/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

num(g)

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

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


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

(0)
Obligation:
Clauses:

num(0).
num(X) :- ','(no(zero(0)), ','(p(X, Y), num(Y))).
p(0, 0).
p(s(X), X).
zero(0).
no(X) :- ','(X, ','(!, failure(a))).
no(X1).
failure(b).


Query: num(g)
----------------------------------------

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(num (0))",
                null
            ],
            [
                "(num X)",
                "(',' (no (zero (0))) (',' (p X Y) (num Y)))"
            ],
            [
                "(p (0) (0))",
                null
            ],
            [
                "(p (s X) X)",
                null
            ],
            [
                "(zero (0))",
                null
            ],
            [
                "(no X)",
                "(',' X (',' (!) (failure (a))))"
            ],
            [
                "(no X1)",
                null
            ],
            [
                "(failure (b))",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "22": {
                "goal": [
                    {
                        "clause": 5,
                        "scope": 2,
                        "term": "(',' (no (zero (0))) (',' (p T4 X6) (num X6)))"
                    },
                    {
                        "clause": 6,
                        "scope": 2,
                        "term": "(',' (no (zero (0))) (',' (p T4 X6) (num X6)))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            },
            "33": {
                "goal": [{
                    "clause": 7,
                    "scope": 5,
                    "term": "(',' (failure (a)) (',' (p T4 X6) (num X6)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            },
            "12": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "13": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "35": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "25": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (',' (call (zero (0))) (',' (!_2) (failure (a)))) (',' (p T4 X6) (num X6)))"
                    },
                    {
                        "clause": 6,
                        "scope": 2,
                        "term": "(',' (no (zero (0))) (',' (p T4 X6) (num X6)))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            },
            "27": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (zero (0)) (',' (',' (!_2) (failure (a))) (',' (p T4 X6) (num X6))))"
                    },
                    {
                        "clause": -1,
                        "scope": 3,
                        "term": null
                    },
                    {
                        "clause": 6,
                        "scope": 2,
                        "term": "(',' (no (zero (0))) (',' (p T4 X6) (num X6)))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            },
            "28": {
                "goal": [
                    {
                        "clause": 4,
                        "scope": 4,
                        "term": "(',' (zero (0)) (',' (',' (!_2) (failure (a))) (',' (p T4 X6) (num X6))))"
                    },
                    {
                        "clause": -1,
                        "scope": 4,
                        "term": null
                    },
                    {
                        "clause": -1,
                        "scope": 3,
                        "term": null
                    },
                    {
                        "clause": 6,
                        "scope": 2,
                        "term": "(',' (no (zero (0))) (',' (p T4 X6) (num X6)))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            },
            "18": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "1": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(num T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "5": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 1,
                        "term": "(num T1)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(num T1)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "8": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(num T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "9": {
                "goal": [{
                    "clause": 1,
                    "scope": 1,
                    "term": "(num T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "20": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (no (zero (0))) (',' (p T4 X6) (num X6)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            },
            "31": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (',' (!_2) (failure (a))) (',' (p T4 X6) (num X6)))"
                    },
                    {
                        "clause": -1,
                        "scope": 4,
                        "term": null
                    },
                    {
                        "clause": -1,
                        "scope": 3,
                        "term": null
                    },
                    {
                        "clause": 6,
                        "scope": 2,
                        "term": "(',' (no (zero (0))) (',' (p T4 X6) (num X6)))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            },
            "32": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (failure (a)) (',' (p T4 X6) (num X6)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X6"],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 1,
                "to": 5,
                "label": "CASE"
            },
            {
                "from": 5,
                "to": 8,
                "label": "PARALLEL"
            },
            {
                "from": 5,
                "to": 9,
                "label": "PARALLEL"
            },
            {
                "from": 8,
                "to": 12,
                "label": "EVAL with clause\nnum(0).\nand substitutionT1 -> 0"
            },
            {
                "from": 8,
                "to": 13,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 9,
                "to": 20,
                "label": "ONLY EVAL with clause\nnum(X5) :- ','(no(zero(0)), ','(p(X5, X6), num(X6))).\nand substitutionT1 -> T4,\nX5 -> T4"
            },
            {
                "from": 12,
                "to": 18,
                "label": "SUCCESS"
            },
            {
                "from": 20,
                "to": 22,
                "label": "CASE"
            },
            {
                "from": 22,
                "to": 25,
                "label": "ONLY EVAL with clause\nno(X9) :- ','(call(X9), ','(!_2, failure(a))).\nand substitutionX9 -> zero(0)"
            },
            {
                "from": 25,
                "to": 27,
                "label": "CALL"
            },
            {
                "from": 27,
                "to": 28,
                "label": "CASE"
            },
            {
                "from": 28,
                "to": 31,
                "label": "ONLY EVAL with clause\nzero(0).\nand substitution"
            },
            {
                "from": 31,
                "to": 32,
                "label": "CUT"
            },
            {
                "from": 32,
                "to": 33,
                "label": "CASE"
            },
            {
                "from": 33,
                "to": 35,
                "label": "BACKTRACK\nfor clause: failure(b)because of non-unification"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE