YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

p(a)

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

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


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

(0)
Obligation:
Clauses:

p(X) :- ','(q(f(Y)), p(Y)).
q(g(Y)).


Query: p(a)
----------------------------------------

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(p X)",
                "(',' (q (f Y)) (p Y))"
            ],
            [
                "(q (g Y))",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "1": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "2": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(p T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "70": {
                "goal": [{
                    "clause": 1,
                    "scope": 2,
                    "term": "(',' (q (f X8)) (p X8))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X8"],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "75": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "43": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (q (f X8)) (p X8))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X8"],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 1,
                "to": 2,
                "label": "CASE"
            },
            {
                "from": 2,
                "to": 43,
                "label": "ONLY EVAL with clause\np(X7) :- ','(q(f(X8)), p(X8)).\nand substitutionT1 -> T4,\nX7 -> T4"
            },
            {
                "from": 43,
                "to": 70,
                "label": "CASE"
            },
            {
                "from": 70,
                "to": 75,
                "label": "BACKTRACK\nfor clause: q(g(Y))because of non-unification"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE