/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern p(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1)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": { "56": { "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": [] } }, "58": { "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": [] } }, "18": { "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": [] } }, "type": "Nodes", "120": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "110": { "goal": [{ "clause": 1, "scope": 2, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "121": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "111": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "122": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "112": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "123": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "113": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "114": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "115": { "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": [] } }, "105": { "goal": [{ "clause": 1, "scope": 1, "term": "(p T4 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T4"], "free": [], "exprvars": [] } }, "116": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "7": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T1 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "106": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } }, "117": { "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": [] } }, "107": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "118": { "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": [] } }, "108": { "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": [] } }, "119": { "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": [] } }, "109": { "goal": [{ "clause": 0, "scope": 2, "term": "(p T7 (g T9))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T7"], "free": [], "exprvars": [] } } }, "edges": [ { "from": 7, "to": 18, "label": "CASE" }, { "from": 18, "to": 56, "label": "EVAL with clause\np(X2, g(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT2 -> g(T4)" }, { "from": 18, "to": 58, "label": "EVAL-BACKTRACK" }, { "from": 56, "to": 105, "label": "SUCCESS" }, { "from": 58, "to": 115, "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": 58, "to": 116, "label": "EVAL-BACKTRACK" }, { "from": 105, "to": 106, "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": 105, "to": 107, "label": "EVAL-BACKTRACK" }, { "from": 106, "to": 108, "label": "CASE" }, { "from": 108, "to": 109, "label": "PARALLEL" }, { "from": 108, "to": 110, "label": "PARALLEL" }, { "from": 109, "to": 111, "label": "EVAL with clause\np(X11, g(X11)).\nand substitutionT7 -> T14,\nX11 -> T14,\nT9 -> T14" }, { "from": 109, "to": 112, "label": "EVAL-BACKTRACK" }, { "from": 110, "to": 114, "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification" }, { "from": 111, "to": 113, "label": "SUCCESS" }, { "from": 115, "to": 117, "label": "CASE" }, { "from": 117, "to": 118, "label": "PARALLEL" }, { "from": 117, "to": 119, "label": "PARALLEL" }, { "from": 118, "to": 120, "label": "EVAL with clause\np(X22, g(X22)).\nand substitutionT18 -> T25,\nX22 -> T25,\nT20 -> T25" }, { "from": 118, "to": 121, "label": "EVAL-BACKTRACK" }, { "from": 119, "to": 123, "label": "BACKTRACK\nfor clause: p(X, f(Y)) :- p(X, g(Y))because of non-unification" }, { "from": 120, "to": 122, "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