YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

f(a,a,g)

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

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


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

(0)
Obligation:
Clauses:

f(0, 1, X) :- f(X, X, X).


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

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [[
            "(f (0) (1) X)",
            "(f X X X)"
        ]]
    },
    "graph": {
        "nodes": {
            "22": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(f T6 T6 T6)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T6"],
                    "free": [],
                    "exprvars": []
                }
            },
            "1": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(f T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T3"],
                    "free": [],
                    "exprvars": []
                }
            },
            "23": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "6": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(f T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T3"],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "42": {
                "goal": [{
                    "clause": 0,
                    "scope": 2,
                    "term": "(f T6 T6 T6)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T6"],
                    "free": [],
                    "exprvars": []
                }
            },
            "43": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 1,
                "to": 6,
                "label": "CASE"
            },
            {
                "from": 6,
                "to": 22,
                "label": "EVAL with clause\nf(0, 1, X3) :- f(X3, X3, X3).\nand substitutionT1 -> 0,\nT2 -> 1,\nT3 -> T6,\nX3 -> T6"
            },
            {
                "from": 6,
                "to": 23,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 22,
                "to": 42,
                "label": "CASE"
            },
            {
                "from": 42,
                "to": 43,
                "label": "BACKTRACK\nfor clause: f(0, 1, X) :- f(X, X, X)because of non-unification"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE