Left Termination proof of /tmp/tmpdwbnUm/divremain2.pl

Left Termination of the query pattern div_in_4(g, g, a, a) w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇐)

↳2 Prolog

↳3 PrologToPiTRSProof (⇐)

↳4 PiTRS

↳5 DependencyPairsProof (⇔)

↳6 PiDP

↳7 DependencyGraphProof (⇔)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔)

            ↳11 PiDP

                ↳12 PiDPToQDPProof (⇐)

                    ↳13 QDP

                        ↳14 QDPSizeChangeProof (⇔)

                            ↳15 TRUE

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔)

            ↳18 PiDP

                ↳19 PiDPToQDPProof (⇐)

                    ↳20 QDP

                        ↳21 QDPSizeChangeProof (⇔)

                            ↳22 TRUE

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔)

            ↳25 PiDP

                ↳26 PiDPToQDPProof (⇐)

                    ↳27 QDP

                        ↳28 QDPSizeChangeProof (⇔)

                            ↳29 TRUE

    ↳30 PiDP

        ↳31 UsableRulesProof (⇔)

            ↳32 PiDP

                ↳33 PiDPToQDPProof (⇐)

                    ↳34 QDP

                        ↳35 QDPSizeChangeProof (⇔)

                            ↳36 TRUE

    ↳37 PiDP

        ↳38 UsableRulesProof (⇔)

            ↳39 PiDP

                ↳40 PiDPToQDPProof (⇐)

                    ↳41 QDP

                        ↳42 QDPSizeChangeProof (⇔)

                            ↳43 TRUE

    ↳44 PiDP

        ↳45 UsableRulesProof (⇔)

            ↳46 PiDP

                ↳47 PiDPToQDPProof (⇐)

                    ↳48 QDP

                        ↳49 QDPSizeChangeProof (⇔)

                            ↳50 TRUE

    ↳51 PiDP

        ↳52 UsableRulesProof (⇔)

            ↳53 PiDP

                ↳54 PiDPToQDPProof (⇐)

                    ↳55 QDP

                        ↳56 QDPSizeChangeProof (⇔)

                            ↳57 TRUE

    ↳58 PiDP

        ↳59 UsableRulesProof (⇔)

            ↳60 PiDP

                ↳61 PiDPToQDPProof (⇐)

                    ↳62 QDP

                        ↳63 QDPSizeChangeProof (⇔)

                            ↳64 TRUE

    ↳65 PiDP

        ↳66 UsableRulesProof (⇔)

            ↳67 PiDP

                ↳68 PiDPToQDPProof (⇐)

                    ↳69 QDP

                        ↳70 MRRProof (⇔)

                            ↳71 QDP

                                ↳72 PisEmptyProof (⇔)

                                    ↳73 TRUE

(0) Obligation:

Clauses:

div(X1, 0, X2, X3) :- failure(a).
div(0, Y, 0, 0) :- no(zero(Y)).
div(X, Y, s(Z), R) :- ','(no(zero(X)), ','(no(zero(Y)), ','(minus(X, Y, U), ','(!, div(U, Y, Z, R))))).
div(X, Y, X4, X) :- ','(no(zero(X)), no(zero(Y))).
minus(X, 0, X).
minus(s(X), s(Y), Z) :- minus(X, Y, Z).
failure(b).
zero(0).
no(X) :- ','(X, ','(!, failure(a))).
no(X5).

Queries:

div(g,g,a,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: div(T1, T2, T3, T4)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 0 | div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 1 | div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 2 | div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 0\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 1 | div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 2 | div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: \n\nX12 is free\nX13 is free; \nX14 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: failure(a), SCOPE: 2, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 2 | div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: no(zero(T8))\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: \n\nX17 is free", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: no(zero(T8)), SCOPE: 3, CLAUSE: 8 | no(zero(T8)), SCOPE: 3, CLAUSE: 9 | ?_3\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: ','(zero(T9), ','(!_3, failure(a))) | no(zero(T9)), SCOPE: 3, CLAUSE: 9 | ?_3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(zero(T9), ','(!_3, failure(a))), SCOPE: 4, CLAUSE: 7 | no(zero(T9)), SCOPE: 3, CLAUSE: 9 | ?_3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(!_3, failure(a)) | no(zero(0)), SCOPE: 3, CLAUSE: 9 | ?_3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: no(zero(T9)), SCOPE: 3, CLAUSE: 9\n\nT9 is ground\nzero(T9) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: failure(a), SCOPE: 5, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(no(zero(T11)), ','(no(zero(T12)), ','(minus(T11, T12, X30), ','(!_1, div(X30, T12, T15, T16))))) | div(T11, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT11 is ground\nT12 is ground\nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: div(T1, T2, T3, T4), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT2 is ground\nX26 is free; \nX27 is free; \nX28 is free; \nX29 is free; \ndiv(T1, T2, T3, T4) !=? div(X26, X27, s(X28), X29)", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(no(zero(T11)), ','(no(zero(T12)), ','(minus(T11, T12, X30), ','(!_1, div(X30, T12, T15, T16))))), SCOPE: 6, CLAUSE: 8 | ','(no(zero(T11)), ','(no(zero(T12)), ','(minus(T11, T12, X30), ','(!_1, div(X30, T12, T15, T16))))), SCOPE: 6, CLAUSE: 9 | ?_6 | div(T11, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT11 is ground\nT12 is ground\nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(zero(T17), ','(!_6, ','(failure(a), ','(no(zero(T12)), ','(minus(T17, T12, X30), ','(!_1, div(X30, T12, T15, T16))))))) | ','(no(zero(T17)), ','(no(zero(T12)), ','(minus(T17, T12, X30), ','(!_1, div(X30, T12, T15, T16))))), SCOPE: 6, CLAUSE: 9 | ?_6 | div(T17, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nT17 is ground\nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(zero(T17), ','(!_6, ','(failure(a), ','(no(zero(T12)), ','(minus(T17, T12, X30), ','(!_1, div(X30, T12, T15, T16))))))), SCOPE: 7, CLAUSE: 7 | ','(no(zero(T17)), ','(no(zero(T12)), ','(minus(T17, T12, X30), ','(!_1, div(X30, T12, T15, T16))))), SCOPE: 6, CLAUSE: 9 | ?_6 | div(T17, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nT17 is ground\nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(!_6, ','(failure(a), ','(no(zero(T12)), ','(minus(0, T12, X30), ','(!_1, div(X30, T12, T15, T16)))))) | ','(no(zero(0)), ','(no(zero(T12)), ','(minus(0, T12, X30), ','(!_1, div(X30, T12, T15, T16))))), SCOPE: 6, CLAUSE: 9 | ?_6 | div(0, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(no(zero(T17)), ','(no(zero(T12)), ','(minus(T17, T12, X30), ','(!_1, div(X30, T12, T15, T16))))), SCOPE: 6, CLAUSE: 9 | div(T17, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nT17 is ground\nX30 is free; \nzero(T17) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(failure(a), ','(no(zero(T12)), ','(minus(0, T12, X30), ','(!_1, div(X30, T12, T15, T16))))) | div(0, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(failure(a), ','(no(zero(T12)), ','(minus(0, T12, X30), ','(!_1, div(X30, T12, T15, T16))))), SCOPE: 8, CLAUSE: 6 | div(0, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nX30 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: div(0, T12, T3, T4), SCOPE: 1, CLAUSE: 3\n\nT12 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(no(zero(0)), no(zero(T18)))\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: \n\nX36 is free\nX37 is free; \nX38 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: ','(no(zero(0)), no(zero(T18))), SCOPE: 9, CLAUSE: 8 | ','(no(zero(0)), no(zero(T18))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: ','(zero(0), ','(!_9, ','(failure(a), no(zero(T18))))) | ','(no(zero(0)), no(zero(T18))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(zero(0), ','(!_9, ','(failure(a), no(zero(T18))))), SCOPE: 10, CLAUSE: 7 | ','(no(zero(0)), no(zero(T18))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: ','(!_9, ','(failure(a), no(zero(T18)))) | ','(no(zero(0)), no(zero(T18))), SCOPE: 9, CLAUSE: 9 | ?_9\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(failure(a), no(zero(T18)))\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(failure(a), no(zero(T18))), SCOPE: 11, CLAUSE: 6\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: ','(no(zero(T12)), ','(minus(T20, T12, X30), ','(!_1, div(X30, T12, T15, T16)))) | div(T20, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nT20 is ground\nX30 is free; \nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(no(zero(T12)), ','(minus(T20, T12, X30), ','(!_1, div(X30, T12, T15, T16)))), SCOPE: 12, CLAUSE: 8 | ','(no(zero(T12)), ','(minus(T20, T12, X30), ','(!_1, div(X30, T12, T15, T16)))), SCOPE: 12, CLAUSE: 9 | ?_12 | div(T20, T12, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT12 is ground\nT20 is ground\nX30 is free; \nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(zero(T21), ','(!_12, ','(failure(a), ','(minus(T20, T21, X30), ','(!_1, div(X30, T21, T15, T16)))))) | ','(no(zero(T21)), ','(minus(T20, T21, X30), ','(!_1, div(X30, T21, T15, T16)))), SCOPE: 12, CLAUSE: 9 | ?_12 | div(T20, T21, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nT21 is ground\nX30 is free; \nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(zero(T21), ','(!_12, ','(failure(a), ','(minus(T20, T21, X30), ','(!_1, div(X30, T21, T15, T16)))))), SCOPE: 13, CLAUSE: 7 | ','(no(zero(T21)), ','(minus(T20, T21, X30), ','(!_1, div(X30, T21, T15, T16)))), SCOPE: 12, CLAUSE: 9 | ?_12 | div(T20, T21, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nT21 is ground\nX30 is free; \nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(!_12, ','(failure(a), ','(minus(T20, 0, X30), ','(!_1, div(X30, 0, T15, T16))))) | ','(no(zero(0)), ','(minus(T20, 0, X30), ','(!_1, div(X30, 0, T15, T16)))), SCOPE: 12, CLAUSE: 9 | ?_12 | div(T20, 0, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nX30 is free; \nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(no(zero(T21)), ','(minus(T20, T21, X30), ','(!_1, div(X30, T21, T15, T16)))), SCOPE: 12, CLAUSE: 9 | div(T20, T21, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nT21 is ground\nX30 is free; \nzero(T20) !=? zero(0)\nzero(T21) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(failure(a), ','(minus(T20, 0, X30), ','(!_1, div(X30, 0, T15, T16)))) | div(T20, 0, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nX30 is free; \nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(failure(a), ','(minus(T20, 0, X30), ','(!_1, div(X30, 0, T15, T16)))), SCOPE: 14, CLAUSE: 6 | div(T20, 0, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nX30 is free; \nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: div(T20, 0, T3, T4), SCOPE: 1, CLAUSE: 3\n\nT20 is ground\nzero(T20) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(no(zero(T22)), no(zero(0)))\n\nT22 is ground\nzero(T22) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: \n\nX48 is free\nX49 is free; \nX50 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(no(zero(T22)), no(zero(0))), SCOPE: 15, CLAUSE: 8 | ','(no(zero(T22)), no(zero(0))), SCOPE: 15, CLAUSE: 9 | ?_15\n\nT22 is ground\nzero(T22) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(zero(T24), ','(!_15, ','(failure(a), no(zero(0))))) | ','(no(zero(T24)), no(zero(0))), SCOPE: 15, CLAUSE: 9 | ?_15\n\nT24 is ground\nzero(T24) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(zero(T24), ','(!_15, ','(failure(a), no(zero(0))))), SCOPE: 16, CLAUSE: 7 | ','(no(zero(T24)), no(zero(0))), SCOPE: 15, CLAUSE: 9 | ?_15\n\nT24 is ground\nzero(T24) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(no(zero(T24)), no(zero(0))), SCOPE: 15, CLAUSE: 9\n\nT24 is ground\nzero(T24) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: no(zero(0))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: no(zero(0)), SCOPE: 17, CLAUSE: 8 | no(zero(0)), SCOPE: 17, CLAUSE: 9 | ?_17\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(zero(0), ','(!_17, failure(a))) | no(zero(0)), SCOPE: 17, CLAUSE: 9 | ?_17\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(zero(0), ','(!_17, failure(a))), SCOPE: 18, CLAUSE: 7 | no(zero(0)), SCOPE: 17, CLAUSE: 9 | ?_17\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(!_17, failure(a)) | no(zero(0)), SCOPE: 17, CLAUSE: 9 | ?_17\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: failure(a), SCOPE: 19, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(minus(T20, T26, X30), ','(!_1, div(X30, T26, T15, T16))) | div(T20, T26, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nT26 is ground\nX30 is free; \nzero(T20) !=? zero(0)\nzero(T26) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(minus(T20, T26, X30), ','(!_1, div(X30, T26, T15, T16))), SCOPE: 20, CLAUSE: 4 | ','(minus(T20, T26, X30), ','(!_1, div(X30, T26, T15, T16))), SCOPE: 20, CLAUSE: 5 | div(T20, T26, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nT26 is ground\nX30 is free; \nzero(T20) !=? zero(0)\nzero(T26) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(minus(T20, T26, X30), ','(!_1, div(X30, T26, T15, T16))), SCOPE: 20, CLAUSE: 5 | div(T20, T26, T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT20 is ground\nT26 is ground\nX30 is free; \nX60 is free; \nzero(T20) !=? zero(0)\nzero(T26) !=? zero(0)\nminus(T20, T26, X30) !=? minus(X60, 0, X60)", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(minus(T27, T28, X67), ','(!_1, div(X67, s(T28), T15, T16))) | div(s(T27), s(T28), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT27 is ground\nT28 is ground\nX30 is free; \nX60 is free; \nX67 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: div(T20, T26, T3, T4), SCOPE: 1, CLAUSE: 3\n\nT20 is ground\nT26 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T20) !=? zero(0)\nzero(T26) !=? zero(0)\nminus(T20, T26, X30) !=? minus(X60, 0, X60)\nminus(T20, T26, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(minus(T27, T28, X67), ','(!_1, div(X67, s(T28), T15, T16))), SCOPE: 21, CLAUSE: 4 | ','(minus(T27, T28, X67), ','(!_1, div(X67, s(T28), T15, T16))), SCOPE: 21, CLAUSE: 5 | div(s(T27), s(T28), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT27 is ground\nT28 is ground\nX67 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(!_1, div(T29, s(0), T15, T16)) | ','(minus(T29, 0, X67), ','(!_1, div(X67, s(0), T15, T16))), SCOPE: 21, CLAUSE: 5 | div(s(T29), s(0), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT29 is ground\nX67 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(minus(T27, T28, X67), ','(!_1, div(X67, s(T28), T15, T16))), SCOPE: 21, CLAUSE: 5 | div(s(T27), s(T28), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT27 is ground\nT28 is ground\nX67 is free; \nX69 is free; \nminus(T27, T28, X67) !=? minus(X69, 0, X69)", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: div(T29, s(0), T15, T16)\n\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ','(minus(T30, T31, X76), ','(!_1, div(X76, s(s(T31)), T15, T16))) | div(s(s(T30)), s(s(T31)), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT30 is ground\nT31 is ground\nX67 is free; \nX69 is free; \nX76 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: div(s(T27), s(T28), T3, T4), SCOPE: 1, CLAUSE: 3\n\nT27 is ground\nT28 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T27, T28, X67) !=? minus(X69, 0, X69)\nminus(T27, T28, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: ','(minus(T30, T31, X76), ','(!_1, div(X76, s(s(T31)), T15, T16))), SCOPE: 22, CLAUSE: 4 | ','(minus(T30, T31, X76), ','(!_1, div(X76, s(s(T31)), T15, T16))), SCOPE: 22, CLAUSE: 5 | div(s(s(T30)), s(s(T31)), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT30 is ground\nT31 is ground\nX76 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ','(!_1, div(T32, s(s(0)), T15, T16)) | ','(minus(T32, 0, X76), ','(!_1, div(X76, s(s(0)), T15, T16))), SCOPE: 22, CLAUSE: 5 | div(s(s(T32)), s(s(0)), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT32 is ground\nX76 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(minus(T30, T31, X76), ','(!_1, div(X76, s(s(T31)), T15, T16))), SCOPE: 22, CLAUSE: 5 | div(s(s(T30)), s(s(T31)), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT30 is ground\nT31 is ground\nX76 is free; \nX78 is free; \nminus(T30, T31, X76) !=? minus(X78, 0, X78)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: div(T32, s(s(0)), T15, T16)\n\nT32 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(minus(T33, T34, X85), ','(!_1, div(X85, s(s(s(T34))), T15, T16))) | div(s(s(s(T33))), s(s(s(T34))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT33 is ground\nT34 is ground\nX76 is free; \nX78 is free; \nX85 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: div(s(s(T30)), s(s(T31)), T3, T4), SCOPE: 1, CLAUSE: 3\n\nT30 is ground\nT31 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T30, T31, X76) !=? minus(X78, 0, X78)\nminus(T30, T31, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(minus(T33, T34, X85), ','(!_1, div(X85, s(s(s(T34))), T15, T16))), SCOPE: 23, CLAUSE: 4 | ','(minus(T33, T34, X85), ','(!_1, div(X85, s(s(s(T34))), T15, T16))), SCOPE: 23, CLAUSE: 5 | div(s(s(s(T33))), s(s(s(T34))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT33 is ground\nT34 is ground\nX85 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ','(!_1, div(T35, s(s(s(0))), T15, T16)) | ','(minus(T35, 0, X85), ','(!_1, div(X85, s(s(s(0))), T15, T16))), SCOPE: 23, CLAUSE: 5 | div(s(s(s(T35))), s(s(s(0))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT35 is ground\nX85 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(minus(T33, T34, X85), ','(!_1, div(X85, s(s(s(T34))), T15, T16))), SCOPE: 23, CLAUSE: 5 | div(s(s(s(T33))), s(s(s(T34))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT33 is ground\nT34 is ground\nX85 is free; \nX87 is free; \nminus(T33, T34, X85) !=? minus(X87, 0, X87)", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: div(T35, s(s(s(0))), T15, T16)\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(minus(T36, T37, X94), ','(!_1, div(X94, s(s(s(s(T37)))), T15, T16))) | div(s(s(s(s(T36)))), s(s(s(s(T37)))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT36 is ground\nT37 is ground\nX85 is free; \nX87 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: div(s(s(s(T33))), s(s(s(T34))), T3, T4), SCOPE: 1, CLAUSE: 3\n\nT33 is ground\nT34 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T33, T34, X85) !=? minus(X87, 0, X87)\nminus(T33, T34, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: ','(minus(T36, T37, X94), ','(!_1, div(X94, s(s(s(s(T37)))), T15, T16))), SCOPE: 24, CLAUSE: 4 | ','(minus(T36, T37, X94), ','(!_1, div(X94, s(s(s(s(T37)))), T15, T16))), SCOPE: 24, CLAUSE: 5 | div(s(s(s(s(T36)))), s(s(s(s(T37)))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT36 is ground\nT37 is ground\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(!_1, div(T38, s(s(s(s(0)))), T15, T16)) | ','(minus(T38, 0, X94), ','(!_1, div(X94, s(s(s(s(0)))), T15, T16))), SCOPE: 24, CLAUSE: 5 | div(s(s(s(s(T38)))), s(s(s(s(0)))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT38 is ground\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(minus(T36, T37, X94), ','(!_1, div(X94, s(s(s(s(T37)))), T15, T16))), SCOPE: 24, CLAUSE: 5 | div(s(s(s(s(T36)))), s(s(s(s(T37)))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT36 is ground\nT37 is ground\nX94 is free; \nX96 is free; \nminus(T36, T37, X94) !=? minus(X96, 0, X96)", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: div(T38, s(s(s(s(0)))), T15, T16)\n\nT38 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ','(minus(T39, T40, X103), ','(!_1, div(X103, s(s(s(s(s(T40))))), T15, T16))) | div(s(s(s(s(s(T39))))), s(s(s(s(s(T40))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT39 is ground\nT40 is ground\nX94 is free; \nX96 is free; \nX103 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: div(s(s(s(s(T36)))), s(s(s(s(T37)))), T3, T4), SCOPE: 1, CLAUSE: 3\n\nT36 is ground\nT37 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T36, T37, X94) !=? minus(X96, 0, X96)\nminus(T36, T37, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(minus(T39, T40, X103), ','(!_1, div(X103, s(s(s(s(s(T40))))), T15, T16))), SCOPE: 25, CLAUSE: 4 | ','(minus(T39, T40, X103), ','(!_1, div(X103, s(s(s(s(s(T40))))), T15, T16))), SCOPE: 25, CLAUSE: 5 | div(s(s(s(s(s(T39))))), s(s(s(s(s(T40))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT39 is ground\nT40 is ground\nX103 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: ','(!_1, div(T41, s(s(s(s(s(0))))), T15, T16)) | ','(minus(T41, 0, X103), ','(!_1, div(X103, s(s(s(s(s(0))))), T15, T16))), SCOPE: 25, CLAUSE: 5 | div(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT41 is ground\nX103 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: ','(minus(T39, T40, X103), ','(!_1, div(X103, s(s(s(s(s(T40))))), T15, T16))), SCOPE: 25, CLAUSE: 5 | div(s(s(s(s(s(T39))))), s(s(s(s(s(T40))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT39 is ground\nT40 is ground\nX103 is free; \nX105 is free; \nminus(T39, T40, X103) !=? minus(X105, 0, X105)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: div(T41, s(s(s(s(s(0))))), T15, T16)\n\nT41 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(minus(T42, T43, X112), ','(!_1, div(X112, s(s(s(s(s(s(T43)))))), T15, T16))) | div(s(s(s(s(s(s(T42)))))), s(s(s(s(s(s(T43)))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT42 is ground\nT43 is ground\nX103 is free; \nX105 is free; \nX112 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: div(s(s(s(s(s(T39))))), s(s(s(s(s(T40))))), T3, T4), SCOPE: 1, CLAUSE: 3\n\nT39 is ground\nT40 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T39, T40, X103) !=? minus(X105, 0, X105)\nminus(T39, T40, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(minus(T42, T43, X112), ','(!_1, div(X112, s(s(s(s(s(s(T43)))))), T15, T16))), SCOPE: 26, CLAUSE: 4 | ','(minus(T42, T43, X112), ','(!_1, div(X112, s(s(s(s(s(s(T43)))))), T15, T16))), SCOPE: 26, CLAUSE: 5 | div(s(s(s(s(s(s(T42)))))), s(s(s(s(s(s(T43)))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT42 is ground\nT43 is ground\nX112 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(!_1, div(T44, s(s(s(s(s(s(0)))))), T15, T16)) | ','(minus(T44, 0, X112), ','(!_1, div(X112, s(s(s(s(s(s(0)))))), T15, T16))), SCOPE: 26, CLAUSE: 5 | div(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT44 is ground\nX112 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(minus(T42, T43, X112), ','(!_1, div(X112, s(s(s(s(s(s(T43)))))), T15, T16))), SCOPE: 26, CLAUSE: 5 | div(s(s(s(s(s(s(T42)))))), s(s(s(s(s(s(T43)))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT42 is ground\nT43 is ground\nX112 is free; \nX114 is free; \nminus(T42, T43, X112) !=? minus(X114, 0, X114)", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: div(T44, s(s(s(s(s(s(0)))))), T15, T16)\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(minus(T45, T46, X121), ','(!_1, div(X121, s(s(s(s(s(s(s(T46))))))), T15, T16))) | div(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), T3, T4), SCOPE: 1, CLAUSE: 3 | ?_1\n\nT45 is ground\nT46 is ground\nX112 is free; \nX114 is free; \nX121 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: div(s(s(s(s(s(s(T42)))))), s(s(s(s(s(s(T43)))))), T3, T4), SCOPE: 1, CLAUSE: 3\n\nT42 is ground\nT43 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T42, T43, X112) !=? minus(X114, 0, X114)\nminus(T42, T43, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(minus(T45, T46, X121), ','(!_1, div(X121, s(T47), T15, T16)))\n\nT45 is ground\nT46 is ground\nT47 is ground\nX121 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: minus(T45, T46, X121)\n\nT45 is ground\nT46 is ground\nX121 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ','(!_1, div(T48, s(T47), T15, T16))\n\nT47 is ground\nT48 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: minus(T45, T46, X121), SCOPE: 27, CLAUSE: 4 | minus(T45, T46, X121), SCOPE: 27, CLAUSE: 5\n\nT45 is ground\nT46 is ground\nX121 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: minus(T45, T46, X121), SCOPE: 27, CLAUSE: 4\n\nT45 is ground\nT46 is ground\nX121 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: minus(T45, T46, X121), SCOPE: 27, CLAUSE: 5\n\nT45 is ground\nT46 is ground\nX121 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: \n\nX121 is free\nX124 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: minus(T50, T51, X131)\n\nT50 is ground\nT51 is ground\nX131 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: \n\nX121 is free\nX128 is free; \nX129 is free; \nX130 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: div(T48, s(T47), T15, T16)\n\nT47 is ground\nT48 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(no(zero(s(s(s(s(s(s(T52)))))))), no(zero(s(s(s(s(s(s(T53)))))))))\n\nT52 is ground\nT53 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T52, T53, X112) !=? minus(X114, 0, X114)\nminus(T52, T53, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: \n\nX112 is free\nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nX135 is free; \nX136 is free; \nX137 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(no(zero(s(s(s(s(s(s(T52)))))))), no(zero(s(s(s(s(s(s(T53))))))))), SCOPE: 28, CLAUSE: 8 | ','(no(zero(s(s(s(s(s(s(T52)))))))), no(zero(s(s(s(s(s(s(T53))))))))), SCOPE: 28, CLAUSE: 9 | ?_28\n\nT52 is ground\nT53 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T52, T53, X112) !=? minus(X114, 0, X114)\nminus(T52, T53, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: ','(zero(s(s(s(s(s(s(T55))))))), ','(!_28, ','(failure(a), no(zero(s(s(s(s(s(s(T53))))))))))) | ','(no(zero(s(s(s(s(s(s(T55)))))))), no(zero(s(s(s(s(s(s(T53))))))))), SCOPE: 28, CLAUSE: 9 | ?_28\n\nT53 is ground\nT55 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T55, T53, X112) !=? minus(X114, 0, X114)\nminus(T55, T53, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: ','(zero(s(s(s(s(s(s(T55))))))), ','(!_28, ','(failure(a), no(zero(s(s(s(s(s(s(T53))))))))))), SCOPE: 29, CLAUSE: 7 | ','(no(zero(s(s(s(s(s(s(T55)))))))), no(zero(s(s(s(s(s(s(T53))))))))), SCOPE: 28, CLAUSE: 9 | ?_28\n\nT53 is ground\nT55 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T55, T53, X112) !=? minus(X114, 0, X114)\nminus(T55, T53, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(no(zero(s(s(s(s(s(s(T55)))))))), no(zero(s(s(s(s(s(s(T53))))))))), SCOPE: 28, CLAUSE: 9\n\nT53 is ground\nT55 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T55, T53, X112) !=? minus(X114, 0, X114)\nminus(T55, T53, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: no(zero(s(s(s(s(s(s(T53))))))))\n\nT53 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T56, T53, X112) !=? minus(X114, 0, X114)\nminus(T56, T53, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: no(zero(s(s(s(s(s(s(T53)))))))), SCOPE: 30, CLAUSE: 8 | no(zero(s(s(s(s(s(s(T53)))))))), SCOPE: 30, CLAUSE: 9 | ?_30\n\nT53 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T56, T53, X112) !=? minus(X114, 0, X114)\nminus(T56, T53, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: ','(zero(s(s(s(s(s(s(T57))))))), ','(!_30, failure(a))) | no(zero(s(s(s(s(s(s(T57)))))))), SCOPE: 30, CLAUSE: 9 | ?_30\n\nT57 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T56, T57, X112) !=? minus(X114, 0, X114)\nminus(T56, T57, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(zero(s(s(s(s(s(s(T57))))))), ','(!_30, failure(a))), SCOPE: 31, CLAUSE: 7 | no(zero(s(s(s(s(s(s(T57)))))))), SCOPE: 30, CLAUSE: 9 | ?_30\n\nT57 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T56, T57, X112) !=? minus(X114, 0, X114)\nminus(T56, T57, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: no(zero(s(s(s(s(s(s(T57)))))))), SCOPE: 30, CLAUSE: 9\n\nT57 is ground\nX112 is free; \nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; \nminus(T56, T57, X112) !=? minus(X114, 0, X114)\nminus(T56, T57, X112) !=? minus(s(X118), s(X119), X120)", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: true\n\nX112 is free\nX114 is free; \nX118 is free; \nX119 is free; \nX120 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(no(zero(s(s(s(s(s(T59))))))), no(zero(s(s(s(s(s(T60))))))))\n\nT59 is ground\nT60 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T59, T60, X103) !=? minus(X105, 0, X105)\nminus(T59, T60, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: \n\nX103 is free\nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nX149 is free; \nX150 is free; \nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: ','(no(zero(s(s(s(s(s(T59))))))), no(zero(s(s(s(s(s(T60)))))))), SCOPE: 32, CLAUSE: 8 | ','(no(zero(s(s(s(s(s(T59))))))), no(zero(s(s(s(s(s(T60)))))))), SCOPE: 32, CLAUSE: 9 | ?_32\n\nT59 is ground\nT60 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T59, T60, X103) !=? minus(X105, 0, X105)\nminus(T59, T60, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(zero(s(s(s(s(s(T62)))))), ','(!_32, ','(failure(a), no(zero(s(s(s(s(s(T60)))))))))) | ','(no(zero(s(s(s(s(s(T62))))))), no(zero(s(s(s(s(s(T60)))))))), SCOPE: 32, CLAUSE: 9 | ?_32\n\nT60 is ground\nT62 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T62, T60, X103) !=? minus(X105, 0, X105)\nminus(T62, T60, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(zero(s(s(s(s(s(T62)))))), ','(!_32, ','(failure(a), no(zero(s(s(s(s(s(T60)))))))))), SCOPE: 33, CLAUSE: 7 | ','(no(zero(s(s(s(s(s(T62))))))), no(zero(s(s(s(s(s(T60)))))))), SCOPE: 32, CLAUSE: 9 | ?_32\n\nT60 is ground\nT62 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T62, T60, X103) !=? minus(X105, 0, X105)\nminus(T62, T60, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: ','(no(zero(s(s(s(s(s(T62))))))), no(zero(s(s(s(s(s(T60)))))))), SCOPE: 32, CLAUSE: 9\n\nT60 is ground\nT62 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T62, T60, X103) !=? minus(X105, 0, X105)\nminus(T62, T60, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: no(zero(s(s(s(s(s(T60)))))))\n\nT60 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T63, T60, X103) !=? minus(X105, 0, X105)\nminus(T63, T60, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: no(zero(s(s(s(s(s(T60))))))), SCOPE: 34, CLAUSE: 8 | no(zero(s(s(s(s(s(T60))))))), SCOPE: 34, CLAUSE: 9 | ?_34\n\nT60 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T63, T60, X103) !=? minus(X105, 0, X105)\nminus(T63, T60, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(zero(s(s(s(s(s(T64)))))), ','(!_34, failure(a))) | no(zero(s(s(s(s(s(T64))))))), SCOPE: 34, CLAUSE: 9 | ?_34\n\nT64 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T63, T64, X103) !=? minus(X105, 0, X105)\nminus(T63, T64, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: ','(zero(s(s(s(s(s(T64)))))), ','(!_34, failure(a))), SCOPE: 35, CLAUSE: 7 | no(zero(s(s(s(s(s(T64))))))), SCOPE: 34, CLAUSE: 9 | ?_34\n\nT64 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T63, T64, X103) !=? minus(X105, 0, X105)\nminus(T63, T64, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: no(zero(s(s(s(s(s(T64))))))), SCOPE: 34, CLAUSE: 9\n\nT64 is ground\nX103 is free; \nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; \nminus(T63, T64, X103) !=? minus(X105, 0, X105)\nminus(T63, T64, X103) !=? minus(s(X109), s(X110), X111)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: true\n\nX103 is free\nX105 is free; \nX109 is free; \nX110 is free; \nX111 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ','(no(zero(s(s(s(s(T66)))))), no(zero(s(s(s(s(T67)))))))\n\nT66 is ground\nT67 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T66, T67, X94) !=? minus(X96, 0, X96)\nminus(T66, T67, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\nX94 is free\nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nX163 is free; \nX164 is free; \nX165 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(no(zero(s(s(s(s(T66)))))), no(zero(s(s(s(s(T67))))))), SCOPE: 36, CLAUSE: 8 | ','(no(zero(s(s(s(s(T66)))))), no(zero(s(s(s(s(T67))))))), SCOPE: 36, CLAUSE: 9 | ?_36\n\nT66 is ground\nT67 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T66, T67, X94) !=? minus(X96, 0, X96)\nminus(T66, T67, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ','(zero(s(s(s(s(T69))))), ','(!_36, ','(failure(a), no(zero(s(s(s(s(T67))))))))) | ','(no(zero(s(s(s(s(T69)))))), no(zero(s(s(s(s(T67))))))), SCOPE: 36, CLAUSE: 9 | ?_36\n\nT67 is ground\nT69 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T69, T67, X94) !=? minus(X96, 0, X96)\nminus(T69, T67, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(zero(s(s(s(s(T69))))), ','(!_36, ','(failure(a), no(zero(s(s(s(s(T67))))))))), SCOPE: 37, CLAUSE: 7 | ','(no(zero(s(s(s(s(T69)))))), no(zero(s(s(s(s(T67))))))), SCOPE: 36, CLAUSE: 9 | ?_36\n\nT67 is ground\nT69 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T69, T67, X94) !=? minus(X96, 0, X96)\nminus(T69, T67, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ','(no(zero(s(s(s(s(T69)))))), no(zero(s(s(s(s(T67))))))), SCOPE: 36, CLAUSE: 9\n\nT67 is ground\nT69 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T69, T67, X94) !=? minus(X96, 0, X96)\nminus(T69, T67, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: no(zero(s(s(s(s(T67))))))\n\nT67 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T70, T67, X94) !=? minus(X96, 0, X96)\nminus(T70, T67, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: no(zero(s(s(s(s(T67)))))), SCOPE: 38, CLAUSE: 8 | no(zero(s(s(s(s(T67)))))), SCOPE: 38, CLAUSE: 9 | ?_38\n\nT67 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T70, T67, X94) !=? minus(X96, 0, X96)\nminus(T70, T67, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(zero(s(s(s(s(T71))))), ','(!_38, failure(a))) | no(zero(s(s(s(s(T71)))))), SCOPE: 38, CLAUSE: 9 | ?_38\n\nT71 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T70, T71, X94) !=? minus(X96, 0, X96)\nminus(T70, T71, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(zero(s(s(s(s(T71))))), ','(!_38, failure(a))), SCOPE: 39, CLAUSE: 7 | no(zero(s(s(s(s(T71)))))), SCOPE: 38, CLAUSE: 9 | ?_38\n\nT71 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T70, T71, X94) !=? minus(X96, 0, X96)\nminus(T70, T71, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: no(zero(s(s(s(s(T71)))))), SCOPE: 38, CLAUSE: 9\n\nT71 is ground\nX94 is free; \nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; \nminus(T70, T71, X94) !=? minus(X96, 0, X96)\nminus(T70, T71, X94) !=? minus(s(X100), s(X101), X102)", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: true\n\nX94 is free\nX96 is free; \nX100 is free; \nX101 is free; \nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(no(zero(s(s(s(T73))))), no(zero(s(s(s(T74))))))\n\nT73 is ground\nT74 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T73, T74, X85) !=? minus(X87, 0, X87)\nminus(T73, T74, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\nX85 is free\nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nX177 is free; \nX178 is free; \nX179 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(no(zero(s(s(s(T73))))), no(zero(s(s(s(T74)))))), SCOPE: 40, CLAUSE: 8 | ','(no(zero(s(s(s(T73))))), no(zero(s(s(s(T74)))))), SCOPE: 40, CLAUSE: 9 | ?_40\n\nT73 is ground\nT74 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T73, T74, X85) !=? minus(X87, 0, X87)\nminus(T73, T74, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(zero(s(s(s(T76)))), ','(!_40, ','(failure(a), no(zero(s(s(s(T74)))))))) | ','(no(zero(s(s(s(T76))))), no(zero(s(s(s(T74)))))), SCOPE: 40, CLAUSE: 9 | ?_40\n\nT74 is ground\nT76 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T76, T74, X85) !=? minus(X87, 0, X87)\nminus(T76, T74, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(zero(s(s(s(T76)))), ','(!_40, ','(failure(a), no(zero(s(s(s(T74)))))))), SCOPE: 41, CLAUSE: 7 | ','(no(zero(s(s(s(T76))))), no(zero(s(s(s(T74)))))), SCOPE: 40, CLAUSE: 9 | ?_40\n\nT74 is ground\nT76 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T76, T74, X85) !=? minus(X87, 0, X87)\nminus(T76, T74, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(no(zero(s(s(s(T76))))), no(zero(s(s(s(T74)))))), SCOPE: 40, CLAUSE: 9\n\nT74 is ground\nT76 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T76, T74, X85) !=? minus(X87, 0, X87)\nminus(T76, T74, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: no(zero(s(s(s(T74)))))\n\nT74 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T77, T74, X85) !=? minus(X87, 0, X87)\nminus(T77, T74, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: no(zero(s(s(s(T74))))), SCOPE: 42, CLAUSE: 8 | no(zero(s(s(s(T74))))), SCOPE: 42, CLAUSE: 9 | ?_42\n\nT74 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T77, T74, X85) !=? minus(X87, 0, X87)\nminus(T77, T74, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(zero(s(s(s(T78)))), ','(!_42, failure(a))) | no(zero(s(s(s(T78))))), SCOPE: 42, CLAUSE: 9 | ?_42\n\nT78 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T77, T78, X85) !=? minus(X87, 0, X87)\nminus(T77, T78, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: ','(zero(s(s(s(T78)))), ','(!_42, failure(a))), SCOPE: 43, CLAUSE: 7 | no(zero(s(s(s(T78))))), SCOPE: 42, CLAUSE: 9 | ?_42\n\nT78 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T77, T78, X85) !=? minus(X87, 0, X87)\nminus(T77, T78, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: no(zero(s(s(s(T78))))), SCOPE: 42, CLAUSE: 9\n\nT78 is ground\nX85 is free; \nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; \nminus(T77, T78, X85) !=? minus(X87, 0, X87)\nminus(T77, T78, X85) !=? minus(s(X91), s(X92), X93)", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: true\n\nX85 is free\nX87 is free; \nX91 is free; \nX92 is free; \nX93 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: ','(no(zero(s(s(T80)))), no(zero(s(s(T81)))))\n\nT80 is ground\nT81 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T80, T81, X76) !=? minus(X78, 0, X78)\nminus(T80, T81, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: \n\nX76 is free\nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nX191 is free; \nX192 is free; \nX193 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: ','(no(zero(s(s(T80)))), no(zero(s(s(T81))))), SCOPE: 44, CLAUSE: 8 | ','(no(zero(s(s(T80)))), no(zero(s(s(T81))))), SCOPE: 44, CLAUSE: 9 | ?_44\n\nT80 is ground\nT81 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T80, T81, X76) !=? minus(X78, 0, X78)\nminus(T80, T81, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(zero(s(s(T83))), ','(!_44, ','(failure(a), no(zero(s(s(T81))))))) | ','(no(zero(s(s(T83)))), no(zero(s(s(T81))))), SCOPE: 44, CLAUSE: 9 | ?_44\n\nT81 is ground\nT83 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T83, T81, X76) !=? minus(X78, 0, X78)\nminus(T83, T81, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: ','(zero(s(s(T83))), ','(!_44, ','(failure(a), no(zero(s(s(T81))))))), SCOPE: 45, CLAUSE: 7 | ','(no(zero(s(s(T83)))), no(zero(s(s(T81))))), SCOPE: 44, CLAUSE: 9 | ?_44\n\nT81 is ground\nT83 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T83, T81, X76) !=? minus(X78, 0, X78)\nminus(T83, T81, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: ','(no(zero(s(s(T83)))), no(zero(s(s(T81))))), SCOPE: 44, CLAUSE: 9\n\nT81 is ground\nT83 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T83, T81, X76) !=? minus(X78, 0, X78)\nminus(T83, T81, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: no(zero(s(s(T81))))\n\nT81 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T84, T81, X76) !=? minus(X78, 0, X78)\nminus(T84, T81, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: no(zero(s(s(T81)))), SCOPE: 46, CLAUSE: 8 | no(zero(s(s(T81)))), SCOPE: 46, CLAUSE: 9 | ?_46\n\nT81 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T84, T81, X76) !=? minus(X78, 0, X78)\nminus(T84, T81, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: ','(zero(s(s(T85))), ','(!_46, failure(a))) | no(zero(s(s(T85)))), SCOPE: 46, CLAUSE: 9 | ?_46\n\nT85 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T84, T85, X76) !=? minus(X78, 0, X78)\nminus(T84, T85, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(zero(s(s(T85))), ','(!_46, failure(a))), SCOPE: 47, CLAUSE: 7 | no(zero(s(s(T85)))), SCOPE: 46, CLAUSE: 9 | ?_46\n\nT85 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T84, T85, X76) !=? minus(X78, 0, X78)\nminus(T84, T85, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: no(zero(s(s(T85)))), SCOPE: 46, CLAUSE: 9\n\nT85 is ground\nX76 is free; \nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; \nminus(T84, T85, X76) !=? minus(X78, 0, X78)\nminus(T84, T85, X76) !=? minus(s(X82), s(X83), X84)", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: true\n\nX76 is free\nX78 is free; \nX82 is free; \nX83 is free; \nX84 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(no(zero(s(T87))), no(zero(s(T88))))\n\nT87 is ground\nT88 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T87, T88, X67) !=? minus(X69, 0, X69)\nminus(T87, T88, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: \n\nX67 is free\nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nX205 is free; \nX206 is free; \nX207 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: ','(no(zero(s(T87))), no(zero(s(T88)))), SCOPE: 48, CLAUSE: 8 | ','(no(zero(s(T87))), no(zero(s(T88)))), SCOPE: 48, CLAUSE: 9 | ?_48\n\nT87 is ground\nT88 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T87, T88, X67) !=? minus(X69, 0, X69)\nminus(T87, T88, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: ','(zero(s(T90)), ','(!_48, ','(failure(a), no(zero(s(T88)))))) | ','(no(zero(s(T90))), no(zero(s(T88)))), SCOPE: 48, CLAUSE: 9 | ?_48\n\nT88 is ground\nT90 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T90, T88, X67) !=? minus(X69, 0, X69)\nminus(T90, T88, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(zero(s(T90)), ','(!_48, ','(failure(a), no(zero(s(T88)))))), SCOPE: 49, CLAUSE: 7 | ','(no(zero(s(T90))), no(zero(s(T88)))), SCOPE: 48, CLAUSE: 9 | ?_48\n\nT88 is ground\nT90 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T90, T88, X67) !=? minus(X69, 0, X69)\nminus(T90, T88, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: ','(no(zero(s(T90))), no(zero(s(T88)))), SCOPE: 48, CLAUSE: 9\n\nT88 is ground\nT90 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T90, T88, X67) !=? minus(X69, 0, X69)\nminus(T90, T88, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: no(zero(s(T88)))\n\nT88 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T91, T88, X67) !=? minus(X69, 0, X69)\nminus(T91, T88, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: no(zero(s(T88))), SCOPE: 50, CLAUSE: 8 | no(zero(s(T88))), SCOPE: 50, CLAUSE: 9 | ?_50\n\nT88 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T91, T88, X67) !=? minus(X69, 0, X69)\nminus(T91, T88, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: ','(zero(s(T92)), ','(!_50, failure(a))) | no(zero(s(T92))), SCOPE: 50, CLAUSE: 9 | ?_50\n\nT92 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T91, T92, X67) !=? minus(X69, 0, X69)\nminus(T91, T92, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ','(zero(s(T92)), ','(!_50, failure(a))), SCOPE: 51, CLAUSE: 7 | no(zero(s(T92))), SCOPE: 50, CLAUSE: 9 | ?_50\n\nT92 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T91, T92, X67) !=? minus(X69, 0, X69)\nminus(T91, T92, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: no(zero(s(T92))), SCOPE: 50, CLAUSE: 9\n\nT92 is ground\nX67 is free; \nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; \nminus(T91, T92, X67) !=? minus(X69, 0, X69)\nminus(T91, T92, X67) !=? minus(s(X73), s(X74), X75)", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: true\n\nX67 is free\nX69 is free; \nX73 is free; \nX74 is free; \nX75 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: ','(no(zero(T94)), no(zero(T95)))\n\nT94 is ground\nT95 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T94) !=? zero(0)\nzero(T95) !=? zero(0)\nminus(T94, T95, X30) !=? minus(X60, 0, X60)\nminus(T94, T95, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\nX30 is free\nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nX219 is free; \nX220 is free; \nX221 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: ','(no(zero(T94)), no(zero(T95))), SCOPE: 52, CLAUSE: 8 | ','(no(zero(T94)), no(zero(T95))), SCOPE: 52, CLAUSE: 9 | ?_52\n\nT94 is ground\nT95 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T94) !=? zero(0)\nzero(T95) !=? zero(0)\nminus(T94, T95, X30) !=? minus(X60, 0, X60)\nminus(T94, T95, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: ','(zero(T97), ','(!_52, ','(failure(a), no(zero(T95))))) | ','(no(zero(T97)), no(zero(T95))), SCOPE: 52, CLAUSE: 9 | ?_52\n\nT95 is ground\nT97 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T97) !=? zero(0)\nzero(T95) !=? zero(0)\nminus(T97, T95, X30) !=? minus(X60, 0, X60)\nminus(T97, T95, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: ','(zero(T97), ','(!_52, ','(failure(a), no(zero(T95))))), SCOPE: 53, CLAUSE: 7 | ','(no(zero(T97)), no(zero(T95))), SCOPE: 52, CLAUSE: 9 | ?_52\n\nT95 is ground\nT97 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T97) !=? zero(0)\nzero(T95) !=? zero(0)\nminus(T97, T95, X30) !=? minus(X60, 0, X60)\nminus(T97, T95, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(no(zero(T97)), no(zero(T95))), SCOPE: 52, CLAUSE: 9\n\nT95 is ground\nT97 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T97) !=? zero(0)\nzero(T95) !=? zero(0)\nminus(T97, T95, X30) !=? minus(X60, 0, X60)\nminus(T97, T95, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: no(zero(T95))\n\nT95 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T95) !=? zero(0)\nminus(T98, T95, X30) !=? minus(X60, 0, X60)\nminus(T98, T95, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: no(zero(T95)), SCOPE: 54, CLAUSE: 8 | no(zero(T95)), SCOPE: 54, CLAUSE: 9 | ?_54\n\nT95 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T95) !=? zero(0)\nminus(T98, T95, X30) !=? minus(X60, 0, X60)\nminus(T98, T95, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: ','(zero(T99), ','(!_54, failure(a))) | no(zero(T99)), SCOPE: 54, CLAUSE: 9 | ?_54\n\nT99 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T99) !=? zero(0)\nminus(T98, T99, X30) !=? minus(X60, 0, X60)\nminus(T98, T99, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: ','(zero(T99), ','(!_54, failure(a))), SCOPE: 55, CLAUSE: 7 | no(zero(T99)), SCOPE: 54, CLAUSE: 9 | ?_54\n\nT99 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T99) !=? zero(0)\nminus(T98, T99, X30) !=? minus(X60, 0, X60)\nminus(T98, T99, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: no(zero(T99)), SCOPE: 54, CLAUSE: 9\n\nT99 is ground\nX30 is free; \nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; \nzero(T99) !=? zero(0)\nminus(T98, T99, X30) !=? minus(X60, 0, X60)\nminus(T98, T99, X30) !=? minus(s(X64), s(X65), X66)", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: true\n\nX30 is free\nX60 is free; \nX64 is free; \nX65 is free; \nX66 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: ','(no(zero(T101)), no(zero(T102)))\n\nT101 is ground\nT102 is ground\nX26 is free; \nX27 is free; \nX28 is free; \nX29 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: \n\nX26 is free\nX27 is free; \nX28 is free; \nX29 is free; \nX233 is free; \nX234 is free; \nX235 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: ','(no(zero(T101)), no(zero(T102))), SCOPE: 56, CLAUSE: 8 | ','(no(zero(T101)), no(zero(T102))), SCOPE: 56, CLAUSE: 9 | ?_56\n\nT101 is ground\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: ','(zero(T104), ','(!_56, ','(failure(a), no(zero(T102))))) | ','(no(zero(T104)), no(zero(T102))), SCOPE: 56, CLAUSE: 9 | ?_56\n\nT102 is ground\nT104 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: ','(zero(T104), ','(!_56, ','(failure(a), no(zero(T102))))), SCOPE: 57, CLAUSE: 7 | ','(no(zero(T104)), no(zero(T102))), SCOPE: 56, CLAUSE: 9 | ?_56\n\nT102 is ground\nT104 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: ','(!_56, ','(failure(a), no(zero(T102)))) | ','(no(zero(0)), no(zero(T102))), SCOPE: 56, CLAUSE: 9 | ?_56\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: ','(no(zero(T104)), no(zero(T102))), SCOPE: 56, CLAUSE: 9\n\nT102 is ground\nT104 is ground\nzero(T104) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: ','(failure(a), no(zero(T102)))\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: ','(failure(a), no(zero(T102))), SCOPE: 58, CLAUSE: 6\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: no(zero(T102))\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: no(zero(T102)), SCOPE: 59, CLAUSE: 8 | no(zero(T102)), SCOPE: 59, CLAUSE: 9 | ?_59\n\nT102 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: ','(zero(T106), ','(!_59, failure(a))) | no(zero(T106)), SCOPE: 59, CLAUSE: 9 | ?_59\n\nT106 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: ','(zero(T106), ','(!_59, failure(a))), SCOPE: 60, CLAUSE: 7 | no(zero(T106)), SCOPE: 59, CLAUSE: 9 | ?_59\n\nT106 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: ','(!_59, failure(a)) | no(zero(0)), SCOPE: 59, CLAUSE: 9 | ?_59\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: no(zero(T106)), SCOPE: 59, CLAUSE: 9\n\nT106 is ground\nzero(T106) !=? zero(0)", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: failure(a), SCOPE: 61, CLAUSE: 6\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 230 [arrowhead = none ];
230 -> 2;

231 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2 -> 231 [arrowhead = none ];
231 -> 3;

232 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
2 -> 232 [arrowhead = none ];
232 -> 4;

233 [label="EVAL with clause\ndiv(X12, 0, X13, X14) :- failure(a).\nand substitution\nT1 -> T5\nX12 -> T5\nT2 -> 0\nT3 -> T6\nX13 -> T6\nT4 -> T7\nX14 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
3 -> 233 [arrowhead = none ];
233 -> 5;

234 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
3 -> 234 [arrowhead = none ];
234 -> 6;

235 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 235 [arrowhead = none ];
235 -> 9;

236 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 236 [arrowhead = none ];
236 -> 10;

237 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5 -> 237 [arrowhead = none ];
237 -> 7;

238 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
7 -> 238 [arrowhead = none ];
238 -> 8;

239 [label="EVAL with clause\ndiv(0, X17, 0, 0) :- no(zero(X17)).\nand substitution\nT1 -> 0\nT2 -> T8\nX17 -> T8\nT3 -> 0\nT4 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 239 [arrowhead = none ];
239 -> 11;

240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 240 [arrowhead = none ];
240 -> 12;

241 [label="EVAL with clause\ndiv(X26, X27, s(X28), X29) :- ','(no(zero(X26)), ','(no(zero(X27)), ','(minus(X26, X27, X30), ','(!, div(X30, X27, X28, X29))))).\nand substitution\nT1 -> T11\nX26 -> T11\nT2 -> T12\nX27 -> T12\nX28 -> T15\nT3 -> s(T15)\nT4 -> T16\nX29 -> T16\nT13 -> T15\nT14 -> T16", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 241 [arrowhead = none ];
241 -> 23;

242 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 242 [arrowhead = none ];
242 -> 24;

243 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
11 -> 243 [arrowhead = none ];
243 -> 13;

244 [label="EVAL with clause\nno(X19) :- ','(X19, ','(!, failure(a))).\nand substitution\nT8 -> T9\nX19 -> zero(T9)", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 244 [arrowhead = none ];
244 -> 14;

245 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 245 [arrowhead = none ];
245 -> 15;

246 [label="EVAL with clause\nzero(0).\nand substitution\nT9 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 246 [arrowhead = none ];
246 -> 16;

247 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 247 [arrowhead = none ];
247 -> 17;

248 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 248 [arrowhead = none ];
248 -> 18;

249 [label="EVAL with clause\nno(X21).\nand substitution\nT9 -> T10\nX21 -> zero(T10)", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 249 [arrowhead = none ];
249 -> 21;

250 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
18 -> 250 [arrowhead = none ];
250 -> 19;

251 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
19 -> 251 [arrowhead = none ];
251 -> 20;

252 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 252 [arrowhead = none ];
252 -> 22;

253 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
23 -> 253 [arrowhead = none ];
253 -> 25;

254 [label="EVAL with clause\ndiv(X233, X234, X235, X233) :- ','(no(zero(X233)), no(zero(X234))).\nand substitution\nT1 -> T101\nX233 -> T101\nT2 -> T102\nX234 -> T102\nT3 -> T103\nX235 -> T103\nT4 -> T101", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 254 [arrowhead = none ];
254 -> 209;

255 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 255 [arrowhead = none ];
255 -> 210;

256 [label="EVAL with clause\nno(X32) :- ','(X32, ','(!, failure(a))).\nand substitution\nT11 -> T17\nX32 -> zero(T17)", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 256 [arrowhead = none ];
256 -> 26;

257 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
26 -> 257 [arrowhead = none ];
257 -> 27;

258 [label="EVAL with clause\nzero(0).\nand substitution\nT17 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 258 [arrowhead = none ];
258 -> 28;

259 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 259 [arrowhead = none ];
259 -> 29;

260 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
28 -> 260 [arrowhead = none ];
260 -> 30;

261 [label="EVAL with clause\nno(X42).\nand substitution\nT17 -> T20\nX42 -> zero(T20)", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 261 [arrowhead = none ];
261 -> 42;

262 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
30 -> 262 [arrowhead = none ];
262 -> 31;

263 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
31 -> 263 [arrowhead = none ];
263 -> 32;

264 [label="EVAL with clause\ndiv(X36, X37, X38, X36) :- ','(no(zero(X36)), no(zero(X37))).\nand substitution\nX36 -> 0\nT12 -> T18\nX37 -> T18\nT3 -> T19\nX38 -> T19\nT4 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 264 [arrowhead = none ];
264 -> 33;

265 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 265 [arrowhead = none ];
265 -> 34;

266 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 266 [arrowhead = none ];
266 -> 35;

267 [label="EVAL with clause\nno(X40) :- ','(X40, ','(!, failure(a))).\nand substitution\nX40 -> zero(0)", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 267 [arrowhead = none ];
267 -> 36;

268 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
36 -> 268 [arrowhead = none ];
268 -> 37;

269 [label="EVAL with clause\nzero(0).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 269 [arrowhead = none ];
269 -> 38;

270 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 270 [arrowhead = none ];
270 -> 39;

271 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 271 [arrowhead = none ];
271 -> 40;

272 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
40 -> 272 [arrowhead = none ];
272 -> 41;

273 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
42 -> 273 [arrowhead = none ];
273 -> 43;

274 [label="EVAL with clause\nno(X44) :- ','(X44, ','(!, failure(a))).\nand substitution\nT12 -> T21\nX44 -> zero(T21)", fontsize=14, style = filled, fillcolor = lightblue];
43 -> 274 [arrowhead = none ];
274 -> 44;

275 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
44 -> 275 [arrowhead = none ];
275 -> 45;

276 [label="EVAL with clause\nzero(0).\nand substitution\nT21 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 276 [arrowhead = none ];
276 -> 46;

277 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 277 [arrowhead = none ];
277 -> 47;

278 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 278 [arrowhead = none ];
278 -> 48;

279 [label="EVAL with clause\nno(X58).\nand substitution\nT21 -> T26\nX58 -> zero(T26)", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 279 [arrowhead = none ];
279 -> 65;

280 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
48 -> 280 [arrowhead = none ];
280 -> 49;

281 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
49 -> 281 [arrowhead = none ];
281 -> 50;

282 [label="EVAL with clause\ndiv(X48, X49, X50, X48) :- ','(no(zero(X48)), no(zero(X49))).\nand substitution\nT20 -> T22\nX48 -> T22\nX49 -> 0\nT3 -> T23\nX50 -> T23\nT4 -> T22", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 282 [arrowhead = none ];
282 -> 51;

283 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 283 [arrowhead = none ];
283 -> 52;

284 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
51 -> 284 [arrowhead = none ];
284 -> 53;

285 [label="EVAL with clause\nno(X52) :- ','(X52, ','(!, failure(a))).\nand substitution\nT22 -> T24\nX52 -> zero(T24)", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 285 [arrowhead = none ];
285 -> 54;

286 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 286 [arrowhead = none ];
286 -> 55;

287 [label="BACKTRACK\nfor clause: zero(0)\nwith clash: (zero(T24), zero(0))", fontsize=14, style = filled, fillcolor = white];
55 -> 287 [arrowhead = none ];
287 -> 56;

288 [label="EVAL with clause\nno(X54).\nand substitution\nT24 -> T25\nX54 -> zero(T25)", fontsize=14, style = filled, fillcolor = lightblue];
56 -> 288 [arrowhead = none ];
288 -> 57;

289 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
57 -> 289 [arrowhead = none ];
289 -> 58;

290 [label="EVAL with clause\nno(X56) :- ','(X56, ','(!, failure(a))).\nand substitution\nX56 -> zero(0)", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 290 [arrowhead = none ];
290 -> 59;

291 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
59 -> 291 [arrowhead = none ];
291 -> 60;

292 [label="EVAL with clause\nzero(0).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
60 -> 292 [arrowhead = none ];
292 -> 61;

293 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 293 [arrowhead = none ];
293 -> 62;

294 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
62 -> 294 [arrowhead = none ];
294 -> 63;

295 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
63 -> 295 [arrowhead = none ];
295 -> 64;

296 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
65 -> 296 [arrowhead = none ];
296 -> 66;

297 [label="BACKTRACK\nfor clause: minus(X, 0, X)\nwith clash: (zero(T26), zero(0))", fontsize=14, style = filled, fillcolor = white];
66 -> 297 [arrowhead = none ];
297 -> 67;

298 [label="EVAL with clause\nminus(s(X64), s(X65), X66) :- minus(X64, X65, X66).\nand substitution\nX64 -> T27\nT20 -> s(T27)\nX65 -> T28\nT26 -> s(T28)\nX30 -> X67\nX66 -> X67", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 298 [arrowhead = none ];
298 -> 68;

299 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
67 -> 299 [arrowhead = none ];
299 -> 69;

300 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 300 [arrowhead = none ];
300 -> 70;

301 [label="EVAL with clause\ndiv(X219, X220, X221, X219) :- ','(no(zero(X219)), no(zero(X220))).\nand substitution\nT20 -> T94\nX219 -> T94\nT26 -> T95\nX220 -> T95\nT3 -> T96\nX221 -> T96\nT4 -> T94", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 301 [arrowhead = none ];
301 -> 196;

302 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 302 [arrowhead = none ];
302 -> 197;

303 [label="EVAL with clause\nminus(X69, 0, X69).\nand substitution\nT27 -> T29\nX69 -> T29\nT28 -> 0\nX67 -> T29", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 303 [arrowhead = none ];
303 -> 71;

304 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 304 [arrowhead = none ];
304 -> 72;

305 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 305 [arrowhead = none ];
305 -> 73;

306 [label="EVAL with clause\nminus(s(X73), s(X74), X75) :- minus(X73, X74, X75).\nand substitution\nX73 -> T30\nT27 -> s(T30)\nX74 -> T31\nT28 -> s(T31)\nX67 -> X76\nX75 -> X76", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 306 [arrowhead = none ];
306 -> 74;

307 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 307 [arrowhead = none ];
307 -> 75;

308 [label="INSTANCE with matching:\nT1 -> T29\nT2 -> s(0)\nT3 -> T15\nT4 -> T16", fontsize=14, style = filled, fillcolor = lightgrey];
73 -> 308 [arrowhead = none , style=dashed];
308 -> 1[style=dashed];

309 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
74 -> 309 [arrowhead = none ];
309 -> 76;

310 [label="EVAL with clause\ndiv(X205, X206, X207, X205) :- ','(no(zero(X205)), no(zero(X206))).\nand substitution\nT27 -> T87\nX205 -> s(T87)\nT28 -> T88\nX206 -> s(T88)\nT3 -> T89\nX207 -> T89\nT4 -> s(T87)", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 310 [arrowhead = none ];
310 -> 183;

311 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 311 [arrowhead = none ];
311 -> 184;

312 [label="EVAL with clause\nminus(X78, 0, X78).\nand substitution\nT30 -> T32\nX78 -> T32\nT31 -> 0\nX76 -> T32", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 312 [arrowhead = none ];
312 -> 77;

313 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 313 [arrowhead = none ];
313 -> 78;

314 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
77 -> 314 [arrowhead = none ];
314 -> 79;

315 [label="EVAL with clause\nminus(s(X82), s(X83), X84) :- minus(X82, X83, X84).\nand substitution\nX82 -> T33\nT30 -> s(T33)\nX83 -> T34\nT31 -> s(T34)\nX76 -> X85\nX84 -> X85", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 315 [arrowhead = none ];
315 -> 80;

316 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 316 [arrowhead = none ];
316 -> 81;

317 [label="INSTANCE with matching:\nT1 -> T32\nT2 -> s(s(0))\nT3 -> T15\nT4 -> T16", fontsize=14, style = filled, fillcolor = lightgrey];
79 -> 317 [arrowhead = none , style=dashed];
317 -> 1[style=dashed];

318 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
80 -> 318 [arrowhead = none ];
318 -> 82;

319 [label="EVAL with clause\ndiv(X191, X192, X193, X191) :- ','(no(zero(X191)), no(zero(X192))).\nand substitution\nT30 -> T80\nX191 -> s(s(T80))\nT31 -> T81\nX192 -> s(s(T81))\nT3 -> T82\nX193 -> T82\nT4 -> s(s(T80))", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 319 [arrowhead = none ];
319 -> 170;

320 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 320 [arrowhead = none ];
320 -> 171;

321 [label="EVAL with clause\nminus(X87, 0, X87).\nand substitution\nT33 -> T35\nX87 -> T35\nT34 -> 0\nX85 -> T35", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 321 [arrowhead = none ];
321 -> 83;

322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 322 [arrowhead = none ];
322 -> 84;

323 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 323 [arrowhead = none ];
323 -> 85;

324 [label="EVAL with clause\nminus(s(X91), s(X92), X93) :- minus(X91, X92, X93).\nand substitution\nX91 -> T36\nT33 -> s(T36)\nX92 -> T37\nT34 -> s(T37)\nX85 -> X94\nX93 -> X94", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 324 [arrowhead = none ];
324 -> 86;

325 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 325 [arrowhead = none ];
325 -> 87;

326 [label="INSTANCE with matching:\nT1 -> T35\nT2 -> s(s(s(0)))\nT3 -> T15\nT4 -> T16", fontsize=14, style = filled, fillcolor = lightgrey];
85 -> 326 [arrowhead = none , style=dashed];
326 -> 1[style=dashed];

327 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
86 -> 327 [arrowhead = none ];
327 -> 88;

328 [label="EVAL with clause\ndiv(X177, X178, X179, X177) :- ','(no(zero(X177)), no(zero(X178))).\nand substitution\nT33 -> T73\nX177 -> s(s(s(T73)))\nT34 -> T74\nX178 -> s(s(s(T74)))\nT3 -> T75\nX179 -> T75\nT4 -> s(s(s(T73)))", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 328 [arrowhead = none ];
328 -> 157;

329 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
87 -> 329 [arrowhead = none ];
329 -> 158;

330 [label="EVAL with clause\nminus(X96, 0, X96).\nand substitution\nT36 -> T38\nX96 -> T38\nT37 -> 0\nX94 -> T38", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 330 [arrowhead = none ];
330 -> 89;

331 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 331 [arrowhead = none ];
331 -> 90;

332 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 332 [arrowhead = none ];
332 -> 91;

333 [label="EVAL with clause\nminus(s(X100), s(X101), X102) :- minus(X100, X101, X102).\nand substitution\nX100 -> T39\nT36 -> s(T39)\nX101 -> T40\nT37 -> s(T40)\nX94 -> X103\nX102 -> X103", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 333 [arrowhead = none ];
333 -> 92;

334 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 334 [arrowhead = none ];
334 -> 93;

335 [label="INSTANCE with matching:\nT1 -> T38\nT2 -> s(s(s(s(0))))\nT3 -> T15\nT4 -> T16", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 335 [arrowhead = none , style=dashed];
335 -> 1[style=dashed];

336 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
92 -> 336 [arrowhead = none ];
336 -> 94;

337 [label="EVAL with clause\ndiv(X163, X164, X165, X163) :- ','(no(zero(X163)), no(zero(X164))).\nand substitution\nT36 -> T66\nX163 -> s(s(s(s(T66))))\nT37 -> T67\nX164 -> s(s(s(s(T67))))\nT3 -> T68\nX165 -> T68\nT4 -> s(s(s(s(T66))))", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 337 [arrowhead = none ];
337 -> 144;

338 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 338 [arrowhead = none ];
338 -> 145;

339 [label="EVAL with clause\nminus(X105, 0, X105).\nand substitution\nT39 -> T41\nX105 -> T41\nT40 -> 0\nX103 -> T41", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 339 [arrowhead = none ];
339 -> 95;

340 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 340 [arrowhead = none ];
340 -> 96;

341 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 341 [arrowhead = none ];
341 -> 97;

342 [label="EVAL with clause\nminus(s(X109), s(X110), X111) :- minus(X109, X110, X111).\nand substitution\nX109 -> T42\nT39 -> s(T42)\nX110 -> T43\nT40 -> s(T43)\nX103 -> X112\nX111 -> X112", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 342 [arrowhead = none ];
342 -> 98;

343 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 343 [arrowhead = none ];
343 -> 99;

344 [label="INSTANCE with matching:\nT1 -> T41\nT2 -> s(s(s(s(s(0)))))\nT3 -> T15\nT4 -> T16", fontsize=14, style = filled, fillcolor = lightgrey];
97 -> 344 [arrowhead = none , style=dashed];
344 -> 1[style=dashed];

345 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
98 -> 345 [arrowhead = none ];
345 -> 100;

346 [label="EVAL with clause\ndiv(X149, X150, X151, X149) :- ','(no(zero(X149)), no(zero(X150))).\nand substitution\nT39 -> T59\nX149 -> s(s(s(s(s(T59)))))\nT40 -> T60\nX150 -> s(s(s(s(s(T60)))))\nT3 -> T61\nX151 -> T61\nT4 -> s(s(s(s(s(T59)))))", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 346 [arrowhead = none ];
346 -> 131;

347 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
99 -> 347 [arrowhead = none ];
347 -> 132;

348 [label="EVAL with clause\nminus(X114, 0, X114).\nand substitution\nT42 -> T44\nX114 -> T44\nT43 -> 0\nX112 -> T44", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 348 [arrowhead = none ];
348 -> 101;

349 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 349 [arrowhead = none ];
349 -> 102;

350 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 350 [arrowhead = none ];
350 -> 103;

351 [label="EVAL with clause\nminus(s(X118), s(X119), X120) :- minus(X118, X119, X120).\nand substitution\nX118 -> T45\nT42 -> s(T45)\nX119 -> T46\nT43 -> s(T46)\nX112 -> X121\nX120 -> X121", fontsize=14, style = filled, fillcolor = lightblue];
102 -> 351 [arrowhead = none ];
351 -> 104;

352 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
102 -> 352 [arrowhead = none ];
352 -> 105;

353 [label="INSTANCE with matching:\nT1 -> T44\nT2 -> s(s(s(s(s(s(0))))))\nT3 -> T15\nT4 -> T16", fontsize=14, style = filled, fillcolor = lightgrey];
103 -> 353 [arrowhead = none , style=dashed];
353 -> 1[style=dashed];

354 [label="GENERALIZATION\nT47 <-- s(s(s(s(s(s(T46))))))\n\nNew Knowledge:\nT47 is ground", fontsize=14, style = filled, fillcolor = violet];
104 -> 354 [arrowhead = none ];
354 -> 106;

355 [label="EVAL with clause\ndiv(X135, X136, X137, X135) :- ','(no(zero(X135)), no(zero(X136))).\nand substitution\nT42 -> T52\nX135 -> s(s(s(s(s(s(T52))))))\nT43 -> T53\nX136 -> s(s(s(s(s(s(T53))))))\nT3 -> T54\nX137 -> T54\nT4 -> s(s(s(s(s(s(T52))))))", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 355 [arrowhead = none ];
355 -> 118;

356 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 356 [arrowhead = none ];
356 -> 119;

357 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
106 -> 357 [arrowhead = none ];
357 -> 107;

358 [label="SPLIT 2\nnew knowledge:\nT48 is ground\nreplacements:\nX121 -> T48", fontsize=14, style = filled, fillcolor = violet];
106 -> 358 [arrowhead = none ];
358 -> 108;

359 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
107 -> 359 [arrowhead = none ];
359 -> 109;

360 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
108 -> 360 [arrowhead = none ];
360 -> 117;

361 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
109 -> 361 [arrowhead = none ];
361 -> 110;

362 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
109 -> 362 [arrowhead = none ];
362 -> 111;

363 [label="EVAL with clause\nminus(X124, 0, X124).\nand substitution\nT45 -> T49\nX124 -> T49\nT46 -> 0\nX121 -> T49", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 363 [arrowhead = none ];
363 -> 112;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 364 [arrowhead = none ];
364 -> 113;

365 [label="EVAL with clause\nminus(s(X128), s(X129), X130) :- minus(X128, X129, X130).\nand substitution\nX128 -> T50\nT45 -> s(T50)\nX129 -> T51\nT46 -> s(T51)\nX121 -> X131\nX130 -> X131", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 365 [arrowhead = none ];
365 -> 115;

366 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 366 [arrowhead = none ];
366 -> 116;

367 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 367 [arrowhead = none ];
367 -> 114;

368 [label="INSTANCE with matching:\nT45 -> T50\nT46 -> T51\nX121 -> X131", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 368 [arrowhead = none , style=dashed];
368 -> 107[style=dashed];

369 [label="INSTANCE with matching:\nT1 -> T48\nT2 -> s(T47)\nT3 -> T15\nT4 -> T16", fontsize=14, style = filled, fillcolor = lightgrey];
117 -> 369 [arrowhead = none , style=dashed];
369 -> 1[style=dashed];

370 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 370 [arrowhead = none ];
370 -> 120;

371 [label="EVAL with clause\nno(X139) :- ','(X139, ','(!, failure(a))).\nand substitution\nT52 -> T55\nX139 -> zero(s(s(s(s(s(s(T55)))))))", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 371 [arrowhead = none ];
371 -> 121;

372 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
121 -> 372 [arrowhead = none ];
372 -> 122;

373 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
122 -> 373 [arrowhead = none ];
373 -> 123;

374 [label="EVAL with clause\nno(X141).\nand substitution\nT55 -> T56\nX141 -> zero(s(s(s(s(s(s(T56)))))))", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 374 [arrowhead = none ];
374 -> 124;

375 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
124 -> 375 [arrowhead = none ];
375 -> 125;

376 [label="EVAL with clause\nno(X143) :- ','(X143, ','(!, failure(a))).\nand substitution\nT53 -> T57\nX143 -> zero(s(s(s(s(s(s(T57)))))))", fontsize=14, style = filled, fillcolor = lightblue];
125 -> 376 [arrowhead = none ];
376 -> 126;

377 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
126 -> 377 [arrowhead = none ];
377 -> 127;

378 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
127 -> 378 [arrowhead = none ];
378 -> 128;

379 [label="EVAL with clause\nno(X145).\nand substitution\nT57 -> T58\nX145 -> zero(s(s(s(s(s(s(T58)))))))", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 379 [arrowhead = none ];
379 -> 129;

380 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 380 [arrowhead = none ];
380 -> 130;

381 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
131 -> 381 [arrowhead = none ];
381 -> 133;

382 [label="EVAL with clause\nno(X153) :- ','(X153, ','(!, failure(a))).\nand substitution\nT59 -> T62\nX153 -> zero(s(s(s(s(s(T62))))))", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 382 [arrowhead = none ];
382 -> 134;

383 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
134 -> 383 [arrowhead = none ];
383 -> 135;

384 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
135 -> 384 [arrowhead = none ];
384 -> 136;

385 [label="EVAL with clause\nno(X155).\nand substitution\nT62 -> T63\nX155 -> zero(s(s(s(s(s(T63))))))", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 385 [arrowhead = none ];
385 -> 137;

386 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
137 -> 386 [arrowhead = none ];
386 -> 138;

387 [label="EVAL with clause\nno(X157) :- ','(X157, ','(!, failure(a))).\nand substitution\nT60 -> T64\nX157 -> zero(s(s(s(s(s(T64))))))", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 387 [arrowhead = none ];
387 -> 139;

388 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
139 -> 388 [arrowhead = none ];
388 -> 140;

389 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
140 -> 389 [arrowhead = none ];
389 -> 141;

390 [label="EVAL with clause\nno(X159).\nand substitution\nT64 -> T65\nX159 -> zero(s(s(s(s(s(T65))))))", fontsize=14, style = filled, fillcolor = lightblue];
141 -> 390 [arrowhead = none ];
390 -> 142;

391 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 391 [arrowhead = none ];
391 -> 143;

392 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
144 -> 392 [arrowhead = none ];
392 -> 146;

393 [label="EVAL with clause\nno(X167) :- ','(X167, ','(!, failure(a))).\nand substitution\nT66 -> T69\nX167 -> zero(s(s(s(s(T69)))))", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 393 [arrowhead = none ];
393 -> 147;

394 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
147 -> 394 [arrowhead = none ];
394 -> 148;

395 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
148 -> 395 [arrowhead = none ];
395 -> 149;

396 [label="EVAL with clause\nno(X169).\nand substitution\nT69 -> T70\nX169 -> zero(s(s(s(s(T70)))))", fontsize=14, style = filled, fillcolor = lightblue];
149 -> 396 [arrowhead = none ];
396 -> 150;

397 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
150 -> 397 [arrowhead = none ];
397 -> 151;

398 [label="EVAL with clause\nno(X171) :- ','(X171, ','(!, failure(a))).\nand substitution\nT67 -> T71\nX171 -> zero(s(s(s(s(T71)))))", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 398 [arrowhead = none ];
398 -> 152;

399 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
152 -> 399 [arrowhead = none ];
399 -> 153;

400 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
153 -> 400 [arrowhead = none ];
400 -> 154;

401 [label="EVAL with clause\nno(X173).\nand substitution\nT71 -> T72\nX173 -> zero(s(s(s(s(T72)))))", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 401 [arrowhead = none ];
401 -> 155;

402 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 402 [arrowhead = none ];
402 -> 156;

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

404 [label="EVAL with clause\nno(X181) :- ','(X181, ','(!, failure(a))).\nand substitution\nT73 -> T76\nX181 -> zero(s(s(s(T76))))", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 404 [arrowhead = none ];
404 -> 160;

405 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
160 -> 405 [arrowhead = none ];
405 -> 161;

406 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
161 -> 406 [arrowhead = none ];
406 -> 162;

407 [label="EVAL with clause\nno(X183).\nand substitution\nT76 -> T77\nX183 -> zero(s(s(s(T77))))", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 407 [arrowhead = none ];
407 -> 163;

408 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
163 -> 408 [arrowhead = none ];
408 -> 164;

409 [label="EVAL with clause\nno(X185) :- ','(X185, ','(!, failure(a))).\nand substitution\nT74 -> T78\nX185 -> zero(s(s(s(T78))))", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 409 [arrowhead = none ];
409 -> 165;

410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
165 -> 410 [arrowhead = none ];
410 -> 166;

411 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
166 -> 411 [arrowhead = none ];
411 -> 167;

412 [label="EVAL with clause\nno(X187).\nand substitution\nT78 -> T79\nX187 -> zero(s(s(s(T79))))", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 412 [arrowhead = none ];
412 -> 168;

413 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 413 [arrowhead = none ];
413 -> 169;

414 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
170 -> 414 [arrowhead = none ];
414 -> 172;

415 [label="EVAL with clause\nno(X195) :- ','(X195, ','(!, failure(a))).\nand substitution\nT80 -> T83\nX195 -> zero(s(s(T83)))", fontsize=14, style = filled, fillcolor = lightblue];
172 -> 415 [arrowhead = none ];
415 -> 173;

416 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
173 -> 416 [arrowhead = none ];
416 -> 174;

417 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
174 -> 417 [arrowhead = none ];
417 -> 175;

418 [label="EVAL with clause\nno(X197).\nand substitution\nT83 -> T84\nX197 -> zero(s(s(T84)))", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 418 [arrowhead = none ];
418 -> 176;

419 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
176 -> 419 [arrowhead = none ];
419 -> 177;

420 [label="EVAL with clause\nno(X199) :- ','(X199, ','(!, failure(a))).\nand substitution\nT81 -> T85\nX199 -> zero(s(s(T85)))", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 420 [arrowhead = none ];
420 -> 178;

421 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
178 -> 421 [arrowhead = none ];
421 -> 179;

422 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
179 -> 422 [arrowhead = none ];
422 -> 180;

423 [label="EVAL with clause\nno(X201).\nand substitution\nT85 -> T86\nX201 -> zero(s(s(T86)))", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 423 [arrowhead = none ];
423 -> 181;

424 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 424 [arrowhead = none ];
424 -> 182;

425 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
183 -> 425 [arrowhead = none ];
425 -> 185;

426 [label="EVAL with clause\nno(X209) :- ','(X209, ','(!, failure(a))).\nand substitution\nT87 -> T90\nX209 -> zero(s(T90))", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 426 [arrowhead = none ];
426 -> 186;

427 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
186 -> 427 [arrowhead = none ];
427 -> 187;

428 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
187 -> 428 [arrowhead = none ];
428 -> 188;

429 [label="EVAL with clause\nno(X211).\nand substitution\nT90 -> T91\nX211 -> zero(s(T91))", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 429 [arrowhead = none ];
429 -> 189;

430 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
189 -> 430 [arrowhead = none ];
430 -> 190;

431 [label="EVAL with clause\nno(X213) :- ','(X213, ','(!, failure(a))).\nand substitution\nT88 -> T92\nX213 -> zero(s(T92))", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 431 [arrowhead = none ];
431 -> 191;

432 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
191 -> 432 [arrowhead = none ];
432 -> 192;

433 [label="BACKTRACK\nfor clause: zero(0)because of non-unification", fontsize=14, style = filled, fillcolor = white];
192 -> 433 [arrowhead = none ];
433 -> 193;

434 [label="EVAL with clause\nno(X215).\nand substitution\nT92 -> T93\nX215 -> zero(s(T93))", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 434 [arrowhead = none ];
434 -> 194;

435 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
194 -> 435 [arrowhead = none ];
435 -> 195;

436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
196 -> 436 [arrowhead = none ];
436 -> 198;

437 [label="EVAL with clause\nno(X223) :- ','(X223, ','(!, failure(a))).\nand substitution\nT94 -> T97\nX223 -> zero(T97)", fontsize=14, style = filled, fillcolor = lightblue];
198 -> 437 [arrowhead = none ];
437 -> 199;

438 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
199 -> 438 [arrowhead = none ];
438 -> 200;

439 [label="BACKTRACK\nfor clause: zero(0)\nwith clash: (zero(T97), zero(0))", fontsize=14, style = filled, fillcolor = white];
200 -> 439 [arrowhead = none ];
439 -> 201;

440 [label="EVAL with clause\nno(X225).\nand substitution\nT97 -> T98\nX225 -> zero(T98)", fontsize=14, style = filled, fillcolor = lightblue];
201 -> 440 [arrowhead = none ];
440 -> 202;

441 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
202 -> 441 [arrowhead = none ];
441 -> 203;

442 [label="EVAL with clause\nno(X227) :- ','(X227, ','(!, failure(a))).\nand substitution\nT95 -> T99\nX227 -> zero(T99)", fontsize=14, style = filled, fillcolor = lightblue];
203 -> 442 [arrowhead = none ];
442 -> 204;

443 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
204 -> 443 [arrowhead = none ];
443 -> 205;

444 [label="BACKTRACK\nfor clause: zero(0)\nwith clash: (zero(T99), zero(0))", fontsize=14, style = filled, fillcolor = white];
205 -> 444 [arrowhead = none ];
444 -> 206;

445 [label="EVAL with clause\nno(X229).\nand substitution\nT99 -> T100\nX229 -> zero(T100)", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 445 [arrowhead = none ];
445 -> 207;

446 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
207 -> 446 [arrowhead = none ];
446 -> 208;

447 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
209 -> 447 [arrowhead = none ];
447 -> 211;

448 [label="EVAL with clause\nno(X237) :- ','(X237, ','(!, failure(a))).\nand substitution\nT101 -> T104\nX237 -> zero(T104)", fontsize=14, style = filled, fillcolor = lightblue];
211 -> 448 [arrowhead = none ];
448 -> 212;

449 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
212 -> 449 [arrowhead = none ];
449 -> 213;

450 [label="EVAL with clause\nzero(0).\nand substitution\nT104 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 450 [arrowhead = none ];
450 -> 214;

451 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
213 -> 451 [arrowhead = none ];
451 -> 215;

452 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
214 -> 452 [arrowhead = none ];
452 -> 216;

453 [label="EVAL with clause\nno(X239).\nand substitution\nT104 -> T105\nX239 -> zero(T105)", fontsize=14, style = filled, fillcolor = lightblue];
215 -> 453 [arrowhead = none ];
453 -> 219;

454 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
216 -> 454 [arrowhead = none ];
454 -> 217;

455 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
217 -> 455 [arrowhead = none ];
455 -> 218;

456 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
219 -> 456 [arrowhead = none ];
456 -> 220;

457 [label="EVAL with clause\nno(X241) :- ','(X241, ','(!, failure(a))).\nand substitution\nT102 -> T106\nX241 -> zero(T106)", fontsize=14, style = filled, fillcolor = lightblue];
220 -> 457 [arrowhead = none ];
457 -> 221;

458 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
221 -> 458 [arrowhead = none ];
458 -> 222;

459 [label="EVAL with clause\nzero(0).\nand substitution\nT106 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
222 -> 459 [arrowhead = none ];
459 -> 223;

460 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
222 -> 460 [arrowhead = none ];
460 -> 224;

461 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
223 -> 461 [arrowhead = none ];
461 -> 225;

462 [label="EVAL with clause\nno(X243).\nand substitution\nT106 -> T107\nX243 -> zero(T107)", fontsize=14, style = filled, fillcolor = lightblue];
224 -> 462 [arrowhead = none ];
462 -> 228;

463 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
225 -> 463 [arrowhead = none ];
463 -> 226;

464 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
226 -> 464 [arrowhead = none ];
464 -> 227;

465 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
228 -> 465 [arrowhead = none ];
465 -> 229;

}

(2) Obligation:

Clauses:

div1(0, T10, 0, 0).
div1(s(T29), s(0), s(T15), T16) :- div1(T29, s(0), T15, T16).
div1(s(s(T32)), s(s(0)), s(T15), T16) :- div1(T32, s(s(0)), T15, T16).
div1(s(s(s(T35))), s(s(s(0))), s(T15), T16) :- div1(T35, s(s(s(0))), T15, T16).
div1(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) :- div1(T38, s(s(s(s(0)))), T15, T16).
div1(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) :- div1(T41, s(s(s(s(s(0))))), T15, T16).
div1(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) :- div1(T44, s(s(s(s(s(s(0)))))), T15, T16).
div1(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) :- minus107(T45, T46, X121).
div1(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) :- ','(minus107(T45, T46, T48), div1(T48, s(T47), T15, T16)).
div1(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))).
div1(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))).
div1(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))).
div1(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))).
div1(s(s(T84)), s(s(T86)), T82, s(s(T84))).
div1(s(T91), s(T93), T89, s(T91)).
div1(T98, T100, T96, T98).
div1(T105, T107, T103, T105).
minus107(T49, 0, T49).
minus107(s(T50), s(T51), X131) :- minus107(T50, T51, X131).

Queries:

div1(g,g,a,a).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
div1_in: (b,b,f,f) (b,f,f,f)
minus107_in: (b,b,f) (b,f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

DIV1_IN_GGAA(s(T29), s(0), s(T15), T16) → U1_GGAA(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
DIV1_IN_GGAA(s(T29), s(0), s(T15), T16) → DIV1_IN_GGAA(T29, s(0), T15, T16)
DIV1_IN_GGAA(s(s(T32)), s(s(0)), s(T15), T16) → U2_GGAA(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
DIV1_IN_GGAA(s(s(T32)), s(s(0)), s(T15), T16) → DIV1_IN_GGAA(T32, s(s(0)), T15, T16)
DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_GGAA(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → DIV1_IN_GGAA(T35, s(s(s(0))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_GGAA(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → DIV1_IN_GGAA(T38, s(s(s(s(0)))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_GGAA(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_GGAA(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_GGAA(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
DIV1_IN_GGAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → MINUS107_IN_GGA(T45, T46, X121)
MINUS107_IN_GGA(s(T50), s(T51), X131) → U10_GGA(T50, T51, X131, minus107_in_gga(T50, T51, X131))
MINUS107_IN_GGA(s(T50), s(T51), X131) → MINUS107_IN_GGA(T50, T51, X131)
DIV1_IN_GGAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_GGAA(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_GGAA(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_GGAA(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
U8_GGAA(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → DIV1_IN_GAAA(T48, s(T47), T15, T16)
DIV1_IN_GAAA(s(T29), s(0), s(T15), T16) → U1_GAAA(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
DIV1_IN_GAAA(s(T29), s(0), s(T15), T16) → DIV1_IN_GGAA(T29, s(0), T15, T16)
DIV1_IN_GAAA(s(s(T32)), s(s(0)), s(T15), T16) → U2_GAAA(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
DIV1_IN_GAAA(s(s(T32)), s(s(0)), s(T15), T16) → DIV1_IN_GGAA(T32, s(s(0)), T15, T16)
DIV1_IN_GAAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_GAAA(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
DIV1_IN_GAAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → DIV1_IN_GGAA(T35, s(s(s(0))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_GAAA(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
DIV1_IN_GAAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → DIV1_IN_GGAA(T38, s(s(s(s(0)))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_GAAA(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
DIV1_IN_GAAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_GAAA(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
DIV1_IN_GAAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_GAAA(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → MINUS107_IN_GAA(T45, T46, X121)
MINUS107_IN_GAA(s(T50), s(T51), X131) → U10_GAA(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
MINUS107_IN_GAA(s(T50), s(T51), X131) → MINUS107_IN_GAA(T50, T51, X131)
DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_GAAA(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_GAAA(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_GAAA(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
U8_GAAA(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → DIV1_IN_GAAA(T48, s(T47), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

The argument filtering Pi contains the following mapping:
div1_in_ggaa(x1, x2, x3, x4) = div1_in_ggaa(x1, x2)
0 = 0
div1_out_ggaa(x1, x2, x3, x4) = div1_out_ggaa
s(x1) = s(x1)
U1_ggaa(x1, x2, x3, x4) = U1_ggaa(x4)
U2_ggaa(x1, x2, x3, x4) = U2_ggaa(x4)
U3_ggaa(x1, x2, x3, x4) = U3_ggaa(x4)
U4_ggaa(x1, x2, x3, x4) = U4_ggaa(x4)
U5_ggaa(x1, x2, x3, x4) = U5_ggaa(x4)
U6_ggaa(x1, x2, x3, x4) = U6_ggaa(x4)
U7_ggaa(x1, x2, x3, x4, x5) = U7_ggaa(x5)
minus107_in_gga(x1, x2, x3) = minus107_in_gga(x1, x2)
minus107_out_gga(x1, x2, x3) = minus107_out_gga(x3)
U10_gga(x1, x2, x3, x4) = U10_gga(x4)
U8_ggaa(x1, x2, x3, x4, x5) = U8_ggaa(x5)
U9_ggaa(x1, x2, x3, x4, x5) = U9_ggaa(x5)
div1_in_gaaa(x1, x2, x3, x4) = div1_in_gaaa(x1)
div1_out_gaaa(x1, x2, x3, x4) = div1_out_gaaa
U1_gaaa(x1, x2, x3, x4) = U1_gaaa(x4)
U2_gaaa(x1, x2, x3, x4) = U2_gaaa(x4)
U3_gaaa(x1, x2, x3, x4) = U3_gaaa(x4)
U4_gaaa(x1, x2, x3, x4) = U4_gaaa(x4)
U5_gaaa(x1, x2, x3, x4) = U5_gaaa(x4)
U6_gaaa(x1, x2, x3, x4) = U6_gaaa(x4)
U7_gaaa(x1, x2, x3, x4, x5) = U7_gaaa(x5)
minus107_in_gaa(x1, x2, x3) = minus107_in_gaa(x1)
minus107_out_gaa(x1, x2, x3) = minus107_out_gaa(x2, x3)
U10_gaa(x1, x2, x3, x4) = U10_gaa(x4)
U8_gaaa(x1, x2, x3, x4, x5) = U8_gaaa(x5)
U9_gaaa(x1, x2, x3, x4, x5) = U9_gaaa(x5)
DIV1_IN_GGAA(x1, x2, x3, x4) = DIV1_IN_GGAA(x1, x2)
U1_GGAA(x1, x2, x3, x4) = U1_GGAA(x4)
U2_GGAA(x1, x2, x3, x4) = U2_GGAA(x4)
U3_GGAA(x1, x2, x3, x4) = U3_GGAA(x4)
U4_GGAA(x1, x2, x3, x4) = U4_GGAA(x4)
U5_GGAA(x1, x2, x3, x4) = U5_GGAA(x4)
U6_GGAA(x1, x2, x3, x4) = U6_GGAA(x4)
U7_GGAA(x1, x2, x3, x4, x5) = U7_GGAA(x5)
MINUS107_IN_GGA(x1, x2, x3) = MINUS107_IN_GGA(x1, x2)
U10_GGA(x1, x2, x3, x4) = U10_GGA(x4)
U8_GGAA(x1, x2, x3, x4, x5) = U8_GGAA(x5)
U9_GGAA(x1, x2, x3, x4, x5) = U9_GGAA(x5)
DIV1_IN_GAAA(x1, x2, x3, x4) = DIV1_IN_GAAA(x1)
U1_GAAA(x1, x2, x3, x4) = U1_GAAA(x4)
U2_GAAA(x1, x2, x3, x4) = U2_GAAA(x4)
U3_GAAA(x1, x2, x3, x4) = U3_GAAA(x4)
U4_GAAA(x1, x2, x3, x4) = U4_GAAA(x4)
U5_GAAA(x1, x2, x3, x4) = U5_GAAA(x4)
U6_GAAA(x1, x2, x3, x4) = U6_GAAA(x4)
U7_GAAA(x1, x2, x3, x4, x5) = U7_GAAA(x5)
MINUS107_IN_GAA(x1, x2, x3) = MINUS107_IN_GAA(x1)
U10_GAA(x1, x2, x3, x4) = U10_GAA(x4)
U8_GAAA(x1, x2, x3, x4, x5) = U8_GAAA(x5)
U9_GAAA(x1, x2, x3, x4, x5) = U9_GAAA(x5)

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

(6) Obligation:

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

DIV1_IN_GGAA(s(T29), s(0), s(T15), T16) → U1_GGAA(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
DIV1_IN_GGAA(s(T29), s(0), s(T15), T16) → DIV1_IN_GGAA(T29, s(0), T15, T16)
DIV1_IN_GGAA(s(s(T32)), s(s(0)), s(T15), T16) → U2_GGAA(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
DIV1_IN_GGAA(s(s(T32)), s(s(0)), s(T15), T16) → DIV1_IN_GGAA(T32, s(s(0)), T15, T16)
DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_GGAA(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → DIV1_IN_GGAA(T35, s(s(s(0))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_GGAA(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → DIV1_IN_GGAA(T38, s(s(s(s(0)))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_GGAA(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_GGAA(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))), T15, T16)
DIV1_IN_GGAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_GGAA(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
DIV1_IN_GGAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → MINUS107_IN_GGA(T45, T46, X121)
MINUS107_IN_GGA(s(T50), s(T51), X131) → U10_GGA(T50, T51, X131, minus107_in_gga(T50, T51, X131))
MINUS107_IN_GGA(s(T50), s(T51), X131) → MINUS107_IN_GGA(T50, T51, X131)
DIV1_IN_GGAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_GGAA(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_GGAA(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_GGAA(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
U8_GGAA(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → DIV1_IN_GAAA(T48, s(T47), T15, T16)
DIV1_IN_GAAA(s(T29), s(0), s(T15), T16) → U1_GAAA(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
DIV1_IN_GAAA(s(T29), s(0), s(T15), T16) → DIV1_IN_GGAA(T29, s(0), T15, T16)
DIV1_IN_GAAA(s(s(T32)), s(s(0)), s(T15), T16) → U2_GAAA(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
DIV1_IN_GAAA(s(s(T32)), s(s(0)), s(T15), T16) → DIV1_IN_GGAA(T32, s(s(0)), T15, T16)
DIV1_IN_GAAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_GAAA(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
DIV1_IN_GAAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → DIV1_IN_GGAA(T35, s(s(s(0))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_GAAA(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
DIV1_IN_GAAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → DIV1_IN_GGAA(T38, s(s(s(s(0)))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_GAAA(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
DIV1_IN_GAAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_GAAA(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
DIV1_IN_GAAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))), T15, T16)
DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_GAAA(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → MINUS107_IN_GAA(T45, T46, X121)
MINUS107_IN_GAA(s(T50), s(T51), X131) → U10_GAA(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
MINUS107_IN_GAA(s(T50), s(T51), X131) → MINUS107_IN_GAA(T50, T51, X131)
DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_GAAA(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_GAAA(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_GAAA(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
U8_GAAA(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → DIV1_IN_GAAA(T48, s(T47), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 9 SCCs with 28 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

MINUS107_IN_GAA(s(T50), s(T51), X131) → MINUS107_IN_GAA(T50, T51, X131)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

MINUS107_IN_GAA(s(T50), s(T51), X131) → MINUS107_IN_GAA(T50, T51, X131)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
MINUS107_IN_GAA(x1, x2, x3) = MINUS107_IN_GAA(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:

MINUS107_IN_GAA(s(T50)) → MINUS107_IN_GAA(T50)

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:

MINUS107_IN_GAA(s(T50)) → MINUS107_IN_GAA(T50)
The graph contains the following edges 1 > 1

(15) TRUE

(16) Obligation:

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

MINUS107_IN_GGA(s(T50), s(T51), X131) → MINUS107_IN_GGA(T50, T51, X131)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

MINUS107_IN_GGA(s(T50), s(T51), X131) → MINUS107_IN_GGA(T50, T51, X131)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1) = s(x1)
MINUS107_IN_GGA(x1, x2, x3) = MINUS107_IN_GGA(x1, x2)

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

MINUS107_IN_GGA(s(T50), s(T51)) → MINUS107_IN_GGA(T50, T51)

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:

MINUS107_IN_GGA(s(T50), s(T51)) → MINUS107_IN_GGA(T50, T51)
The graph contains the following edges 1 > 1, 2 > 2

(22) TRUE

(23) Obligation:

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

DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))), T15, T16)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
DIV1_IN_GGAA(x1, x2, x3, x4) = DIV1_IN_GGAA(x1, x2)

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:

DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0))))))) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))))

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:

DIV1_IN_GGAA(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0))))))) → DIV1_IN_GGAA(T44, s(s(s(s(s(s(0)))))))
The graph contains the following edges 1 > 1, 2 >= 2

(29) TRUE

(30) Obligation:

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

DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))), T15, T16)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
DIV1_IN_GGAA(x1, x2, x3, x4) = DIV1_IN_GGAA(x1, x2)

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:

DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0)))))) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))))

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:

DIV1_IN_GGAA(s(s(s(s(s(T41))))), s(s(s(s(s(0)))))) → DIV1_IN_GGAA(T41, s(s(s(s(s(0))))))
The graph contains the following edges 1 > 1, 2 >= 2

(36) TRUE

(37) Obligation:

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

DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → DIV1_IN_GGAA(T38, s(s(s(s(0)))), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → DIV1_IN_GGAA(T38, s(s(s(s(0)))), T15, T16)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
DIV1_IN_GGAA(x1, x2, x3, x4) = DIV1_IN_GGAA(x1, x2)

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:

DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0))))) → DIV1_IN_GGAA(T38, s(s(s(s(0)))))

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:

DIV1_IN_GGAA(s(s(s(s(T38)))), s(s(s(s(0))))) → DIV1_IN_GGAA(T38, s(s(s(s(0)))))
The graph contains the following edges 1 > 1, 2 >= 2

(43) TRUE

(44) Obligation:

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

DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → DIV1_IN_GGAA(T35, s(s(s(0))), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0))), s(T15), T16) → DIV1_IN_GGAA(T35, s(s(s(0))), T15, T16)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
DIV1_IN_GGAA(x1, x2, x3, x4) = DIV1_IN_GGAA(x1, x2)

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:

DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0)))) → DIV1_IN_GGAA(T35, s(s(s(0))))

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:

DIV1_IN_GGAA(s(s(s(T35))), s(s(s(0)))) → DIV1_IN_GGAA(T35, s(s(s(0))))
The graph contains the following edges 1 > 1, 2 >= 2

(50) TRUE

(51) Obligation:

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

DIV1_IN_GGAA(s(s(T32)), s(s(0)), s(T15), T16) → DIV1_IN_GGAA(T32, s(s(0)), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

DIV1_IN_GGAA(s(s(T32)), s(s(0)), s(T15), T16) → DIV1_IN_GGAA(T32, s(s(0)), T15, T16)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
DIV1_IN_GGAA(x1, x2, x3, x4) = DIV1_IN_GGAA(x1, x2)

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:

DIV1_IN_GGAA(s(s(T32)), s(s(0))) → DIV1_IN_GGAA(T32, s(s(0)))

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:

DIV1_IN_GGAA(s(s(T32)), s(s(0))) → DIV1_IN_GGAA(T32, s(s(0)))
The graph contains the following edges 1 > 1, 2 >= 2

(57) TRUE

(58) Obligation:

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

DIV1_IN_GGAA(s(T29), s(0), s(T15), T16) → DIV1_IN_GGAA(T29, s(0), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(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:

DIV1_IN_GGAA(s(T29), s(0), s(T15), T16) → DIV1_IN_GGAA(T29, s(0), T15, T16)

R is empty.
The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
DIV1_IN_GGAA(x1, x2, x3, x4) = DIV1_IN_GGAA(x1, x2)

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:

DIV1_IN_GGAA(s(T29), s(0)) → DIV1_IN_GGAA(T29, s(0))

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:

DIV1_IN_GGAA(s(T29), s(0)) → DIV1_IN_GGAA(T29, s(0))
The graph contains the following edges 1 > 1, 2 >= 2

(64) TRUE

(65) Obligation:

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

DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_GAAA(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_GAAA(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → DIV1_IN_GAAA(T48, s(T47), T15, T16)

The TRS R consists of the following rules:

div1_in_ggaa(0, T10, 0, 0) → div1_out_ggaa(0, T10, 0, 0)
div1_in_ggaa(s(T29), s(0), s(T15), T16) → U1_ggaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_ggaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
div1_in_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_ggaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
div1_in_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_ggaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
div1_in_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_ggaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_ggaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, X121))
minus107_in_gga(T49, 0, T49) → minus107_out_gga(T49, 0, T49)
minus107_in_gga(s(T50), s(T51), X131) → U10_gga(T50, T51, X131, minus107_in_gga(T50, T51, X131))
U10_gga(T50, T51, X131, minus107_out_gga(T50, T51, X131)) → minus107_out_gga(s(T50), s(T51), X131)
U7_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, X121)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_ggaa(T45, T46, T15, T16, minus107_in_gga(T45, T46, T48))
U8_ggaa(T45, T46, T15, T16, minus107_out_gga(T45, T46, T48)) → U9_ggaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(0, T10, 0, 0) → div1_out_gaaa(0, T10, 0, 0)
div1_in_gaaa(s(T29), s(0), s(T15), T16) → U1_gaaa(T29, T15, T16, div1_in_ggaa(T29, s(0), T15, T16))
div1_in_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_ggaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_ggaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_ggaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_ggaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_ggaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_ggaa(s(T91), s(T93), T89, s(T91)) → div1_out_ggaa(s(T91), s(T93), T89, s(T91))
div1_in_ggaa(T98, T100, T96, T98) → div1_out_ggaa(T98, T100, T96, T98)
U1_gaaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_gaaa(s(T29), s(0), s(T15), T16)
div1_in_gaaa(s(s(T32)), s(s(0)), s(T15), T16) → U2_gaaa(T32, T15, T16, div1_in_ggaa(T32, s(s(0)), T15, T16))
U2_gaaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_gaaa(s(s(T32)), s(s(0)), s(T15), T16)
div1_in_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16) → U3_gaaa(T35, T15, T16, div1_in_ggaa(T35, s(s(s(0))), T15, T16))
U3_gaaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_gaaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
div1_in_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16) → U4_gaaa(T38, T15, T16, div1_in_ggaa(T38, s(s(s(s(0)))), T15, T16))
U4_gaaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_gaaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16) → U5_gaaa(T41, T15, T16, div1_in_ggaa(T41, s(s(s(s(s(0))))), T15, T16))
U5_gaaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16) → U6_gaaa(T44, T15, T16, div1_in_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16))
U6_gaaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U7_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, X121))
minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)
U7_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, X121)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
div1_in_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_gaaa(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_gaaa(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → U9_gaaa(T45, T46, T15, T16, div1_in_gaaa(T48, s(T47), T15, T16))
div1_in_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56))))))) → div1_out_gaaa(s(s(s(s(s(s(T56)))))), s(s(s(s(s(s(T58)))))), T54, s(s(s(s(s(s(T56)))))))
div1_in_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63)))))) → div1_out_gaaa(s(s(s(s(s(T63))))), s(s(s(s(s(T65))))), T61, s(s(s(s(s(T63))))))
div1_in_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70))))) → div1_out_gaaa(s(s(s(s(T70)))), s(s(s(s(T72)))), T68, s(s(s(s(T70)))))
div1_in_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77)))) → div1_out_gaaa(s(s(s(T77))), s(s(s(T79))), T75, s(s(s(T77))))
div1_in_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84))) → div1_out_gaaa(s(s(T84)), s(s(T86)), T82, s(s(T84)))
div1_in_gaaa(s(T91), s(T93), T89, s(T91)) → div1_out_gaaa(s(T91), s(T93), T89, s(T91))
div1_in_gaaa(T98, T100, T96, T98) → div1_out_gaaa(T98, T100, T96, T98)
U9_gaaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_gaaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U9_ggaa(T45, T46, T15, T16, div1_out_gaaa(T48, s(T47), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16)
U6_ggaa(T44, T15, T16, div1_out_ggaa(T44, s(s(s(s(s(s(0)))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(s(T44)))))), s(s(s(s(s(s(0)))))), s(T15), T16)
U5_ggaa(T41, T15, T16, div1_out_ggaa(T41, s(s(s(s(s(0))))), T15, T16)) → div1_out_ggaa(s(s(s(s(s(T41))))), s(s(s(s(s(0))))), s(T15), T16)
U4_ggaa(T38, T15, T16, div1_out_ggaa(T38, s(s(s(s(0)))), T15, T16)) → div1_out_ggaa(s(s(s(s(T38)))), s(s(s(s(0)))), s(T15), T16)
U3_ggaa(T35, T15, T16, div1_out_ggaa(T35, s(s(s(0))), T15, T16)) → div1_out_ggaa(s(s(s(T35))), s(s(s(0))), s(T15), T16)
U2_ggaa(T32, T15, T16, div1_out_ggaa(T32, s(s(0)), T15, T16)) → div1_out_ggaa(s(s(T32)), s(s(0)), s(T15), T16)
U1_ggaa(T29, T15, T16, div1_out_ggaa(T29, s(0), T15, T16)) → div1_out_ggaa(s(T29), s(0), s(T15), T16)

(66) UsableRulesProof (EQUIVALENT transformation)

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

(67) Obligation:

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

DIV1_IN_GAAA(s(s(s(s(s(s(s(T45))))))), s(s(s(s(s(s(s(T46))))))), s(T15), T16) → U8_GAAA(T45, T46, T15, T16, minus107_in_gaa(T45, T46, T48))
U8_GAAA(T45, T46, T15, T16, minus107_out_gaa(T45, T46, T48)) → DIV1_IN_GAAA(T48, s(T47), T15, T16)

The TRS R consists of the following rules:

minus107_in_gaa(T49, 0, T49) → minus107_out_gaa(T49, 0, T49)
minus107_in_gaa(s(T50), s(T51), X131) → U10_gaa(T50, T51, X131, minus107_in_gaa(T50, T51, X131))
U10_gaa(T50, T51, X131, minus107_out_gaa(T50, T51, X131)) → minus107_out_gaa(s(T50), s(T51), X131)

The argument filtering Pi contains the following mapping:
0 = 0
s(x1) = s(x1)
minus107_in_gaa(x1, x2, x3) = minus107_in_gaa(x1)
minus107_out_gaa(x1, x2, x3) = minus107_out_gaa(x2, x3)
U10_gaa(x1, x2, x3, x4) = U10_gaa(x4)
DIV1_IN_GAAA(x1, x2, x3, x4) = DIV1_IN_GAAA(x1)
U8_GAAA(x1, x2, x3, x4, x5) = U8_GAAA(x5)

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

(68) PiDPToQDPProof (SOUND transformation)

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

(69) Obligation:

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

DIV1_IN_GAAA(s(s(s(s(s(s(s(T45)))))))) → U8_GAAA(minus107_in_gaa(T45))
U8_GAAA(minus107_out_gaa(T46, T48)) → DIV1_IN_GAAA(T48)

The TRS R consists of the following rules:

minus107_in_gaa(T49) → minus107_out_gaa(0, T49)
minus107_in_gaa(s(T50)) → U10_gaa(minus107_in_gaa(T50))
U10_gaa(minus107_out_gaa(T51, X131)) → minus107_out_gaa(s(T51), X131)

The set Q consists of the following terms:

minus107_in_gaa(x0)
U10_gaa(x0)

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

(70) MRRProof (EQUIVALENT transformation)

By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
Strictly oriented dependency pairs:

DIV1_IN_GAAA(s(s(s(s(s(s(s(T45)))))))) → U8_GAAA(minus107_in_gaa(T45))
U8_GAAA(minus107_out_gaa(T46, T48)) → DIV1_IN_GAAA(T48)

Strictly oriented rules of the TRS R:

minus107_in_gaa(T49) → minus107_out_gaa(0, T49)

Used ordering: Polynomial interpretation [POLO]:

POL(0) = 0
POL(DIV1_IN_GAAA(x₁)) = x₁
POL(U10_gaa(x₁)) = 1 + x₁
POL(U8_GAAA(x₁)) = x₁
POL(minus107_in_gaa(x₁)) = 2 + x₁
POL(minus107_out_gaa(x₁, x₂)) = 1 + x₁ + x₂
POL(s(x₁)) = 1 + x₁

(71) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following rules:

minus107_in_gaa(s(T50)) → U10_gaa(minus107_in_gaa(T50))
U10_gaa(minus107_out_gaa(T51, X131)) → minus107_out_gaa(s(T51), X131)

The set Q consists of the following terms:

minus107_in_gaa(x0)
U10_gaa(x0)

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

(72) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(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) TRUE

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) TRUE

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (SOUND transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) TRUE

(30) Obligation:

(31) UsableRulesProof (EQUIVALENT transformation)

(32) Obligation:

(33) PiDPToQDPProof (SOUND transformation)

(34) Obligation:

(35) QDPSizeChangeProof (EQUIVALENT transformation)

(36) TRUE

(37) Obligation:

(38) UsableRulesProof (EQUIVALENT transformation)

(39) Obligation:

(40) PiDPToQDPProof (SOUND transformation)

(41) Obligation:

(42) QDPSizeChangeProof (EQUIVALENT transformation)

(43) TRUE

(44) Obligation:

(45) UsableRulesProof (EQUIVALENT transformation)

(46) Obligation:

(47) PiDPToQDPProof (SOUND transformation)

(48) Obligation:

(49) QDPSizeChangeProof (EQUIVALENT transformation)

(50) TRUE

(51) Obligation:

(52) UsableRulesProof (EQUIVALENT transformation)

(53) Obligation:

(54) PiDPToQDPProof (SOUND transformation)

(55) Obligation:

(56) QDPSizeChangeProof (EQUIVALENT transformation)

(57) TRUE

(58) Obligation:

(59) UsableRulesProof (EQUIVALENT transformation)

(60) Obligation:

(61) PiDPToQDPProof (SOUND transformation)

(62) Obligation:

(63) QDPSizeChangeProof (EQUIVALENT transformation)

(64) TRUE

(65) Obligation:

(66) UsableRulesProof (EQUIVALENT transformation)

(67) Obligation:

(68) PiDPToQDPProof (SOUND transformation)

(69) Obligation:

(70) MRRProof (EQUIVALENT transformation)

(71) Obligation:

(72) PisEmptyProof (EQUIVALENT transformation)

(73) TRUE