/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern test_fun(g,g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 91 ms] (2) TRUE ---------------------------------------- (0) Obligation: Clauses: test_fun(X, Y, Z) :- loop(X, Y, Z, 0). loop(X, Y, Z, C) :- ','(<(X, Y), loop_body(X, Y, Z, C)). loop(X, Y, Z, C) :- >=(X, Y). loop_body(X, Y, Z, C) :- ','(<(X, Z), ','(is(X1, +(X, 1)), ','(is(C1, +(C, 1)), loop(X1, Y, Z, C1)))). loop_body(X, Y, Z, C) :- ','(>=(X, Z), ','(is(Z1, +(Z, 1)), ','(is(C1, +(C, 1)), loop(X, Y, Z1, C1)))). Query: test_fun(g,g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 1, "program": { "directives": [], "clauses": [ [ "(test_fun X Y Z)", "(loop X Y Z (0))" ], [ "(loop X Y Z C)", "(',' (< X Y) (loop_body X Y Z C))" ], [ "(loop X Y Z C)", "(>= X Y)" ], [ "(loop_body X Y Z C)", "(',' (< X Z) (',' (is X1 (+ X (1))) (',' (is C1 (+ C (1))) (loop X1 Y Z C1))))" ], [ "(loop_body X Y Z C)", "(',' (>= X Z) (',' (is Z1 (+ Z (1))) (',' (is C1 (+ C (1))) (loop X Y Z1 C1))))" ] ] }, "graph": { "nodes": { "3280": { "goal": [{ "clause": -1, "scope": -1, "term": "(>= T143 T144)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T143", "T144" ], "free": [], "exprvars": [] } }, "3263": { "goal": [{ "clause": -1, "scope": -1, "term": "(>= T133 T134)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T99", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": 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"operation": "=" }, { "lhs": { "name": "T31", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T32", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T50", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T32", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T49", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T51", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T32", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T32", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T32", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T32", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T88", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T51", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T86", "T87" ], "free": [], "exprvars": [ "T31", "T53", "T86", "T52", "T51", "T89", "T50", "T88", "T49", "T32", "T87" ] } }, "1669": { "goal": [{ "clause": -1, "scope": -1, "term": "(loop_body T31 T32 T33 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T31", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T32", "type": "PlainIntegerVariable" }, "operation": "<" }] }, "ground": [ "T31", "T33", "T32" ], "free": [], "exprvars": [ "T31", "T32" ] } } }, "edges": [ { "from": 1, "to": 6, "label": "CASE" }, { "from": 6, "to": 7, "label": "ONLY EVAL with clause\ntest_fun(X12, X13, X14) :- loop(X12, X13, X14, 0).\nand substitutionT1 -> T13,\nX12 -> T13,\nT2 -> T14,\nX13 -> T14,\nT3 -> T15,\nX14 -> T15" }, { "from": 7, "to": 16, "label": "CASE" }, { "from": 16, "to": 17, "label": "PARALLEL" }, { "from": 16, "to": 18, "label": "PARALLEL" }, { "from": 17, "to": 19, "label": "ONLY EVAL with clause\nloop(X35, X36, X37, X38) :- ','(<(X35, X36), loop_body(X35, X36, X37, X38)).\nand substitutionT13 -> T31,\nX35 -> T31,\nT14 -> T32,\nX36 -> T32,\nT15 -> T33,\nX37 -> T33,\nX38 -> 0" }, { "from": 18, "to": 3280, "label": "ONLY EVAL with clause\nloop(X167, X168, X169, X170) :- >=(X167, X168).\nand substitutionT13 -> T143,\nX167 -> T143,\nT14 -> T144,\nX168 -> T144,\nT15 -> T145,\nX169 -> T145,\nX170 -> 0" }, { "from": 19, "to": 20, "label": "IS ERROR" }, { "from": 19, "to": 1669, "label": "ARITHCOMP SUCCESS" }, { "from": 19, "to": 1671, "label": "ARITHCOMP FAIL" }, { "from": 1669, "to": 1686, "label": "CASE" }, { "from": 1686, "to": 1705, "label": "PARALLEL" }, { "from": 1686, "to": 1706, "label": "PARALLEL" }, { "from": 1705, "to": 1735, "label": "ONLY EVAL with clause\nloop_body(X65, X66, X67, X68) :- ','(<(X65, X67), ','(is(X69, +(X65, 1)), ','(is(X70, +(X68, 1)), loop(X69, X66, X67, X70)))).\nand substitutionT31 -> T49,\nX65 -> T49,\nT32 -> T50,\nX66 -> T50,\nT33 -> T51,\nX67 -> T51,\nX68 -> 0" }, { "from": 1706, "to": 3152, "label": "ONLY EVAL with clause\nloop_body(X117, X118, X119, X120) :- ','(>=(X117, X119), ','(is(X121, +(X119, 1)), ','(is(X122, +(X120, 1)), loop(X117, X118, X121, X122)))).\nand substitutionT31 -> T96,\nX117 -> T96,\nT32 -> T97,\nX118 -> T97,\nT33 -> T98,\nX119 -> T98,\nX120 -> 0" }, { "from": 1735, "to": 1737, "label": "IS ERROR" }, { "from": 1735, "to": 1953, "label": "ARITHCOMP SUCCESS" }, { "from": 1735, "to": 1954, "label": "ARITHCOMP FAIL" }, { "from": 1953, "to": 1955, "label": "\nX69 -> T52" }, { "from": 1955, "to": 1956, "label": "\nX70 -> T53" }, { "from": 1956, "to": 1957, "label": "CASE" }, { "from": 1957, "to": 1958, "label": "PARALLEL" }, { "from": 1957, "to": 1959, "label": "PARALLEL" }, { "from": 1958, "to": 1960, "label": "ONLY EVAL with clause\nloop(X91, X92, X93, X94) :- ','(<(X91, X92), loop_body(X91, X92, X93, X94)).\nand substitutionT52 -> T74,\nX91 -> T74,\nT50 -> T75,\nX92 -> T75,\nT51 -> T76,\nX93 -> T76,\nT53 -> T77,\nX94 -> T77" }, { "from": 1959, "to": 2979, "label": "ONLY EVAL with clause\nloop(X103, X104, X105, X106) :- >=(X103, X104).\nand substitutionT52 -> T86,\nX103 -> T86,\nT50 -> T87,\nX104 -> T87,\nT51 -> T88,\nX105 -> T88,\nT53 -> T89,\nX106 -> T89" }, { "from": 3152, "to": 3153, "label": "IS ERROR" }, { "from": 3152, "to": 3236, "label": "ARITHCOMP SUCCESS" }, { "from": 3152, "to": 3237, "label": "ARITHCOMP FAIL" }, { "from": 3236, "to": 3238, "label": "\nX121 -> T99" }, { "from": 3238, "to": 3239, "label": "\nX122 -> T100" }, { "from": 3239, "to": 3248, "label": "CASE" }, { "from": 3248, "to": 3250, "label": "PARALLEL" }, { "from": 3248, "to": 3252, "label": "PARALLEL" }, { "from": 3250, "to": 3255, "label": "ONLY EVAL with clause\nloop(X143, X144, X145, X146) :- ','(<(X143, X144), loop_body(X143, X144, X145, X146)).\nand substitutionT96 -> T121,\nX143 -> T121,\nT97 -> T122,\nX144 -> T122,\nT99 -> T123,\nX145 -> T123,\nT100 -> T124,\nX146 -> T124" }, { "from": 3252, "to": 3263, "label": "ONLY EVAL with clause\nloop(X155, X156, X157, X158) :- >=(X155, X156).\nand substitutionT96 -> T133,\nX155 -> T133,\nT97 -> T134,\nX156 -> T134,\nT99 -> T135,\nX157 -> T135,\nT100 -> T136,\nX158 -> T136" }, { "from": 3280, "to": 3281, "label": "IS ERROR" }, { "from": 3280, "to": 3293, "label": "ARITHCOMP SUCCESS" }, { "from": 3280, "to": 3294, "label": "ARITHCOMP FAIL" }, { "from": 3293, "to": 3295, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) TRUE