YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern p(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1)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: p(X, g(X)). p(X, f(Y)) :- p(X, g(Y)). Query: p(g,a) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 7, "program": { "directives": [], "clauses": [ [ "(p X (g X))", null ], [ "(p X (f Y))", "(p X (g Y))" ] ] }, "graph": { "nodes": { "11": { "goal": [ { "clause": -1, "scope": -1, "term": "(true)" }, { "clause": 1, "scope": 1, "term": "(p T4 T2)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T4"], "free": [], "exprvars": [] } }, "66": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "99": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "67": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "78": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "13": { "goal": [{ "clause": 1, "scope": 1, "term": "(p T1 T2)" }], "kb": { "nonunifying": [[ "(p T1 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": ["X2"], "exprvars": [] } }, "57": { "goal": [{ "clause": 1, "scope": 1, "term": "(p T4 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T4"], "free": [], "exprvars": [] } }, "68": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "58": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "69": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T18 (g T20))" }], "kb": { "nonunifying": [[ "(p T18 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T18"], "free": ["X2"], "exprvars": [] } }, "type": "Nodes", "7": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T1 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "8": { "goal": [ { "clause": 0, "scope": 1, "term": "(p T1 T2)" }, { "clause": 1, "scope": 1, "term": "(p T1 T2)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "91": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "70": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "60": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "71": { "goal": [ { "clause": 0, "scope": 3, "term": "(p T18 (g T20))" }, { "clause": 1, "scope": 3, "term": "(p T18 (g T20))" } ], "kb": { "nonunifying": [[ "(p T18 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T18"], "free": ["X2"], "exprvars": [] } }, "72": { "goal": [{ "clause": 0, "scope": 3, "term": "(p T18 (g T20))" }], "kb": { "nonunifying": [[ "(p T18 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T18"], "free": ["X2"], "exprvars": [] } }, "62": { "goal": [ { "clause": 0, "scope": 2, "term": "(p T7 (g T9))" }, { "clause": 1, "scope": 2, "term": "(p T7 (g T9))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "73": { "goal": [{ "clause": 1, "scope": 3, "term": "(p T18 (g T20))" }], "kb": { "nonunifying": [[ "(p T18 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T18"], "free": ["X2"], "exprvars": [] } }, "84": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "63": { "goal": [{ "clause": 0, "scope": 2, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "64": { "goal": [{ "clause": 1, "scope": 2, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "65": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 7, "to": 8, "label": "CASE" }, { "from": 8, "to": 11, "label": "EVAL with clause\np(X2, g(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT2 -> g(T4)" }, { "from": 8, "to": 13, "label": "EVAL-BACKTRACK" }, { "from": 11, "to": 57, "label": "SUCCESS" }, { "from": 13, "to": 69, "label": "EVAL with clause\np(X16, f(X17)) :- p(X16, g(X17)).\nand substitutionT1 -> T18,\nX16 -> T18,\nX17 -> T20,\nT2 -> f(T20),\nT19 -> T20" }, { "from": 13, "to": 70, "label": "EVAL-BACKTRACK" }, { "from": 57, "to": 58, "label": "EVAL with clause\np(X5, f(X6)) :- p(X5, g(X6)).\nand substitutionT4 -> T7,\nX5 -> T7,\nX6 -> T9,\nT2 -> f(T9),\nT8 -> T9" }, { "from": 57, "to": 60, "label": "EVAL-BACKTRACK" }, { "from": 58, "to": 62, "label": "CASE" }, { "from": 62, "to": 63, "label": "PARALLEL" }, { "from": 62, "to": 64, "label": "PARALLEL" }, { "from": 63, "to": 65, "label": "EVAL with clause\np(X11, g(X11)).\nand substitutionT7 -> T14,\nX11 -> T14,\nT9 -> T14" }, { "from": 63, "to": 66, "label": "EVAL-BACKTRACK" }, { "from": 64, "to": 68, "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification" }, { "from": 65, "to": 67, "label": "SUCCESS" }, { "from": 69, "to": 71, "label": "CASE" }, { "from": 71, "to": 72, "label": "PARALLEL" }, { "from": 71, "to": 73, "label": "PARALLEL" }, { "from": 72, "to": 78, "label": "EVAL with clause\np(X22, g(X22)).\nand substitutionT18 -> T25,\nX22 -> T25,\nT20 -> T25" }, { "from": 72, "to": 84, "label": "EVAL-BACKTRACK" }, { "from": 73, "to": 99, "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification" }, { "from": 78, "to": 91, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Triples: Clauses: Afs: ---------------------------------------- (3) TPisEmptyProof (EQUIVALENT) There are no more dependency triples. Hence, the dependency triple problem trivially terminates. ---------------------------------------- (4) YES