/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern test_fun(g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 74 ms] (2) TRUE ---------------------------------------- (0) Obligation: Clauses: test_fun(X, Y) :- loop(X, Y, 0). loop(X, Y, C) :- ','(>(+(X, Y), 0), loop_body(X, Y, C)). loop(X, Y, C) :- =<(+(X, Y), 0). loop_body(X, Y, C) :- ','(>(X, Y), ','(is(X1, -(X, 1)), ','(is(C1, +(C, 1)), loop(X1, Y, C1)))). loop_body(X, Y, C) :- ','(=<(X, Y), ','(=:=(X, Y), ','(is(X1, -(X, 1)), ','(is(C1, +(C, 1)), loop(X1, Y, C1))))). loop_body(X, Y, C) :- ','(=<(X, 0), ','(=\=(X, Y), ','(is(Y1, -(Y, 1)), ','(is(C1, +(C, 1)), loop(X, Y1, C1))))). Query: test_fun(g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 2, "program": { "directives": [], "clauses": [ [ "(test_fun X Y)", "(loop X Y (0))" ], [ "(loop X Y C)", "(',' (> (+ X Y) (0)) (loop_body X Y C))" ], [ "(loop X Y C)", "(=< (+ X Y) (0))" ], [ "(loop_body X Y C)", "(',' (> X Y) (',' (is X1 (- X (1))) (',' (is C1 (+ C (1))) (loop X1 Y C1))))" ], [ "(loop_body X Y C)", "(',' (=< X Y) (',' (=:= X Y) (',' (is X1 (- X (1))) (',' (is C1 (+ C (1))) (loop X1 Y C1)))))" ], [ "(loop_body X Y C)", "(',' (=< X (0)) (',' (=\\= X Y) (',' (is Y1 (- Y (1))) (',' (is C1 (+ C (1))) (loop X Y1 C1)))))" ] ] }, "graph": { "nodes": { "4691": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> (+ T126 T127) (0)) (loop_body T126 T127 T128))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T109", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T108", "type": "PlainIntegerVariable" }, { "type": 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{ "name": "T92", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T73", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T91", "T92", "T93" ], "free": [], "exprvars": [ "T92", "T75", "T91", "T74", "T73", "T72", "T22", "T93", "T21" ] } }, "4744": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "arguments": [ { "name": "T142", "type": "PlainIntegerVariable" }, { "name": "T143", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": ">" }] }, "ground": [ "T142", "T143" ], "free": [], "exprvars": [ "T142", "T143" ] } }, "4745": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "arguments": [ { "name": "T142", "type": 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"PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T101", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T73", "type": "PlainIntegerVariable" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T72", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T72", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T72", "type": "PlainIntegerVariable" }, { "name": "T73", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "name": "T72", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T73", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T101", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T73", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T100", "T101" ], "free": [], "exprvars": [ "T75", "T74", "T100", "T73", "T101", "T72", "T22", "T21", "T102" ] } }, "1770": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T33", "type": "PlainIntegerVariable" }, { "name": "T34", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "name": "T34", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T33", "type": "PlainIntegerVariable" }, "operation": ">=" } ] }, "ground": [ "T34", "T33" ], "free": [ "X53", "X54" ], "exprvars": [ "T34", "T22", "T33", "T21" ] } }, "1047": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> T33 T34) (',' (is X53 (- T33 (1))) (',' (is X54 (+ (0) (1))) (loop X53 T34 X54))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T33", "type": "PlainIntegerVariable" }, { "name": "T34", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" } ] }, "ground": [ "T33", "T34" ], "free": [ "X53", "X54" ], "exprvars": [ "T34", "T22", "T33", "T21" ] } }, "4510": { "goal": [{ "clause": 4, "scope": 3, "term": "(loop_body T21 T22 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }] }, "ground": [ "T22", "T21" ], "free": [], "exprvars": [ "T22", "T21" ] } }, "4511": { "goal": [{ "clause": 5, "scope": 3, "term": "(loop_body T21 T22 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }] }, "ground": [ "T22", "T21" ], "free": [], "exprvars": [ "T22", "T21" ] } }, "945": { "goal": [ { "clause": 3, "scope": 3, "term": "(loop_body T21 T22 (0))" }, { "clause": 4, "scope": 3, "term": "(loop_body T21 T22 (0))" }, { "clause": 5, "scope": 3, "term": "(loop_body T21 T22 (0))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }] }, "ground": [ "T22", "T21" ], "free": [], "exprvars": [ "T22", "T21" ] } }, "4557": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (=< T107 (0)) (',' (=\\= T107 T108) (',' (is X141 (- T108 (1))) (',' (is X142 (+ (0) (1))) (loop T107 X141 X142)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T107", "type": "PlainIntegerVariable" }, { "name": "T108", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" } ] }, "ground": [ "T107", "T108" ], "free": [ "X141", "X142" ], "exprvars": [ "T22", "T108", "T21", "T107" ] } }, "1769": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X53 (- T33 (1))) (',' (is X54 (+ (0) (1))) (loop X53 T34 X54)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T33", "type": "PlainIntegerVariable" }, { "name": "T34", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "name": "T34", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T33", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T34", "T33" ], "free": [ "X53", "X54" ], "exprvars": [ "T34", "T22", "T33", "T21" ] } }, "4517": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (=< T72 T73) (',' (=:= T72 T73) (',' (is X101 (- T72 (1))) (',' (is X102 (+ (0) (1))) (loop X101 T73 X102)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T72", "type": "PlainIntegerVariable" }, { "name": "T73", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T21", "type": "PlainIntegerVariable" }, { "name": "T22", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "<" } ] }, "ground": [ "T72", "T73" ], "free": [ "X101", "X102" ], "exprvars": [ "T73", "T72", "T22", "T21" ] } } }, "edges": [ { "from": 2, "to": 6, "label": "CASE" }, { "from": 6, "to": 9, "label": "ONLY EVAL with clause\ntest_fun(X9, X10) :- loop(X9, X10, 0).\nand substitutionT1 -> T9,\nX9 -> T9,\nT2 -> T10,\nX10 -> T10" }, { "from": 9, "to": 14, "label": "CASE" }, { "from": 14, "to": 15, "label": "PARALLEL" }, { "from": 14, "to": 16, "label": "PARALLEL" }, { "from": 15, "to": 17, "label": "ONLY EVAL with clause\nloop(X26, X27, X28) :- ','(>(+(X26, X27), 0), loop_body(X26, X27, X28)).\nand substitutionT9 -> T21,\nX26 -> T21,\nT10 -> T22,\nX27 -> T22,\nX28 -> 0" }, { "from": 16, "to": 4736, "label": "ONLY EVAL with clause\nloop(X176, X177, X178) :- =<(+(X176, X177), 0).\nand substitutionT9 -> T142,\nX176 -> T142,\nT10 -> T143,\nX177 -> T143,\nX178 -> 0" }, { "from": 17, "to": 18, "label": "IS ERROR" }, { "from": 17, "to": 887, "label": "ARITHCOMP SUCCESS" }, { "from": 17, "to": 889, "label": "ARITHCOMP FAIL" }, { "from": 887, "to": 945, "label": "CASE" }, { "from": 945, "to": 1013, "label": "PARALLEL" }, { "from": 945, "to": 1014, "label": "PARALLEL" }, { "from": 1013, "to": 1047, "label": "ONLY EVAL with clause\nloop_body(X50, X51, X52) :- ','(>(X50, X51), ','(is(X53, -(X50, 1)), ','(is(X54, +(X52, 1)), loop(X53, X51, X54)))).\nand substitutionT21 -> T33,\nX50 -> T33,\nT22 -> T34,\nX51 -> T34,\nX52 -> 0" }, { "from": 1014, "to": 4510, "label": "PARALLEL" }, { "from": 1014, "to": 4511, "label": "PARALLEL" }, { "from": 1047, "to": 1769, "label": "ARITHCOMP SUCCESS" }, { "from": 1047, "to": 1770, "label": "ARITHCOMP FAIL" }, { "from": 1769, "to": 1771, "label": "\nX53 -> T35" }, { "from": 1771, "to": 1772, "label": "\nX54 -> T36" }, { "from": 1772, "to": 1781, "label": "CASE" }, { "from": 1781, "to": 1782, "label": "PARALLEL" }, { "from": 1781, "to": 1783, "label": "PARALLEL" }, { "from": 1782, "to": 1784, "label": "ONLY EVAL with clause\nloop(X70, X71, X72) :- ','(>(+(X70, X71), 0), loop_body(X70, X71, X72)).\nand substitutionT35 -> T52,\nX70 -> T52,\nT34 -> T53,\nX71 -> T53,\nT36 -> T54,\nX72 -> T54" }, { "from": 1783, "to": 4196, "label": "ONLY EVAL with clause\nloop(X79, X80, X81) :- =<(+(X79, X80), 0).\nand substitutionT35 -> T61,\nX79 -> T61,\nT34 -> T62,\nX80 -> T62,\nT36 -> T63,\nX81 -> T63" }, { "from": 4510, "to": 4517, "label": "ONLY EVAL with clause\nloop_body(X98, X99, X100) :- ','(=<(X98, X99), ','(=:=(X98, X99), ','(is(X101, -(X98, 1)), ','(is(X102, +(X100, 1)), loop(X101, X99, X102))))).\nand substitutionT21 -> T72,\nX98 -> T72,\nT22 -> T73,\nX99 -> T73,\nX100 -> 0" }, { "from": 4511, "to": 4557, "label": "ONLY EVAL with clause\nloop_body(X138, X139, X140) :- ','(=<(X138, 0), ','(=\\=(X138, X139), ','(is(X141, -(X139, 1)), ','(is(X142, +(X140, 1)), loop(X138, X141, X142))))).\nand substitutionT21 -> T107,\nX138 -> T107,\nT22 -> T108,\nX139 -> T108,\nX140 -> 0" }, { "from": 4517, "to": 4528, "label": "ARITHCOMP SUCCESS" }, { "from": 4517, "to": 4529, "label": "ARITHCOMP FAIL" }, { "from": 4528, "to": 4534, "label": "ARITHCOMP SUCCESS" }, { "from": 4528, "to": 4535, "label": "ARITHCOMP FAIL" }, { "from": 4534, "to": 4536, "label": "\nX101 -> T74" }, { "from": 4536, "to": 4537, "label": "\nX102 -> T75" }, { "from": 4537, "to": 4543, "label": "CASE" }, { "from": 4543, "to": 4544, "label": "PARALLEL" }, { "from": 4543, "to": 4545, "label": "PARALLEL" }, { "from": 4544, "to": 4546, "label": "ONLY EVAL with clause\nloop(X118, X119, X120) :- ','(>(+(X118, X119), 0), loop_body(X118, X119, X120)).\nand substitutionT74 -> T91,\nX118 -> T91,\nT73 -> T92,\nX119 -> T92,\nT75 -> T93,\nX120 -> T93" }, { "from": 4545, "to": 4549, "label": "ONLY EVAL with clause\nloop(X127, X128, X129) :- =<(+(X127, X128), 0).\nand substitutionT74 -> T100,\nX127 -> T100,\nT73 -> T101,\nX128 -> T101,\nT75 -> T102,\nX129 -> T102" }, { "from": 4557, "to": 4642, "label": "ARITHCOMP SUCCESS" }, { "from": 4557, "to": 4643, "label": "ARITHCOMP FAIL" }, { "from": 4642, "to": 4644, "label": "ARITHCOMP SUCCESS" }, { "from": 4642, "to": 4645, "label": "ARITHCOMP FAIL" }, { "from": 4644, "to": 4646, "label": "\nX141 -> T109" }, { "from": 4646, "to": 4647, "label": "\nX142 -> T110" }, { "from": 4647, "to": 4657, "label": "CASE" }, { "from": 4657, "to": 4661, "label": "PARALLEL" }, { "from": 4657, "to": 4662, "label": "PARALLEL" }, { "from": 4661, "to": 4691, "label": "ONLY EVAL with clause\nloop(X158, X159, X160) :- ','(>(+(X158, X159), 0), loop_body(X158, X159, X160)).\nand substitutionT107 -> T126,\nX158 -> T126,\nT109 -> T127,\nX159 -> T127,\nT110 -> T128,\nX160 -> T128" }, { "from": 4662, "to": 4731, "label": "ONLY EVAL with clause\nloop(X167, X168, X169) :- =<(+(X167, X168), 0).\nand substitutionT107 -> T135,\nX167 -> T135,\nT109 -> T136,\nX168 -> T136,\nT110 -> T137,\nX169 -> T137" }, { "from": 4736, "to": 4737, "label": "IS ERROR" }, { "from": 4736, "to": 4743, "label": "ARITHCOMP SUCCESS" }, { "from": 4736, "to": 4744, "label": "ARITHCOMP FAIL" }, { "from": 4743, "to": 4745, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) TRUE