/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

double(g,g)

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

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 26 ms]
(2) TRUE


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

(0)
Obligation:
Clauses:

double(X, Y) :- ','(=<(Y, 0), ','(!, =:=(X, 0))).
double(X, Y) :- ','(>(Y, 0), ','(!, double(-(X, 1), -(Y, 2)))).


Query: double(g,g)
----------------------------------------

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

{
    "root": 3,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(double X Y)",
                "(',' (=< Y (0)) (',' (!) (=:= X (0))))"
            ],
            [
                "(double X Y)",
                "(',' (> Y (0)) (',' (!) (double (- X (1)) (- Y (2)))))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "11": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (=< T8 (0)) (',' (!_1) (=:= T7 (0))))"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(double T7 T8)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T7",
                        "T8"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "12": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "13": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (!_1) (=:= T7 (0)))"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(double T7 T8)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T8",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": [
                        "T7",
                        "T8"
                    ],
                    "free": [],
                    "exprvars": ["T8"]
                }
            },
            "16": {
                "goal": [{
                    "clause": 1,
                    "scope": 1,
                    "term": "(double T7 T8)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T8",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": ">"
                        }]
                    },
                    "ground": [
                        "T7",
                        "T8"
                    ],
                    "free": [],
                    "exprvars": ["T8"]
                }
            },
            "18": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(=:= T7 (0))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T8",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": ["T7"],
                    "free": [],
                    "exprvars": ["T8"]
                }
            },
            "type": "Nodes",
            "3": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(double T1 T2)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "4": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 1,
                        "term": "(double T1 T2)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(double T1 T2)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "203": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "="
                            },
                            {
                                "lhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": ["T7"],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T8"
                    ]
                }
            },
            "204": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "!="
                            },
                            {
                                "lhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": ["T7"],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T8"
                    ]
                }
            },
            "205": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "="
                            },
                            {
                                "lhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T8"
                    ]
                }
            },
            "206": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (> T14 (0)) (',' (!_1) (double (- T13 (1)) (- T14 (2)))))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T13",
                        "T14"
                    ],
                    "free": [],
                    "exprvars": [
                        "T14",
                        "T8"
                    ]
                }
            },
            "20": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 3,
                "to": 4,
                "label": "CASE"
            },
            {
                "from": 4,
                "to": 11,
                "label": "ONLY EVAL with clause\ndouble(X5, X6) :- ','(=<(X6, 0), ','(!_1, =:=(X5, 0))).\nand substitutionT1 -> T7,\nX5 -> T7,\nT2 -> T8,\nX6 -> T8"
            },
            {
                "from": 11,
                "to": 12,
                "label": "IS ERROR"
            },
            {
                "from": 11,
                "to": 13,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 11,
                "to": 16,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 13,
                "to": 18,
                "label": "CUT"
            },
            {
                "from": 16,
                "to": 206,
                "label": "ONLY EVAL with clause\ndouble(X11, X12) :- ','(>(X12, 0), ','(!_1, double(-(X11, 1), -(X12, 2)))).\nand substitutionT7 -> T13,\nX11 -> T13,\nT8 -> T14,\nX12 -> T14"
            },
            {
                "from": 18,
                "to": 20,
                "label": "IS ERROR"
            },
            {
                "from": 18,
                "to": 203,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 18,
                "to": 204,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 203,
                "to": 205,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE