead = none ];
816 -> 348;

817 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
348 -> 817 [arrowhead = none ];
817 -> 349;

818 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
348 -> 818 [arrowhead = none ];
818 -> 350;

819 [label="EVAL with clause\nquot(0, s(X1215), s(X1216), 0).\nand substitutionT545 -> 0,\nX1215 -> 0,\nX1216 -> s(s(s(0))),\nT547 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
349 -> 819 [arrowhead = none ];
819 -> 351;

820 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
349 -> 820 [arrowhead = none ];
820 -> 352;

821 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
350 -> 821 [arrowhead = none ];
821 -> 354;

822 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
350 -> 822 [arrowhead = none ];
822 -> 355;

823 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
351 -> 823 [arrowhead = none ];
823 -> 353;

824 [label="EVAL with clause\nquot(s(X1233), s(X1234), X1235, X1236) :- quot(X1233, X1234, X1235, X1236).\nand substitutionX1233 -> T556,\nT545 -> s(T556),\nX1234 -> 0,\nX1235 -> s(s(s(s(0)))),\nT547 -> T558,\nX1236 -> T558,\nT557 -> T558", fontsize=14, style = filled, fillcolor = lightblue];
354 -> 824 [arrowhead = none ];
824 -> 356;

825 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
354 -> 825 [arrowhead = none ];
825 -> 357;

826 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
355 -> 826 [arrowhead = none ];
826 -> 363;

827 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
356 -> 827 [arrowhead = none ];
827 -> 358;

828 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
358 -> 828 [arrowhead = none ];
828 -> 359;

829 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
359 -> 829 [arrowhead = none ];
829 -> 360;

830 [label="EVAL with clause\nquot(X1253, 0, s(X1254), s(X1255)) :- quot(X1253, s(X1254), s(X1254), X1255).\nand substitutionT556 -> T564,\nX1253 -> T564,\nX1254 -> s(s(s(0))),\nX1255 -> T566,\nT558 -> s(T566),\nT565 -> T566", fontsize=14, style = filled, fillcolor = lightblue];
360 -> 830 [arrowhead = none ];
830 -> 361;

831 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
360 -> 831 [arrowhead = none ];
831 -> 362;

832 [label="INSTANCE with matching:\nT512 -> T564\nT514 -> T566", fontsize=14, style = filled, fillcolor = lightgrey];
361 -> 832 [arrowhead = none , style=dashed];
832 -> 316[style=dashed];

833 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
367 -> 833 [arrowhead = none ];
833 -> 369;

834 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
369 -> 834 [arrowhead = none ];
834 -> 370;

835 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
369 -> 835 [arrowhead = none ];
835 -> 371;

836 [label="EVAL with clause\nquot(0, s(X1293), s(X1294), 0).\nand substitutionT575 -> 0,\nX1293 -> s(s(0)),\nX1294 -> s(s(0)),\nT577 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
370 -> 836 [arrowhead = none ];
836 -> 372;

837 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
370 -> 837 [arrowhead = none ];
837 -> 373;

838 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
371 -> 838 [arrowhead = none ];
838 -> 375;

839 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
371 -> 839 [arrowhead = none ];
839 -> 376;

840 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
372 -> 840 [arrowhead = none ];
840 -> 374;

841 [label="EVAL with clause\nquot(s(X1311), s(X1312), X1313, X1314) :- quot(X1311, X1312, X1313, X1314).\nand substitutionX1311 -> T586,\nT575 -> s(T586),\nX1312 -> s(s(0)),\nX1313 -> s(s(s(0))),\nT577 -> T588,\nX1314 -> T588,\nT587 -> T588", fontsize=14, style = filled, fillcolor = lightblue];
375 -> 841 [arrowhead = none ];
841 -> 377;

842 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
375 -> 842 [arrowhead = none ];
842 -> 378;

843 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
376 -> 843 [arrowhead = none ];
843 -> 406;

844 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
377 -> 844 [arrowhead = none ];
844 -> 379;

845 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
379 -> 845 [arrowhead = none ];
845 -> 380;

846 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
379 -> 846 [arrowhead = none ];
846 -> 381;

847 [label="EVAL with clause\nquot(0, s(X1327), s(X1328), 0).\nand substitutionT586 -> 0,\nX1327 -> s(0),\nX1328 -> s(s(0)),\nT588 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
380 -> 847 [arrowhead = none ];
847 -> 382;

848 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
380 -> 848 [arrowhead = none ];
848 -> 383;

849 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
381 -> 849 [arrowhead = none ];
849 -> 385;

850 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
381 -> 850 [arrowhead = none ];
850 -> 386;

851 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
382 -> 851 [arrowhead = none ];
851 -> 384;

852 [label="EVAL with clause\nquot(s(X1345), s(X1346), X1347, X1348) :- quot(X1345, X1346, X1347, X1348).\nand substitutionX1345 -> T597,\nT586 -> s(T597),\nX1346 -> s(0),\nX1347 -> s(s(s(0))),\nT588 -> T599,\nX1348 -> T599,\nT598 -> T599", fontsize=14, style = filled, fillcolor = lightblue];
385 -> 852 [arrowhead = none ];
852 -> 387;

853 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
385 -> 853 [arrowhead = none ];
853 -> 388;

854 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
386 -> 854 [arrowhead = none ];
854 -> 405;

855 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
387 -> 855 [arrowhead = none ];
855 -> 389;

856 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
389 -> 856 [arrowhead = none ];
856 -> 390;

857 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
389 -> 857 [arrowhead = none ];
857 -> 391;

858 [label="EVAL with clause\nquot(0, s(X1361), s(X1362), 0).\nand substitutionT597 -> 0,\nX1361 -> 0,\nX1362 -> s(s(0)),\nT599 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
390 -> 858 [arrowhead = none ];
858 -> 392;

859 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
390 -> 859 [arrowhead = none ];
859 -> 393;

860 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
391 -> 860 [arrowhead = none ];
860 -> 395;

861 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
391 -> 861 [arrowhead = none ];
861 -> 396;

862 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
392 -> 862 [arrowhead = none ];
862 -> 394;

863 [label="EVAL with clause\nquot(s(X1379), s(X1380), X1381, X1382) :- quot(X1379, X1380, X1381, X1382).\nand substitutionX1379 -> T608,\nT597 -> s(T608),\nX1380 -> 0,\nX1381 -> s(s(s(0))),\nT599 -> T610,\nX1382 -> T610,\nT609 -> T610", fontsize=14, style = filled, fillcolor = lightblue];
395 -> 863 [arrowhead = none ];
863 -> 397;

864 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
395 -> 864 [arrowhead = none ];
864 -> 398;

865 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
396 -> 865 [arrowhead = none ];
865 -> 404;

866 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
397 -> 866 [arrowhead = none ];
866 -> 399;

867 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
399 -> 867 [arrowhead = none ];
867 -> 400;

868 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
400 -> 868 [arrowhead = none ];
868 -> 401;

869 [label="EVAL with clause\nquot(X1399, 0, s(X1400), s(X1401)) :- quot(X1399, s(X1400), s(X1400), X1401).\nand substitutionT608 -> T616,\nX1399 -> T616,\nX1400 -> s(s(0)),\nX1401 -> T618,\nT610 -> s(T618),\nT617 -> T618", fontsize=14, style = filled, fillcolor = lightblue];
401 -> 869 [arrowhead = none ];
869 -> 402;

870 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
401 -> 870 [arrowhead = none ];
870 -> 403;

871 [label="INSTANCE with matching:\nT575 -> T616\nT577 -> T618", fontsize=14, style = filled, fillcolor = lightgrey];
402 -> 871 [arrowhead = none , style=dashed];
871 -> 367[style=dashed];

872 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
407 -> 872 [arrowhead = none ];
872 -> 409;

873 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
409 -> 873 [arrowhead = none ];
873 -> 410;

874 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
409 -> 874 [arrowhead = none ];
874 -> 411;

875 [label="EVAL with clause\nquot(0, s(X1436), s(X1437), 0).\nand substitutionT626 -> 0,\nX1436 -> s(0),\nX1437 -> s(0),\nT628 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
410 -> 875 [arrowhead = none ];
875 -> 412;

876 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
410 -> 876 [arrowhead = none ];
876 -> 413;

877 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
411 -> 877 [arrowhead = none ];
877 -> 415;

878 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
411 -> 878 [arrowhead = none ];
878 -> 416;

879 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
412 -> 879 [arrowhead = none ];
879 -> 414;

880 [label="EVAL with clause\nquot(s(X1454), s(X1455), X1456, X1457) :- quot(X1454, X1455, X1456, X1457).\nand substitutionX1454 -> T637,\nT626 -> s(T637),\nX1455 -> s(0),\nX1456 -> s(s(0)),\nT628 -> T639,\nX1457 -> T639,\nT638 -> T639", fontsize=14, style = filled, fillcolor = lightblue];
415 -> 880 [arrowhead = none ];
880 -> 417;

881 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
415 -> 881 [arrowhead = none ];
881 -> 418;

882 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
416 -> 882 [arrowhead = none ];
882 -> 435;

883 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
417 -> 883 [arrowhead = none ];
883 -> 419;

884 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
419 -> 884 [arrowhead = none ];
884 -> 420;

885 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
419 -> 885 [arrowhead = none ];
885 -> 421;

886 [label="EVAL with clause\nquot(0, s(X1470), s(X1471), 0).\nand substitutionT637 -> 0,\nX1470 -> 0,\nX1471 -> s(0),\nT639 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
420 -> 886 [arrowhead = none ];
886 -> 422;

887 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
420 -> 887 [arrowhead = none ];
887 -> 423;

888 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
421 -> 888 [arrowhead = none ];
888 -> 425;

889 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
421 -> 889 [arrowhead = none ];
889 -> 426;

890 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
422 -> 890 [arrowhead = none ];
890 -> 424;

891 [label="EVAL with clause\nquot(s(X1488), s(X1489), X1490, X1491) :- quot(X1488, X1489, X1490, X1491).\nand substitutionX1488 -> T648,\nT637 -> s(T648),\nX1489 -> 0,\nX1490 -> s(s(0)),\nT639 -> T650,\nX1491 -> T650,\nT649 -> T650", fontsize=14, style = filled, fillcolor = lightblue];
425 -> 891 [arrowhead = none ];
891 -> 427;

892 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
425 -> 892 [arrowhead = none ];
892 -> 428;

893 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
426 -> 893 [arrowhead = none ];
893 -> 434;

894 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
427 -> 894 [arrowhead = none ];
894 -> 429;

895 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
429 -> 895 [arrowhead = none ];
895 -> 430;

896 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
430 -> 896 [arrowhead = none ];
896 -> 431;

897 [label="EVAL with clause\nquot(X1508, 0, s(X1509), s(X1510)) :- quot(X1508, s(X1509), s(X1509), X1510).\nand substitutionT648 -> T656,\nX1508 -> T656,\nX1509 -> s(0),\nX1510 -> T658,\nT650 -> s(T658),\nT657 -> T658", fontsize=14, style = filled, fillcolor = lightblue];
431 -> 897 [arrowhead = none ];
897 -> 432;

898 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
431 -> 898 [arrowhead = none ];
898 -> 433;

899 [label="INSTANCE with matching:\nT626 -> T656\nT628 -> T658", fontsize=14, style = filled, fillcolor = lightgrey];
432 -> 899 [arrowhead = none , style=dashed];
899 -> 407[style=dashed];

900 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
436 -> 900 [arrowhead = none ];
900 -> 438;

901 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
438 -> 901 [arrowhead = none ];
901 -> 439;

902 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
438 -> 902 [arrowhead = none ];
902 -> 440;

903 [label="EVAL with clause\nquot(0, s(X1542), s(X1543), 0).\nand substitutionT665 -> 0,\nX1542 -> 0,\nX1543 -> 0,\nT667 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
439 -> 903 [arrowhead = none ];
903 -> 441;

904 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
439 -> 904 [arrowhead = none ];
904 -> 442;

905 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
440 -> 905 [arrowhead = none ];
905 -> 444;

906 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
440 -> 906 [arrowhead = none ];
906 -> 445;

907 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
441 -> 907 [arrowhead = none ];
907 -> 443;

908 [label="EVAL with clause\nquot(s(X1560), s(X1561), X1562, X1563) :- quot(X1560, X1561, X1562, X1563).\nand substitutionX1560 -> T676,\nT665 -> s(T676),\nX1561 -> 0,\nX1562 -> s(0),\nT667 -> T678,\nX1563 -> T678,\nT677 -> T678", fontsize=14, style = filled, fillcolor = lightblue];
444 -> 908 [arrowhead = none ];
908 -> 446;

909 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
444 -> 909 [arrowhead = none ];
909 -> 447;

910 [label="BACKTRACK\nfor clause: quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
445 -> 910 [arrowhead = none ];
910 -> 453;

911 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
446 -> 911 [arrowhead = none ];
911 -> 448;

912 [label="BACKTRACK\nfor clause: quot(0, s(Y), s(Z), 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
448 -> 912 [arrowhead = none ];
912 -> 449;

913 [label="BACKTRACK\nfor clause: quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
449 -> 913 [arrowhead = none ];
913 -> 450;

914 [label="EVAL with clause\nquot(X1580, 0, s(X1581), s(X1582)) :- quot(X1580, s(X1581), s(X1581), X1582).\nand substitutionT676 -> T684,\nX1580 -> T684,\nX1581 -> 0,\nX1582 -> T686,\nT678 -> s(T686),\nT685 -> T686", fontsize=14, style = filled, fillcolor = lightblue];
450 -> 914 [arrowhead = none ];
914 -> 451;

915 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
450 -> 915 [arrowhead = none ];
915 -> 452;

916 [label="INSTANCE with matching:\nT665 -> T684\nT667 -> T686", fontsize=14, style = filled, fillcolor = lightgrey];
451 -> 916 [arrowhead = none , style=dashed];
916 -> 436[style=dashed];

}

(2) Obligation:

Clauses:

quotA(0, s(T208), T209, 0).
quotA(s(T226), s(T227), T228, T230) :- quotA(T226, T227, T228, T230).
quotA(T241, 0, T242, s(T244)) :- quotB(T241, s(T242), T244).
quotB(0, s(T15), 0).
quotB(s(0), s(s(T38)), 0).
quotB(s(s(0)), s(s(s(T61))), 0).
quotB(s(s(s(0))), s(s(s(s(T84)))), 0).
quotB(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0).
quotB(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0).
quotB(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0).
quotB(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0).
quotB(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) :- quotA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192).
quotB(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) :- quotC(T251, T253).
quotB(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) :- quotD(T350, T352).
quotB(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) :- quotE(T437, T439).
quotB(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) :- quotF(T512, T514).
quotB(s(s(s(T575))), s(s(s(0))), s(T577)) :- quotG(T575, T577).
quotB(s(s(T626)), s(s(0)), s(T628)) :- quotH(T626, T628).
quotB(s(T665), s(0), s(T667)) :- quotI(T665, T667).
quotC(0, 0).
quotC(s(0), 0).
quotC(s(s(0)), 0).
quotC(s(s(s(0))), 0).
quotC(s(s(s(s(0)))), 0).
quotC(s(s(s(s(s(0))))), 0).
quotC(s(s(s(s(s(s(0)))))), 0).
quotC(s(s(s(s(s(s(s(T336))))))), s(T338)) :- quotC(T336, T338).
quotD(0, 0).
quotD(s(0), 0).
quotD(s(s(0)), 0).
quotD(s(s(s(0))), 0).
quotD(s(s(s(s(0)))), 0).
quotD(s(s(s(s(s(0))))), 0).
quotD(s(s(s(s(s(s(T424)))))), s(T426)) :- quotD(T424, T426).
quotE(0, 0).
quotE(s(0), 0).
quotE(s(s(0)), 0).
quotE(s(s(s(0))), 0).
quotE(s(s(s(s(0)))), 0).
quotE(s(s(s(s(s(T500))))), s(T502)) :- quotE(T500, T502).
quotF(0, 0).
quotF(s(0), 0).
quotF(s(s(0)), 0).
quotF(s(s(s(0))), 0).
quotF(s(s(s(s(T564)))), s(T566)) :- quotF(T564, T566).
quotG(0, 0).
quotG(s(0), 0).
quotG(s(s(0)), 0).
quotG(s(s(s(T616))), s(T618)) :- quotG(T616, T618).
quotH(0, 0).
quotH(s(0), 0).
quotH(s(s(T656)), s(T658)) :- quotH(T656, T658).
quotI(0, 0).
quotI(s(T684), s(T686)) :- quotI(T684, T686).
divJ(T7, T8, T10) :- quotB(T7, T8, T10).

Query: divJ(g,g,a)

(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:
divJ_in: (b,b,f)
quotB_in: (b,b,f)
quotA_in: (b,b,b,f)
quotC_in: (b,f)
quotD_in: (b,f)
quotE_in: (b,f)
quotF_in: (b,f)
quotG_in: (b,f)
quotH_in: (b,f)
quotI_in: (b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(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:

DIVJ_IN_GGA(T7, T8, T10) → U18_GGA(T7, T8, T10, quotB_in_gga(T7, T8, T10))
DIVJ_IN_GGA(T7, T8, T10) → QUOTB_IN_GGA(T7, T8, T10)
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_GGA(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTA_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTA_IN_GGGA(s(T226), s(T227), T228, T230) → U1_GGGA(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
QUOTA_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTA_IN_GGGA(T226, T227, T228, T230)
QUOTA_IN_GGGA(T241, 0, T242, s(T244)) → U2_GGGA(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
QUOTA_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_GGA(T251, T253, quotC_in_ga(T251, T253))
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → QUOTC_IN_GA(T251, T253)
QUOTC_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_GA(T336, T338, quotC_in_ga(T336, T338))
QUOTC_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTC_IN_GA(T336, T338)
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_GGA(T350, T352, quotD_in_ga(T350, T352))
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → QUOTD_IN_GA(T350, T352)
QUOTD_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → U12_GA(T424, T426, quotD_in_ga(T424, T426))
QUOTD_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTD_IN_GA(T424, T426)
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_GGA(T437, T439, quotE_in_ga(T437, T439))
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → QUOTE_IN_GA(T437, T439)
QUOTE_IN_GA(s(s(s(s(s(T500))))), s(T502)) → U13_GA(T500, T502, quotE_in_ga(T500, T502))
QUOTE_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTE_IN_GA(T500, T502)
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_GGA(T512, T514, quotF_in_ga(T512, T514))
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → QUOTF_IN_GA(T512, T514)
QUOTF_IN_GA(s(s(s(s(T564)))), s(T566)) → U14_GA(T564, T566, quotF_in_ga(T564, T566))
QUOTF_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTF_IN_GA(T564, T566)
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_GGA(T575, T577, quotG_in_ga(T575, T577))
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → QUOTG_IN_GA(T575, T577)
QUOTG_IN_GA(s(s(s(T616))), s(T618)) → U15_GA(T616, T618, quotG_in_ga(T616, T618))
QUOTG_IN_GA(s(s(s(T616))), s(T618)) → QUOTG_IN_GA(T616, T618)
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → U9_GGA(T626, T628, quotH_in_ga(T626, T628))
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → QUOTH_IN_GA(T626, T628)
QUOTH_IN_GA(s(s(T656)), s(T658)) → U16_GA(T656, T658, quotH_in_ga(T656, T658))
QUOTH_IN_GA(s(s(T656)), s(T658)) → QUOTH_IN_GA(T656, T658)
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → U10_GGA(T665, T667, quotI_in_ga(T665, T667))
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → QUOTI_IN_GA(T665, T667)
QUOTI_IN_GA(s(T684), s(T686)) → U17_GA(T684, T686, quotI_in_ga(T684, T686))
QUOTI_IN_GA(s(T684), s(T686)) → QUOTI_IN_GA(T684, T686)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

The argument filtering Pi contains the following mapping:
divJ_in_gga(x1, x2, x3) = divJ_in_gga(x1, x2)
U18_gga(x1, x2, x3, x4) = U18_gga(x4)
quotB_in_gga(x1, x2, x3) = quotB_in_gga(x1, x2)
0 = 0
s(x1) = s(x1)
quotB_out_gga(x1, x2, x3) = quotB_out_gga(x3)
U3_gga(x1, x2, x3, x4) = U3_gga(x4)
quotA_in_ggga(x1, x2, x3, x4) = quotA_in_ggga(x1, x2, x3)
quotA_out_ggga(x1, x2, x3, x4) = quotA_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5) = U1_ggga(x5)
U2_ggga(x1, x2, x3, x4) = U2_ggga(x4)
U4_gga(x1, x2, x3) = U4_gga(x3)
quotC_in_ga(x1, x2) = quotC_in_ga(x1)
quotC_out_ga(x1, x2) = quotC_out_ga(x2)
U11_ga(x1, x2, x3) = U11_ga(x3)
U5_gga(x1, x2, x3) = U5_gga(x3)
quotD_in_ga(x1, x2) = quotD_in_ga(x1)
quotD_out_ga(x1, x2) = quotD_out_ga(x2)
U12_ga(x1, x2, x3) = U12_ga(x3)
U6_gga(x1, x2, x3) = U6_gga(x3)
quotE_in_ga(x1, x2) = quotE_in_ga(x1)
quotE_out_ga(x1, x2) = quotE_out_ga(x2)
U13_ga(x1, x2, x3) = U13_ga(x3)
U7_gga(x1, x2, x3) = U7_gga(x3)
quotF_in_ga(x1, x2) = quotF_in_ga(x1)
quotF_out_ga(x1, x2) = quotF_out_ga(x2)
U14_ga(x1, x2, x3) = U14_ga(x3)
U8_gga(x1, x2, x3) = U8_gga(x3)
quotG_in_ga(x1, x2) = quotG_in_ga(x1)
quotG_out_ga(x1, x2) = quotG_out_ga(x2)
U15_ga(x1, x2, x3) = U15_ga(x3)
U9_gga(x1, x2, x3) = U9_gga(x3)
quotH_in_ga(x1, x2) = quotH_in_ga(x1)
quotH_out_ga(x1, x2) = quotH_out_ga(x2)
U16_ga(x1, x2, x3) = U16_ga(x3)
U10_gga(x1, x2, x3) = U10_gga(x3)
quotI_in_ga(x1, x2) = quotI_in_ga(x1)
quotI_out_ga(x1, x2) = quotI_out_ga(x2)
U17_ga(x1, x2, x3) = U17_ga(x3)
divJ_out_gga(x1, x2, x3) = divJ_out_gga(x3)
DIVJ_IN_GGA(x1, x2, x3) = DIVJ_IN_GGA(x1, x2)
U18_GGA(x1, x2, x3, x4) = U18_GGA(x4)
QUOTB_IN_GGA(x1, x2, x3) = QUOTB_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4) = U3_GGA(x4)
QUOTA_IN_GGGA(x1, x2, x3, x4) = QUOTA_IN_GGGA(x1, x2, x3)
U1_GGGA(x1, x2, x3, x4, x5) = U1_GGGA(x5)
U2_GGGA(x1, x2, x3, x4) = U2_GGGA(x4)
U4_GGA(x1, x2, x3) = U4_GGA(x3)
QUOTC_IN_GA(x1, x2) = QUOTC_IN_GA(x1)
U11_GA(x1, x2, x3) = U11_GA(x3)
U5_GGA(x1, x2, x3) = U5_GGA(x3)
QUOTD_IN_GA(x1, x2) = QUOTD_IN_GA(x1)
U12_GA(x1, x2, x3) = U12_GA(x3)
U6_GGA(x1, x2, x3) = U6_GGA(x3)
QUOTE_IN_GA(x1, x2) = QUOTE_IN_GA(x1)
U13_GA(x1, x2, x3) = U13_GA(x3)
U7_GGA(x1, x2, x3) = U7_GGA(x3)
QUOTF_IN_GA(x1, x2) = QUOTF_IN_GA(x1)
U14_GA(x1, x2, x3) = U14_GA(x3)
U8_GGA(x1, x2, x3) = U8_GGA(x3)
QUOTG_IN_GA(x1, x2) = QUOTG_IN_GA(x1)
U15_GA(x1, x2, x3) = U15_GA(x3)
U9_GGA(x1, x2, x3) = U9_GGA(x3)
QUOTH_IN_GA(x1, x2) = QUOTH_IN_GA(x1)
U16_GA(x1, x2, x3) = U16_GA(x3)
U10_GGA(x1, x2, x3) = U10_GGA(x3)
QUOTI_IN_GA(x1, x2) = QUOTI_IN_GA(x1)
U17_GA(x1, x2, x3) = U17_GA(x3)

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

(6) Obligation:

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

DIVJ_IN_GGA(T7, T8, T10) → U18_GGA(T7, T8, T10, quotB_in_gga(T7, T8, T10))
DIVJ_IN_GGA(T7, T8, T10) → QUOTB_IN_GGA(T7, T8, T10)
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_GGA(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTA_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTA_IN_GGGA(s(T226), s(T227), T228, T230) → U1_GGGA(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
QUOTA_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTA_IN_GGGA(T226, T227, T228, T230)
QUOTA_IN_GGGA(T241, 0, T242, s(T244)) → U2_GGGA(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
QUOTA_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_GGA(T251, T253, quotC_in_ga(T251, T253))
QUOTB_IN_GGA(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → QUOTC_IN_GA(T251, T253)
QUOTC_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_GA(T336, T338, quotC_in_ga(T336, T338))
QUOTC_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTC_IN_GA(T336, T338)
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_GGA(T350, T352, quotD_in_ga(T350, T352))
QUOTB_IN_GGA(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → QUOTD_IN_GA(T350, T352)
QUOTD_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → U12_GA(T424, T426, quotD_in_ga(T424, T426))
QUOTD_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTD_IN_GA(T424, T426)
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_GGA(T437, T439, quotE_in_ga(T437, T439))
QUOTB_IN_GGA(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → QUOTE_IN_GA(T437, T439)
QUOTE_IN_GA(s(s(s(s(s(T500))))), s(T502)) → U13_GA(T500, T502, quotE_in_ga(T500, T502))
QUOTE_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTE_IN_GA(T500, T502)
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_GGA(T512, T514, quotF_in_ga(T512, T514))
QUOTB_IN_GGA(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → QUOTF_IN_GA(T512, T514)
QUOTF_IN_GA(s(s(s(s(T564)))), s(T566)) → U14_GA(T564, T566, quotF_in_ga(T564, T566))
QUOTF_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTF_IN_GA(T564, T566)
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_GGA(T575, T577, quotG_in_ga(T575, T577))
QUOTB_IN_GGA(s(s(s(T575))), s(s(s(0))), s(T577)) → QUOTG_IN_GA(T575, T577)
QUOTG_IN_GA(s(s(s(T616))), s(T618)) → U15_GA(T616, T618, quotG_in_ga(T616, T618))
QUOTG_IN_GA(s(s(s(T616))), s(T618)) → QUOTG_IN_GA(T616, T618)
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → U9_GGA(T626, T628, quotH_in_ga(T626, T628))
QUOTB_IN_GGA(s(s(T626)), s(s(0)), s(T628)) → QUOTH_IN_GA(T626, T628)
QUOTH_IN_GA(s(s(T656)), s(T658)) → U16_GA(T656, T658, quotH_in_ga(T656, T658))
QUOTH_IN_GA(s(s(T656)), s(T658)) → QUOTH_IN_GA(T656, T658)
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → U10_GGA(T665, T667, quotI_in_ga(T665, T667))
QUOTB_IN_GGA(s(T665), s(0), s(T667)) → QUOTI_IN_GA(T665, T667)
QUOTI_IN_GA(s(T684), s(T686)) → U17_GA(T684, T686, quotI_in_ga(T684, T686))
QUOTI_IN_GA(s(T684), s(T686)) → QUOTI_IN_GA(T684, T686)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 26 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

QUOTI_IN_GA(s(T684), s(T686)) → QUOTI_IN_GA(T684, T686)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(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:

QUOTI_IN_GA(s(T684), s(T686)) → QUOTI_IN_GA(T684, T686)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTI_IN_GA(x1, x2) = QUOTI_IN_GA(x1)

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

(12) PiDPToQDPProof (SOUND 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:

QUOTI_IN_GA(s(T684)) → QUOTI_IN_GA(T684)

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:

QUOTI_IN_GA(s(T684)) → QUOTI_IN_GA(T684)
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

QUOTH_IN_GA(s(s(T656)), s(T658)) → QUOTH_IN_GA(T656, T658)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(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:

QUOTH_IN_GA(s(s(T656)), s(T658)) → QUOTH_IN_GA(T656, T658)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTH_IN_GA(x1, x2) = QUOTH_IN_GA(x1)

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

QUOTH_IN_GA(s(s(T656))) → QUOTH_IN_GA(T656)

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:

QUOTH_IN_GA(s(s(T656))) → QUOTH_IN_GA(T656)
The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

QUOTG_IN_GA(s(s(s(T616))), s(T618)) → QUOTG_IN_GA(T616, T618)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

QUOTG_IN_GA(s(s(s(T616))), s(T618)) → QUOTG_IN_GA(T616, T618)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTG_IN_GA(x1, x2) = QUOTG_IN_GA(x1)

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

(26) PiDPToQDPProof (SOUND transformation)

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

(27) Obligation:

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

QUOTG_IN_GA(s(s(s(T616)))) → QUOTG_IN_GA(T616)

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

(28) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

QUOTG_IN_GA(s(s(s(T616)))) → QUOTG_IN_GA(T616)
The graph contains the following edges 1 > 1

(29) YES

(30) Obligation:

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

QUOTF_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTF_IN_GA(T564, T566)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(31) UsableRulesProof (EQUIVALENT transformation)

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

(32) Obligation:

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

QUOTF_IN_GA(s(s(s(s(T564)))), s(T566)) → QUOTF_IN_GA(T564, T566)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTF_IN_GA(x1, x2) = QUOTF_IN_GA(x1)

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

(33) PiDPToQDPProof (SOUND transformation)

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

(34) Obligation:

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

QUOTF_IN_GA(s(s(s(s(T564))))) → QUOTF_IN_GA(T564)

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

(35) 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:

QUOTF_IN_GA(s(s(s(s(T564))))) → QUOTF_IN_GA(T564)
The graph contains the following edges 1 > 1

(36) YES

(37) Obligation:

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

QUOTE_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTE_IN_GA(T500, T502)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(38) UsableRulesProof (EQUIVALENT transformation)

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

(39) Obligation:

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

QUOTE_IN_GA(s(s(s(s(s(T500))))), s(T502)) → QUOTE_IN_GA(T500, T502)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTE_IN_GA(x1, x2) = QUOTE_IN_GA(x1)

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

(40) PiDPToQDPProof (SOUND transformation)

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

(41) Obligation:

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

QUOTE_IN_GA(s(s(s(s(s(T500)))))) → QUOTE_IN_GA(T500)

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

(42) 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:

QUOTE_IN_GA(s(s(s(s(s(T500)))))) → QUOTE_IN_GA(T500)
The graph contains the following edges 1 > 1

(43) YES

(44) Obligation:

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

QUOTD_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTD_IN_GA(T424, T426)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(45) UsableRulesProof (EQUIVALENT transformation)

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

(46) Obligation:

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

QUOTD_IN_GA(s(s(s(s(s(s(T424)))))), s(T426)) → QUOTD_IN_GA(T424, T426)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTD_IN_GA(x1, x2) = QUOTD_IN_GA(x1)

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

(47) PiDPToQDPProof (SOUND transformation)

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

(48) Obligation:

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

QUOTD_IN_GA(s(s(s(s(s(s(T424))))))) → QUOTD_IN_GA(T424)

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

(49) 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:

QUOTD_IN_GA(s(s(s(s(s(s(T424))))))) → QUOTD_IN_GA(T424)
The graph contains the following edges 1 > 1

(50) YES

(51) Obligation:

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

QUOTC_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTC_IN_GA(T336, T338)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(52) UsableRulesProof (EQUIVALENT transformation)

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

(53) Obligation:

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

QUOTC_IN_GA(s(s(s(s(s(s(s(T336))))))), s(T338)) → QUOTC_IN_GA(T336, T338)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
QUOTC_IN_GA(x1, x2) = QUOTC_IN_GA(x1)

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

(54) PiDPToQDPProof (SOUND transformation)

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

(55) Obligation:

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

QUOTC_IN_GA(s(s(s(s(s(s(s(T336)))))))) → QUOTC_IN_GA(T336)

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

(56) 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:

QUOTC_IN_GA(s(s(s(s(s(s(s(T336)))))))) → QUOTC_IN_GA(T336)
The graph contains the following edges 1 > 1

(57) YES

(58) Obligation:

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

QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTA_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTA_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTA_IN_GGGA(T226, T227, T228, T230)
QUOTA_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)

The TRS R consists of the following rules:

divJ_in_gga(T7, T8, T10) → U18_gga(T7, T8, T10, quotB_in_gga(T7, T8, T10))
quotB_in_gga(0, s(T15), 0) → quotB_out_gga(0, s(T15), 0)
quotB_in_gga(s(0), s(s(T38)), 0) → quotB_out_gga(s(0), s(s(T38)), 0)
quotB_in_gga(s(s(0)), s(s(s(T61))), 0) → quotB_out_gga(s(s(0)), s(s(s(T61))), 0)
quotB_in_gga(s(s(s(0))), s(s(s(s(T84)))), 0) → quotB_out_gga(s(s(s(0))), s(s(s(s(T84)))), 0)
quotB_in_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0) → quotB_out_gga(s(s(s(s(0)))), s(s(s(s(s(T107))))), 0)
quotB_in_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0) → quotB_out_gga(s(s(s(s(s(0))))), s(s(s(s(s(s(T130)))))), 0)
quotB_in_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0) → quotB_out_gga(s(s(s(s(s(s(0)))))), s(s(s(s(s(s(s(T153))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0) → quotB_out_gga(s(s(s(s(s(s(s(0))))))), s(s(s(s(s(s(s(s(T176)))))))), 0)
quotB_in_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → U3_gga(T189, T190, T192, quotA_in_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192))
quotA_in_ggga(0, s(T208), T209, 0) → quotA_out_ggga(0, s(T208), T209, 0)
quotA_in_ggga(s(T226), s(T227), T228, T230) → U1_ggga(T226, T227, T228, T230, quotA_in_ggga(T226, T227, T228, T230))
quotA_in_ggga(T241, 0, T242, s(T244)) → U2_ggga(T241, T242, T244, quotB_in_gga(T241, s(T242), T244))
quotB_in_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253)) → U4_gga(T251, T253, quotC_in_ga(T251, T253))
quotC_in_ga(0, 0) → quotC_out_ga(0, 0)
quotC_in_ga(s(0), 0) → quotC_out_ga(s(0), 0)
quotC_in_ga(s(s(0)), 0) → quotC_out_ga(s(s(0)), 0)
quotC_in_ga(s(s(s(0))), 0) → quotC_out_ga(s(s(s(0))), 0)
quotC_in_ga(s(s(s(s(0)))), 0) → quotC_out_ga(s(s(s(s(0)))), 0)
quotC_in_ga(s(s(s(s(s(0))))), 0) → quotC_out_ga(s(s(s(s(s(0))))), 0)
quotC_in_ga(s(s(s(s(s(s(0)))))), 0) → quotC_out_ga(s(s(s(s(s(s(0)))))), 0)
quotC_in_ga(s(s(s(s(s(s(s(T336))))))), s(T338)) → U11_ga(T336, T338, quotC_in_ga(T336, T338))
U11_ga(T336, T338, quotC_out_ga(T336, T338)) → quotC_out_ga(s(s(s(s(s(s(s(T336))))))), s(T338))
U4_gga(T251, T253, quotC_out_ga(T251, T253)) → quotB_out_gga(s(s(s(s(s(s(s(T251))))))), s(s(s(s(s(s(s(0))))))), s(T253))
quotB_in_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352)) → U5_gga(T350, T352, quotD_in_ga(T350, T352))
quotD_in_ga(0, 0) → quotD_out_ga(0, 0)
quotD_in_ga(s(0), 0) → quotD_out_ga(s(0), 0)
quotD_in_ga(s(s(0)), 0) → quotD_out_ga(s(s(0)), 0)
quotD_in_ga(s(s(s(0))), 0) → quotD_out_ga(s(s(s(0))), 0)
quotD_in_ga(s(s(s(s(0)))), 0) → quotD_out_ga(s(s(s(s(0)))), 0)
quotD_in_ga(s(s(s(s(s(0))))), 0) → quotD_out_ga(s(s(s(s(s(0))))), 0)
quotD_in_ga(s(s(s(s(s(s(T424)))))), s(T426)) → U12_ga(T424, T426, quotD_in_ga(T424, T426))
U12_ga(T424, T426, quotD_out_ga(T424, T426)) → quotD_out_ga(s(s(s(s(s(s(T424)))))), s(T426))
U5_gga(T350, T352, quotD_out_ga(T350, T352)) → quotB_out_gga(s(s(s(s(s(s(T350)))))), s(s(s(s(s(s(0)))))), s(T352))
quotB_in_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439)) → U6_gga(T437, T439, quotE_in_ga(T437, T439))
quotE_in_ga(0, 0) → quotE_out_ga(0, 0)
quotE_in_ga(s(0), 0) → quotE_out_ga(s(0), 0)
quotE_in_ga(s(s(0)), 0) → quotE_out_ga(s(s(0)), 0)
quotE_in_ga(s(s(s(0))), 0) → quotE_out_ga(s(s(s(0))), 0)
quotE_in_ga(s(s(s(s(0)))), 0) → quotE_out_ga(s(s(s(s(0)))), 0)
quotE_in_ga(s(s(s(s(s(T500))))), s(T502)) → U13_ga(T500, T502, quotE_in_ga(T500, T502))
U13_ga(T500, T502, quotE_out_ga(T500, T502)) → quotE_out_ga(s(s(s(s(s(T500))))), s(T502))
U6_gga(T437, T439, quotE_out_ga(T437, T439)) → quotB_out_gga(s(s(s(s(s(T437))))), s(s(s(s(s(0))))), s(T439))
quotB_in_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514)) → U7_gga(T512, T514, quotF_in_ga(T512, T514))
quotF_in_ga(0, 0) → quotF_out_ga(0, 0)
quotF_in_ga(s(0), 0) → quotF_out_ga(s(0), 0)
quotF_in_ga(s(s(0)), 0) → quotF_out_ga(s(s(0)), 0)
quotF_in_ga(s(s(s(0))), 0) → quotF_out_ga(s(s(s(0))), 0)
quotF_in_ga(s(s(s(s(T564)))), s(T566)) → U14_ga(T564, T566, quotF_in_ga(T564, T566))
U14_ga(T564, T566, quotF_out_ga(T564, T566)) → quotF_out_ga(s(s(s(s(T564)))), s(T566))
U7_gga(T512, T514, quotF_out_ga(T512, T514)) → quotB_out_gga(s(s(s(s(T512)))), s(s(s(s(0)))), s(T514))
quotB_in_gga(s(s(s(T575))), s(s(s(0))), s(T577)) → U8_gga(T575, T577, quotG_in_ga(T575, T577))
quotG_in_ga(0, 0) → quotG_out_ga(0, 0)
quotG_in_ga(s(0), 0) → quotG_out_ga(s(0), 0)
quotG_in_ga(s(s(0)), 0) → quotG_out_ga(s(s(0)), 0)
quotG_in_ga(s(s(s(T616))), s(T618)) → U15_ga(T616, T618, quotG_in_ga(T616, T618))
U15_ga(T616, T618, quotG_out_ga(T616, T618)) → quotG_out_ga(s(s(s(T616))), s(T618))
U8_gga(T575, T577, quotG_out_ga(T575, T577)) → quotB_out_gga(s(s(s(T575))), s(s(s(0))), s(T577))
quotB_in_gga(s(s(T626)), s(s(0)), s(T628)) → U9_gga(T626, T628, quotH_in_ga(T626, T628))
quotH_in_ga(0, 0) → quotH_out_ga(0, 0)
quotH_in_ga(s(0), 0) → quotH_out_ga(s(0), 0)
quotH_in_ga(s(s(T656)), s(T658)) → U16_ga(T656, T658, quotH_in_ga(T656, T658))
U16_ga(T656, T658, quotH_out_ga(T656, T658)) → quotH_out_ga(s(s(T656)), s(T658))
U9_gga(T626, T628, quotH_out_ga(T626, T628)) → quotB_out_gga(s(s(T626)), s(s(0)), s(T628))
quotB_in_gga(s(T665), s(0), s(T667)) → U10_gga(T665, T667, quotI_in_ga(T665, T667))
quotI_in_ga(0, 0) → quotI_out_ga(0, 0)
quotI_in_ga(s(T684), s(T686)) → U17_ga(T684, T686, quotI_in_ga(T684, T686))
U17_ga(T684, T686, quotI_out_ga(T684, T686)) → quotI_out_ga(s(T684), s(T686))
U10_gga(T665, T667, quotI_out_ga(T665, T667)) → quotB_out_gga(s(T665), s(0), s(T667))
U2_ggga(T241, T242, T244, quotB_out_gga(T241, s(T242), T244)) → quotA_out_ggga(T241, 0, T242, s(T244))
U1_ggga(T226, T227, T228, T230, quotA_out_ggga(T226, T227, T228, T230)) → quotA_out_ggga(s(T226), s(T227), T228, T230)
U3_gga(T189, T190, T192, quotA_out_ggga(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)) → quotB_out_gga(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192)
U18_gga(T7, T8, T10, quotB_out_gga(T7, T8, T10)) → divJ_out_gga(T7, T8, T10)

(59) UsableRulesProof (EQUIVALENT transformation)

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

(60) Obligation:

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

QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190)))))))), T192) → QUOTA_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))), T192)
QUOTA_IN_GGGA(s(T226), s(T227), T228, T230) → QUOTA_IN_GGGA(T226, T227, T228, T230)
QUOTA_IN_GGGA(T241, 0, T242, s(T244)) → QUOTB_IN_GGA(T241, s(T242), T244)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
QUOTB_IN_GGA(x1, x2, x3) = QUOTB_IN_GGA(x1, x2)
QUOTA_IN_GGGA(x1, x2, x3, x4) = QUOTA_IN_GGGA(x1, x2, x3)

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

(61) PiDPToQDPProof (SOUND transformation)

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

(62) Obligation:

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

QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190))))))))) → QUOTA_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))))
QUOTA_IN_GGGA(s(T226), s(T227), T228) → QUOTA_IN_GGGA(T226, T227, T228)
QUOTA_IN_GGGA(T241, 0, T242) → QUOTB_IN_GGA(T241, s(T242))

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

(63) 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:

QUOTA_IN_GGGA(T241, 0, T242) → QUOTB_IN_GGA(T241, s(T242))
The graph contains the following edges 1 >= 1
QUOTA_IN_GGGA(s(T226), s(T227), T228) → QUOTA_IN_GGGA(T226, T227, T228)
The graph contains the following edges 1 > 1, 2 > 2, 3 >= 3
QUOTB_IN_GGA(s(s(s(s(s(s(s(s(T189)))))))), s(s(s(s(s(s(s(s(T190))))))))) → QUOTA_IN_GGGA(T189, T190, s(s(s(s(s(s(s(T190))))))))
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3

(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 (SOUND transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (SOUND transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) YES

(30) Obligation:

(31) UsableRulesProof (EQUIVALENT transformation)

(32) Obligation:

(33) PiDPToQDPProof (SOUND transformation)

(34) Obligation:

(35) QDPSizeChangeProof (EQUIVALENT transformation)

(36) YES

(37) Obligation:

(38) UsableRulesProof (EQUIVALENT transformation)

(39) Obligation:

(40) PiDPToQDPProof (SOUND transformation)

(41) Obligation:

(42) QDPSizeChangeProof (EQUIVALENT transformation)

(43) YES

(44) Obligation:

(45) UsableRulesProof (EQUIVALENT transformation)

(46) Obligation:

(47) PiDPToQDPProof (SOUND transformation)

(48) Obligation:

(49) QDPSizeChangeProof (EQUIVALENT transformation)

(50) YES

(51) Obligation:

(52) UsableRulesProof (EQUIVALENT transformation)

(53) Obligation:

(54) PiDPToQDPProof (SOUND transformation)

(55) Obligation:

(56) QDPSizeChangeProof (EQUIVALENT transformation)

(57) YES

(58) Obligation:

(59) UsableRulesProof (EQUIVALENT transformation)

(60) Obligation:

(61) PiDPToQDPProof (SOUND transformation)

(62) Obligation:

(63) QDPSizeChangeProof (EQUIVALENT transformation)

(64) YES