/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern test_fun(g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1)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, 138 ms] (2) TRUE ---------------------------------------- (0) Obligation: Clauses: test_fun(X, Y) :- loop(X, Y, 0). loop(X, Y, C) :- ','(>(X, 0), loop_body(X, Y, C)). loop(X, Y, C) :- ','(>(Y, 0), loop_body(X, Y, C)). loop(X, Y, C) :- ','(=<(X, 0), =<(Y, 0)). loop_body(X, Y, C) :- ','(>(X, 0), ','(is(X1, -(X, 1)), ','(is(C1, +(C, 1)), loop(X1, Y, C1)))). loop_body(X, Y, C) :- ','(=<(X, 0), ','(>(Y, 0), ','(is(Y1, -(Y, 1)), ','(is(C1, +(C, 1)), loop(X, Y1, C1))))). loop_body(X, Y, C) :- ','(=<(X, 0), ','(=<(Y, 0), ','(is(C1, +(C, 1)), loop(X, Y, C1)))). Query: test_fun(g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 3, "program": { "directives": [], "clauses": [ [ "(test_fun X Y)", "(loop X Y (0))" ], [ "(loop X Y C)", "(',' (> X (0)) (loop_body X Y C))" ], [ "(loop X Y C)", "(',' (> Y (0)) (loop_body X Y C))" ], [ "(loop X Y C)", "(',' (=< X (0)) (=< Y (0)))" ], [ "(loop_body X Y C)", "(',' (> X (0)) (',' (is X1 (- X (1))) (',' (is C1 (+ C (1))) (loop X1 Y C1))))" ], [ "(loop_body X Y C)", "(',' (=< X (0)) (',' (> Y (0)) (',' (is Y1 (- Y (1))) (',' (is C1 (+ C (1))) (loop X Y1 C1)))))" ], [ "(loop_body X Y C)", "(',' (=< X (0)) (',' (=< Y (0)) (',' (is C1 (+ C (1))) (loop X Y C1))))" ] ] }, "graph": { "nodes": { "6234": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T355", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<=" }, { "lhs": { "name": 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"T139", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "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": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T137", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T21", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T21", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T137", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<=" }, { "lhs": { "name": "T138", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<=" } ] }, "ground": [ "T179", "T180" ], "free": [], "exprvars": [ "T137", "T181", "T138", "T139", "T180", "T21", "T179" ] } } }, "edges": [ { "from": 3, "to": 4, "label": "CASE" }, { "from": 4, "to": 7, "label": "ONLY EVAL with clause\ntest_fun(X9, X10) :- loop(X9, X10, 0).\nand substitutionT1 -> T9,\nX9 -> T9,\nT2 -> T10,\nX10 -> T10" }, { "from": 7, "to": 17, "label": "CASE" }, { "from": 17, "to": 19, "label": "PARALLEL" }, { "from": 17, "to": 20, "label": "PARALLEL" }, { "from": 19, "to": 23, "label": "ONLY EVAL with clause\nloop(X26, X27, X28) :- ','(>(X26, 0), loop_body(X26, X27, X28)).\nand substitutionT9 -> T21,\nX26 -> T21,\nT10 -> T22,\nX27 -> T22,\nX28 -> 0" }, { "from": 20, "to": 4838, "label": "PARALLEL" }, { "from": 20, "to": 4839, "label": "PARALLEL" }, { "from": 23, "to": 24, "label": "IS ERROR" }, { "from": 23, "to": 2324, "label": "ARITHCOMP SUCCESS" }, { "from": 23, "to": 2325, "label": "ARITHCOMP FAIL" }, { "from": 2324, "to": 2335, "label": "CASE" }, { "from": 2335, "to": 2344, "label": "PARALLEL" }, { "from": 2335, "to": 2345, "label": "PARALLEL" }, { "from": 2344, "to": 2356, "label": "ONLY EVAL with clause\nloop_body(X50, X51, X52) :- ','(>(X50, 0), ','(is(X53, -(X50, 1)), ','(is(X54, +(X52, 1)), loop(X53, X51, X54)))).\nand substitutionT21 -> T33,\nX50 -> T33,\nT22 -> T34,\nX51 -> T34,\nX52 -> 0" }, { "from": 2345, "to": 4738, "label": "PARALLEL" }, { "from": 2345, "to": 4739, "label": "PARALLEL" }, { "from": 2356, "to": 4018, "label": "ARITHCOMP SUCCESS" }, { "from": 2356, "to": 4019, "label": "ARITHCOMP FAIL" }, { "from": 4018, "to": 4027, "label": "\nX53 -> T35" }, { "from": 4027, "to": 4028, "label": "\nX54 -> T36" }, { "from": 4028, "to": 4029, "label": "CASE" }, { "from": 4029, "to": 4030, "label": "PARALLEL" }, { "from": 4029, "to": 4031, "label": "PARALLEL" }, { "from": 4030, "to": 4032, "label": "ONLY EVAL with clause\nloop(X70, X71, X72) :- ','(>(X70, 0), loop_body(X70, X71, X72)).\nand substitutionT35 -> T52,\nX70 -> T52,\nT34 -> T53,\nX71 -> T53,\nT36 -> T54,\nX72 -> T54" }, { "from": 4031, "to": 4383, "label": "PARALLEL" }, { "from": 4031, "to": 4384, "label": "PARALLEL" }, { "from": 4383, "to": 4385, "label": "ONLY EVAL with clause\nloop(X85, X86, X87) :- ','(>(X86, 0), loop_body(X85, X86, X87)).\nand substitutionT35 -> T67,\nX85 -> T67,\nT34 -> T68,\nX86 -> T68,\nT36 -> T69,\nX87 -> T69" }, { "from": 4384, "to": 4736, "label": "ONLY EVAL with clause\nloop(X94, X95, X96) :- ','(=<(X94, 0), =<(X95, 0)).\nand substitutionT35 -> T76,\nX94 -> T76,\nT34 -> T77,\nX95 -> T77,\nT36 -> T78,\nX96 -> T78" }, { "from": 4385, "to": 4386, "label": "IS ERROR" }, { "from": 4738, "to": 4740, "label": "ONLY EVAL with clause\nloop_body(X113, X114, X115) :- ','(=<(X113, 0), ','(>(X114, 0), ','(is(X116, -(X114, 1)), ','(is(X117, +(X115, 1)), loop(X113, X116, X117))))).\nand substitutionT21 -> T87,\nX113 -> T87,\nT22 -> T88,\nX114 -> T88,\nX115 -> 0" }, { "from": 4739, "to": 4792, "label": "ONLY EVAL with clause\nloop_body(X167, X168, X169) :- ','(=<(X167, 0), ','(=<(X168, 0), ','(is(X170, +(X169, 1)), loop(X167, X168, X170)))).\nand substitutionT21 -> T137,\nX167 -> T137,\nT22 -> T138,\nX168 -> T138,\nX169 -> 0" }, { "from": 4740, "to": 4751, "label": "ARITHCOMP SUCCESS" }, { "from": 4740, "to": 4752, "label": "ARITHCOMP FAIL" }, { "from": 4751, "to": 4753, "label": "IS ERROR" }, { "from": 4751, "to": 4761, "label": "ARITHCOMP SUCCESS" }, { "from": 4751, "to": 4762, "label": "ARITHCOMP FAIL" }, { "from": 4761, "to": 4763, "label": "\nX116 -> T89" }, { "from": 4763, "to": 4764, "label": "\nX117 -> T90" }, { "from": 4764, "to": 4773, "label": "CASE" }, { "from": 4773, "to": 4774, "label": "PARALLEL" }, { "from": 4773, "to": 4775, "label": "PARALLEL" }, { "from": 4774, "to": 4776, "label": "ONLY EVAL with clause\nloop(X133, X134, X135) :- ','(>(X133, 0), loop_body(X133, X134, X135)).\nand substitutionT87 -> T106,\nX133 -> T106,\nT89 -> T107,\nX134 -> T107,\nT90 -> T108,\nX135 -> T108" }, { "from": 4775, "to": 4780, "label": "PARALLEL" }, { "from": 4775, "to": 4781, "label": "PARALLEL" }, { "from": 4780, "to": 4782, "label": "ONLY EVAL with clause\nloop(X148, X149, X150) :- ','(>(X149, 0), loop_body(X148, X149, X150)).\nand substitutionT87 -> T121,\nX148 -> T121,\nT89 -> T122,\nX149 -> T122,\nT90 -> T123,\nX150 -> T123" }, { "from": 4781, "to": 4791, "label": "ONLY EVAL with clause\nloop(X157, X158, X159) :- ','(=<(X157, 0), =<(X158, 0)).\nand substitutionT87 -> T130,\nX157 -> T130,\nT89 -> T131,\nX158 -> T131,\nT90 -> T132,\nX159 -> T132" }, { "from": 4792, "to": 4795, "label": "ARITHCOMP SUCCESS" }, { "from": 4792, "to": 4796, "label": "ARITHCOMP FAIL" }, { "from": 4795, "to": 4797, "label": "IS ERROR" }, { "from": 4795, "to": 4802, "label": "ARITHCOMP SUCCESS" }, { "from": 4795, "to": 4803, "label": "ARITHCOMP FAIL" }, { "from": 4802, "to": 4804, "label": "\nX170 -> T139" }, { "from": 4804, "to": 4805, "label": "CASE" }, { "from": 4805, "to": 4806, "label": "PARALLEL" }, { "from": 4805, "to": 4807, "label": "PARALLEL" }, { "from": 4806, "to": 4808, "label": "ONLY EVAL with clause\nloop(X186, X187, X188) :- ','(>(X186, 0), loop_body(X186, X187, X188)).\nand substitutionT137 -> T155,\nX186 -> T155,\nT138 -> T156,\nX187 -> T156,\nT139 -> T157,\nX188 -> T157" }, { "from": 4807, "to": 4828, "label": "PARALLEL" }, { "from": 4807, "to": 4829, "label": "PARALLEL" }, { "from": 4828, "to": 4830, "label": "ONLY EVAL with clause\nloop(X201, X202, X203) :- ','(>(X202, 0), loop_body(X201, X202, X203)).\nand substitutionT137 -> T170,\nX201 -> T170,\nT138 -> T171,\nX202 -> T171,\nT139 -> T172,\nX203 -> T172" }, { "from": 4829, "to": 4836, "label": "ONLY EVAL with clause\nloop(X210, X211, X212) :- ','(=<(X210, 0), =<(X211, 0)).\nand substitutionT137 -> T179,\nX210 -> T179,\nT138 -> T180,\nX211 -> T180,\nT139 -> T181,\nX212 -> T181" }, { "from": 4838, "to": 4840, "label": "ONLY EVAL with clause\nloop(X225, X226, X227) :- ','(>(X226, 0), loop_body(X225, X226, X227)).\nand substitutionT9 -> T190,\nX225 -> T190,\nT10 -> T191,\nX226 -> T191,\nX227 -> 0" }, { "from": 4839, "to": 6201, "label": "ONLY EVAL with clause\nloop(X418, X419, X420) :- ','(=<(X418, 0), =<(X419, 0)).\nand substitutionT9 -> T355,\nX418 -> T355,\nT10 -> T356,\nX419 -> T356,\nX420 -> 0" }, { "from": 4840, "to": 4841, "label": "IS ERROR" }, { "from": 4840, "to": 4850, "label": "ARITHCOMP SUCCESS" }, { "from": 4840, "to": 4851, "label": "ARITHCOMP FAIL" }, { "from": 4850, "to": 4854, "label": "CASE" }, { "from": 4854, "to": 4855, "label": "PARALLEL" }, { "from": 4854, "to": 4856, "label": "PARALLEL" }, { "from": 4855, "to": 4857, "label": "ONLY EVAL with clause\nloop_body(X249, X250, X251) :- ','(>(X249, 0), ','(is(X252, -(X249, 1)), ','(is(X253, +(X251, 1)), loop(X252, X250, X253)))).\nand substitutionT190 -> T202,\nX249 -> T202,\nT191 -> T203,\nX250 -> T203,\nX251 -> 0" }, { "from": 4856, "to": 4985, "label": "PARALLEL" }, { "from": 4856, "to": 4986, "label": "PARALLEL" }, { "from": 4857, "to": 4858, "label": "IS ERROR" }, { "from": 4857, "to": 4871, "label": "ARITHCOMP SUCCESS" }, { "from": 4857, "to": 4872, "label": "ARITHCOMP FAIL" }, { "from": 4871, "to": 4873, "label": "\nX252 -> T204" }, { "from": 4873, "to": 4874, "label": "\nX253 -> T205" }, { "from": 4874, "to": 4883, "label": "CASE" }, { "from": 4883, "to": 4884, "label": "PARALLEL" }, { "from": 4883, "to": 4885, "label": "PARALLEL" }, { "from": 4884, "to": 4886, "label": "ONLY EVAL with clause\nloop(X269, X270, X271) :- ','(>(X269, 0), loop_body(X269, X270, X271)).\nand substitutionT204 -> T221,\nX269 -> T221,\nT203 -> T222,\nX270 -> T222,\nT205 -> T223,\nX271 -> T223" }, { "from": 4885, "to": 4939, "label": "PARALLEL" }, { "from": 4885, "to": 4940, "label": "PARALLEL" }, { "from": 4939, "to": 4946, "label": "ONLY EVAL with clause\nloop(X284, X285, X286) :- ','(>(X285, 0), loop_body(X284, X285, X286)).\nand substitutionT204 -> T236,\nX284 -> T236,\nT203 -> T237,\nX285 -> T237,\nT205 -> T238,\nX286 -> T238" }, { "from": 4940, "to": 4972, "label": "ONLY EVAL with clause\nloop(X293, X294, X295) :- ','(=<(X293, 0), =<(X294, 0)).\nand substitutionT204 -> T245,\nX293 -> T245,\nT203 -> T246,\nX294 -> T246,\nT205 -> T247,\nX295 -> T247" }, { "from": 4985, "to": 4987, "label": "ONLY EVAL with clause\nloop_body(X312, X313, X314) :- ','(=<(X312, 0), ','(>(X313, 0), ','(is(X315, -(X313, 1)), ','(is(X316, +(X314, 1)), loop(X312, X315, X316))))).\nand substitutionT190 -> T256,\nX312 -> T256,\nT191 -> T257,\nX313 -> T257,\nX314 -> 0" }, { "from": 4986, "to": 5915, "label": "ONLY EVAL with clause\nloop_body(X366, X367, X368) :- ','(=<(X366, 0), ','(=<(X367, 0), ','(is(X369, +(X368, 1)), loop(X366, X367, X369)))).\nand substitutionT190 -> T306,\nX366 -> T306,\nT191 -> T307,\nX367 -> T307,\nX368 -> 0" }, { "from": 4987, "to": 4988, "label": "IS ERROR" }, { "from": 4987, "to": 4991, "label": "ARITHCOMP SUCCESS" }, { "from": 4987, "to": 4992, "label": "ARITHCOMP FAIL" }, { "from": 4991, "to": 5013, "label": "ARITHCOMP SUCCESS" }, { "from": 4991, "to": 5014, "label": "ARITHCOMP FAIL" }, { "from": 5013, "to": 5015, "label": "\nX315 -> T258" }, { "from": 5015, "to": 5016, "label": "\nX316 -> T259" }, { "from": 5016, "to": 5116, "label": "CASE" }, { "from": 5116, "to": 5117, "label": "PARALLEL" }, { "from": 5116, "to": 5118, "label": "PARALLEL" }, { "from": 5117, "to": 5122, "label": "ONLY EVAL with clause\nloop(X332, X333, X334) :- ','(>(X332, 0), loop_body(X332, X333, X334)).\nand substitutionT256 -> T275,\nX332 -> T275,\nT258 -> T276,\nX333 -> T276,\nT259 -> T277,\nX334 -> T277" }, { "from": 5118, "to": 5124, "label": "PARALLEL" }, { "from": 5118, "to": 5125, "label": "PARALLEL" }, { "from": 5124, "to": 5126, "label": "ONLY EVAL with clause\nloop(X347, X348, X349) :- ','(>(X348, 0), loop_body(X347, X348, X349)).\nand substitutionT256 -> T290,\nX347 -> T290,\nT258 -> T291,\nX348 -> T291,\nT259 -> T292,\nX349 -> T292" }, { "from": 5125, "to": 5213, "label": "ONLY EVAL with clause\nloop(X356, X357, X358) :- ','(=<(X356, 0), =<(X357, 0)).\nand substitutionT256 -> T299,\nX356 -> T299,\nT258 -> T300,\nX357 -> T300,\nT259 -> T301,\nX358 -> T301" }, { "from": 5915, "to": 5916, "label": "IS ERROR" }, { "from": 5915, "to": 5949, "label": "ARITHCOMP SUCCESS" }, { "from": 5915, "to": 5950, "label": "ARITHCOMP FAIL" }, { "from": 5949, "to": 6028, "label": "ARITHCOMP SUCCESS" }, { "from": 5949, "to": 6030, "label": "ARITHCOMP FAIL" }, { "from": 6028, "to": 6047, "label": "\nX369 -> T308" }, { "from": 6047, "to": 6128, "label": "CASE" }, { "from": 6128, "to": 6129, "label": "PARALLEL" }, { "from": 6128, "to": 6130, "label": "PARALLEL" }, { "from": 6129, "to": 6131, "label": "ONLY EVAL with clause\nloop(X385, X386, X387) :- ','(>(X385, 0), loop_body(X385, X386, X387)).\nand substitutionT306 -> T324,\nX385 -> T324,\nT307 -> T325,\nX386 -> T325,\nT308 -> T326,\nX387 -> T326" }, { "from": 6130, "to": 6153, "label": "PARALLEL" }, { "from": 6130, "to": 6154, "label": "PARALLEL" }, { "from": 6153, "to": 6155, "label": "ONLY EVAL with clause\nloop(X400, X401, X402) :- ','(>(X401, 0), loop_body(X400, X401, X402)).\nand substitutionT306 -> T339,\nX400 -> T339,\nT307 -> T340,\nX401 -> T340,\nT308 -> T341,\nX402 -> T341" }, { "from": 6154, "to": 6194, "label": "ONLY EVAL with clause\nloop(X409, X410, X411) :- ','(=<(X409, 0), =<(X410, 0)).\nand substitutionT306 -> T348,\nX409 -> T348,\nT307 -> T349,\nX410 -> T349,\nT308 -> T350,\nX411 -> T350" }, { "from": 6201, "to": 6202, "label": "IS ERROR" }, { "from": 6201, "to": 6225, "label": "ARITHCOMP SUCCESS" }, { "from": 6201, "to": 6226, "label": "ARITHCOMP FAIL" }, { "from": 6225, "to": 6227, "label": "IS ERROR" }, { "from": 6225, "to": 6234, "label": "ARITHCOMP SUCCESS" }, { "from": 6225, "to": 6235, "label": "ARITHCOMP FAIL" }, { "from": 6234, "to": 6236, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) TRUE