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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

f(a)

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

(0) Prolog
(1) PrologToDTProblemTransformerProof [SOUND, 0 ms]
(2) TRIPLES
(3) TPisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

(0)
Obligation:
Clauses:

f(X) :- ','(p(X), q(X)).
p(a) :- !.
p(X) :- p(Y).
q(b).


Query: f(a)
----------------------------------------

(1) PrologToDTProblemTransformerProof (SOUND)
Built DT problem from termination graph DT10.

{
    "root": 3,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(f X)",
                "(',' (p X) (q X))"
            ],
            [
                "(p (a))",
                "(!)"
            ],
            [
                "(p X)",
                "(p Y)"
            ],
            [
                "(q (b))",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "11": {
                "goal": [{
                    "clause": 2,
                    "scope": 2,
                    "term": "(',' (p T4) (q T4))"
                }],
                "kb": {
                    "nonunifying": [[
                        "(p T4)",
                        "(p (a))"
                    ]],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "12": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(q (a))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "34": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 4,
                        "term": "(p X7)"
                    },
                    {
                        "clause": 2,
                        "scope": 4,
                        "term": "(p X7)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X7"],
                    "exprvars": []
                }
            },
            "13": {
                "goal": [{
                    "clause": 3,
                    "scope": 3,
                    "term": "(q (a))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "35": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_4)"
                    },
                    {
                        "clause": 2,
                        "scope": 4,
                        "term": "(p X7)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X7"],
                    "exprvars": []
                }
            },
            "14": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "36": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "37": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "38": {
                "goal": [{
                    "clause": 3,
                    "scope": 5,
                    "term": "(q T9)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "17": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (p X7) (q T9))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X7"],
                    "exprvars": []
                }
            },
            "39": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "18": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p X7)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X7"],
                    "exprvars": []
                }
            },
            "19": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(q T9)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "3": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(f T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "6": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(f T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "7": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (p T4) (q T4))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "9": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 2,
                        "term": "(',' (p T4) (q T4))"
                    },
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(',' (p T4) (q T4))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "40": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "41": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "10": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (!_2) (q (a)))"
                    },
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(',' (p T4) (q T4))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 3,
                "to": 6,
                "label": "CASE"
            },
            {
                "from": 6,
                "to": 7,
                "label": "ONLY EVAL with clause\nf(X2) :- ','(p(X2), q(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT3 -> T4"
            },
            {
                "from": 7,
                "to": 9,
                "label": "CASE"
            },
            {
                "from": 9,
                "to": 10,
                "label": "EVAL with clause\np(a) :- !_2.\nand substitutionT4 -> a"
            },
            {
                "from": 9,
                "to": 11,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 10,
                "to": 12,
                "label": "CUT"
            },
            {
                "from": 11,
                "to": 17,
                "label": "ONLY EVAL with clause\np(X6) :- p(X7).\nand substitutionT4 -> T9,\nX6 -> T9,\nT8 -> T9"
            },
            {
                "from": 12,
                "to": 13,
                "label": "CASE"
            },
            {
                "from": 13,
                "to": 14,
                "label": "BACKTRACK\nfor clause: q(b)because of non-unification"
            },
            {
                "from": 17,
                "to": 18,
                "label": "SPLIT 1"
            },
            {
                "from": 17,
                "to": 19,
                "label": "SPLIT 2\nreplacements:X7 -> T10"
            },
            {
                "from": 18,
                "to": 34,
                "label": "CASE"
            },
            {
                "from": 19,
                "to": 38,
                "label": "CASE"
            },
            {
                "from": 34,
                "to": 35,
                "label": "ONLY EVAL with clause\np(a) :- !_4.\nand substitutionX7 -> a"
            },
            {
                "from": 35,
                "to": 36,
                "label": "CUT"
            },
            {
                "from": 36,
                "to": 37,
                "label": "SUCCESS"
            },
            {
                "from": 38,
                "to": 39,
                "label": "EVAL with clause\nq(b).\nand substitutionT9 -> b"
            },
            {
                "from": 38,
                "to": 40,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 39,
                "to": 41,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
Obligation:
Triples:


Clauses:

pcA(a).

Afs:


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

(3) TPisEmptyProof (EQUIVALENT)
There are no more dependency triples. Hence, the dependency triple problem trivially terminates.
----------------------------------------

(4)
YES