/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern p(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1)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(X)) :- 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 X))", "(p X (g Y))" ] ] }, "graph": { "nodes": { "77": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "78": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "68": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T6 (g X5))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": ["X5"], "exprvars": [] } }, "79": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "69": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "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": [] } }, "80": { "goal": [{ "clause": -1, "scope": -1, "term": "(p T14 (g X14))" }], "kb": { "nonunifying": [[ "(p T14 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T14"], "free": [ "X2", "X14" ], "exprvars": [] } }, "70": { "goal": [ { "clause": 0, "scope": 2, "term": "(p T6 (g X5))" }, { "clause": 1, "scope": 2, "term": "(p T6 (g X5))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": ["X5"], "exprvars": [] } }, "81": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "82": { "goal": [ { "clause": 0, "scope": 3, "term": "(p T14 (g X14))" }, { "clause": 1, "scope": 3, "term": "(p T14 (g X14))" } ], "kb": { "nonunifying": [[ "(p T14 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T14"], "free": [ "X2", "X14" ], "exprvars": [] } }, "83": { "goal": [{ "clause": 0, "scope": 3, "term": "(p T14 (g X14))" }], "kb": { "nonunifying": [[ "(p T14 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T14"], "free": [ "X2", "X14" ], "exprvars": [] } }, "84": { "goal": [{ "clause": 1, "scope": 3, "term": "(p T14 (g X14))" }], "kb": { "nonunifying": [[ "(p T14 T2)", "(p X2 (g X2))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T14"], "free": [ "X2", "X14" ], "exprvars": [] } }, "63": { "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": [] } }, "85": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "64": { "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": [] } }, "75": { "goal": [{ "clause": 0, "scope": 2, "term": "(p T6 (g X5))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": ["X5"], "exprvars": [] } }, "86": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "54": { "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": [] } }, "65": { "goal": [{ "clause": 1, "scope": 1, "term": "(p T4 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T4"], "free": [], "exprvars": [] } }, "76": { "goal": [{ "clause": 1, "scope": 2, "term": "(p T6 (g X5))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": ["X5"], "exprvars": [] } }, "87": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 2, "to": 54, "label": "CASE" }, { "from": 54, "to": 63, "label": "EVAL with clause\np(X2, g(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT2 -> g(T4)" }, { "from": 54, "to": 64, "label": "EVAL-BACKTRACK" }, { "from": 63, "to": 65, "label": "SUCCESS" }, { "from": 64, "to": 80, "label": "EVAL with clause\np(X13, f(X13)) :- p(X13, g(X14)).\nand substitutionT1 -> T14,\nX13 -> T14,\nT2 -> f(T14)" }, { "from": 64, "to": 81, "label": "EVAL-BACKTRACK" }, { "from": 65, "to": 68, "label": "EVAL with clause\np(X4, f(X4)) :- p(X4, g(X5)).\nand substitutionT4 -> T6,\nX4 -> T6,\nT2 -> f(T6)" }, { "from": 65, "to": 69, "label": "EVAL-BACKTRACK" }, { "from": 68, "to": 70, "label": "CASE" }, { "from": 70, "to": 75, "label": "PARALLEL" }, { "from": 70, "to": 76, "label": "PARALLEL" }, { "from": 75, "to": 77, "label": "ONLY EVAL with clause\np(X10, g(X10)).\nand substitutionT6 -> T11,\nX10 -> T11,\nX5 -> T11" }, { "from": 76, "to": 79, "label": "BACKTRACK\nfor clause: p(X, f(X)) :- p(X, g(Y))because of non-unification" }, { "from": 77, "to": 78, "label": "SUCCESS" }, { "from": 80, "to": 82, "label": "CASE" }, { "from": 82, "to": 83, "label": "PARALLEL" }, { "from": 82, "to": 84, "label": "PARALLEL" }, { "from": 83, "to": 85, "label": "ONLY EVAL with clause\np(X19, g(X19)).\nand substitutionT14 -> T19,\nX19 -> T19,\nX14 -> T19" }, { "from": 84, "to": 87, "label": "BACKTRACK\nfor clause: p(X, f(X)) :- p(X, g(Y))because of non-unification" }, { "from": 85, "to": 86, "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