/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern p(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1)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": 2, "program": { "directives": [], "clauses": [ [ "(p X (g X))", null ], [ "(p X (f Y))", "(p X (g Y))" ] ] }, "graph": { "nodes": { "55": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "66": { "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": [] } }, "56": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "35": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "57": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "79": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "36": { "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": [] } }, "58": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "69": { "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": [] } }, "59": { "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": [] } }, "29": { "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": [] } }, "type": "Nodes", "2": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T1 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "5": { "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": [] } }, "81": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "60": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "50": { "goal": [{ "clause": 0, "scope": 2, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "83": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "51": { "goal": [{ "clause": 1, "scope": 2, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "62": { "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": [] } }, "30": { "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": [] } }, "31": { "goal": [{ "clause": 1, "scope": 1, "term": "(p T4 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T4"], "free": [], "exprvars": [] } }, "32": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "76": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 2, "to": 5, "label": "CASE" }, { "from": 5, "to": 29, "label": "EVAL with clause\np(X2, g(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT2 -> g(T4)" }, { "from": 5, "to": 30, "label": "EVAL-BACKTRACK" }, { "from": 29, "to": 31, "label": "SUCCESS" }, { "from": 30, "to": 59, "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": 30, "to": 60, "label": "EVAL-BACKTRACK" }, { "from": 31, "to": 32, "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": 31, "to": 35, "label": "EVAL-BACKTRACK" }, { "from": 32, "to": 36, "label": "CASE" }, { "from": 36, "to": 50, "label": "PARALLEL" }, { "from": 36, "to": 51, "label": "PARALLEL" }, { "from": 50, "to": 55, "label": "EVAL with clause\np(X11, g(X11)).\nand substitutionT7 -> T14,\nX11 -> T14,\nT9 -> T14" }, { "from": 50, "to": 56, "label": "EVAL-BACKTRACK" }, { "from": 51, "to": 58, "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification" }, { "from": 55, "to": 57, "label": "SUCCESS" }, { "from": 59, "to": 62, "label": "CASE" }, { "from": 62, "to": 66, "label": "PARALLEL" }, { "from": 62, "to": 69, "label": "PARALLEL" }, { "from": 66, "to": 76, "label": "EVAL with clause\np(X22, g(X22)).\nand substitutionT18 -> T25,\nX22 -> T25,\nT20 -> T25" }, { "from": 66, "to": 79, "label": "EVAL-BACKTRACK" }, { "from": 69, "to": 83, "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification" }, { "from": 76, "to": 81, "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