/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

parts(g,g,a)

w.r.t. the given Prolog program could successfully be proven:

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 25 ms]
(2) TRUE


----------------------------------------

(0)
Obligation:
Clauses:

parts(P, Q, Ret) :- ','(=<(P, 0), ','(!, is(Ret, 1))).
parts(P, Q, Ret) :- ','(=<(Q, 0), ','(!, is(Ret, 0))).
parts(P, Q, Ret) :- ','(>(Q, P), ','(!, ','(parts(P, P, Ret1), is(Ret, Ret1)))).
parts(P, Q, Ret) :- ','(!, ','(is(P1, -(P, 1)), ','(parts(P1, Q, Ret1), ','(is(Q2, -(Q, 1)), ','(parts(P, Q2, Ret2), is(Ret, +(Ret1, Ret2))))))).


Query: parts(g,g,a)
----------------------------------------

(1) PrologToIRSwTTransformerProof (SOUND)
Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert

{
    "root": 3,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(parts P Q Ret)",
                "(',' (=< P (0)) (',' (!) (is Ret (1))))"
            ],
            [
                "(parts P Q Ret)",
                "(',' (=< Q (0)) (',' (!) (is Ret (0))))"
            ],
            [
                "(parts P Q Ret)",
                "(',' (> Q P) (',' (!) (',' (parts P P Ret1) (is Ret Ret1))))"
            ],
            [
                "(parts P Q Ret)",
                "(',' (!) (',' (is P1 (- P (1))) (',' (parts P1 Q Ret1) (',' (is Q2 (- Q (1))) (',' (parts P Q2 Ret2) (is Ret (+ Ret1 Ret2)))))))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "type": "Nodes",
            "2801": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "="
                            },
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": ["T15"],
                    "free": [],
                    "exprvars": [
                        "T11",
                        "T15"
                    ]
                }
            },
            "2800": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(is T14 (1))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "2799": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    },
                    {
                        "clause": 2,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    },
                    {
                        "clause": 3,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": ">"
                        }]
                    },
                    "ground": [
                        "T12",
                        "T11"
                    ],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "3": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(parts T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "2798": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (!_1) (is T14 (1)))"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    },
                    {
                        "clause": 2,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    },
                    {
                        "clause": 3,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": [
                        "T12",
                        "T11"
                    ],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "6": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 1,
                        "term": "(parts T1 T2 T3)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(parts T1 T2 T3)"
                    },
                    {
                        "clause": 2,
                        "scope": 1,
                        "term": "(parts T1 T2 T3)"
                    },
                    {
                        "clause": 3,
                        "scope": 1,
                        "term": "(parts T1 T2 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "8": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (=< T11 (0)) (',' (!_1) (is T14 (1))))"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    },
                    {
                        "clause": 2,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    },
                    {
                        "clause": 3,
                        "scope": 1,
                        "term": "(parts T11 T12 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T11",
                        "T12"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "2819": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "2818": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (=< T24 (0)) (',' (!_1) (is T26 (0))))"
                    },
                    {
                        "clause": 2,
                        "scope": 1,
                        "term": "(parts T23 T24 T3)"
                    },
                    {
                        "clause": 3,
                        "scope": 1,
                        "term": "(parts T23 T24 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T23",
                        "T24"
                    ],
                    "free": [],
                    "exprvars": [
                        "T23",
                        "T11"
                    ]
                }
            },
            "2805": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "="
                            },
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": [
                        "T11",
                        "T15"
                    ]
                }
            },
            "10": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "2802": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": ["T11"]
                }
            }
        },
        "edges": [
            {
                "from": 3,
                "to": 6,
                "label": "CASE"
            },
            {
                "from": 6,
                "to": 8,
                "label": "ONLY EVAL with clause\nparts(X7, X8, X9) :- ','(=<(X7, 0), ','(!_1, is(X9, 1))).\nand substitutionT1 -> T11,\nX7 -> T11,\nT2 -> T12,\nX8 -> T12,\nT3 -> T14,\nX9 -> T14,\nT13 -> T14"
            },
            {
                "from": 8,
                "to": 10,
                "label": "IS ERROR"
            },
            {
                "from": 8,
                "to": 2798,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 8,
                "to": 2799,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 2798,
                "to": 2800,
                "label": "CUT"
            },
            {
                "from": 2799,
                "to": 2818,
                "label": "ONLY EVAL with clause\nparts(X16, X17, X18) :- ','(=<(X17, 0), ','(!_1, is(X18, 0))).\nand substitutionT11 -> T23,\nX16 -> T23,\nT12 -> T24,\nX17 -> T24,\nT3 -> T26,\nX18 -> T26,\nT25 -> T26"
            },
            {
                "from": 2800,
                "to": 2801,
                "label": "\nT14 -> T15"
            },
            {
                "from": 2800,
                "to": 2802,
                "label": "IS FAIL"
            },
            {
                "from": 2801,
                "to": 2805,
                "label": "SUCCESS"
            },
            {
                "from": 2818,
                "to": 2819,
                "label": "IS ERROR"
            }
        ],
        "type": "Graph"
    }
}

----------------------------------------

(2)
TRUE