/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern g(a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 27 ms] (2) IRSwT (3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (4) TRUE ---------------------------------------- (0) Obligation: Clauses: g(W) :- ','(eq(X, .(.(a, []), .(.(R, []), []))), ','(eq(Y, .(.(S, .(c, [])), .([], []))), ','(app_1(X, Y, Z), ','(eq(Z, .(U, V)), app_2(U, U, W))))). app_1([], X, X). app_1(.(X, Xs), Ys, .(X, Zs)) :- app_1(Xs, Ys, Zs). app_2([], X, X). app_2(.(X, Xs), Ys, .(X, Zs)) :- app_2(Xs, Ys, Zs). eq(X, X). Query: g(a) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 3, "program": { "directives": [], "clauses": [ [ "(g W)", "(',' (eq X (. (. (a) ([])) (. (. R ([])) ([])))) (',' (eq Y (. (. S (. (c) ([]))) (. ([]) ([])))) (',' (app_1 X Y Z) (',' (eq Z (. U V)) (app_2 U U W)))))" ], [ "(app_1 ([]) X X)", null ], [ "(app_1 (. X Xs) Ys (. X Zs))", "(app_1 Xs Ys Zs)" ], [ "(app_2 ([]) X X)", null ], [ "(app_2 (. X Xs) Ys (. X Zs))", "(app_2 Xs Ys Zs)" ], [ "(eq X X)", null ] ] }, "graph": { "nodes": { "type": "Nodes", "590": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "591": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T470 (. 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T329 (. T330 (. T331 (. T332 (. T333 (. T334 T326))))))) T327)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "564": { "goal": [{ "clause": 4, "scope": 15, "term": "(app_2 T326 (. T328 (. T329 (. T330 (. T331 (. T332 (. T333 (. T334 T326))))))) T327)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "569": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "66": { "goal": [{ "clause": 5, "scope": 2, "term": "(',' (eq X15 (. (. (a) ([])) (. (. X16 ([])) ([])))) (',' (eq X17 (. (. X18 (. (c) ([]))) (. ([]) ([])))) (',' (app_1 X15 X17 X19) (',' (eq X19 (. X20 X21)) (app_2 X20 X20 T6)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [ "X15", "X16", "X17", "X18", "X19", "X20", "X21" ], "exprvars": [] } }, "294": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X19"], "exprvars": [] } }, "295": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (eq T7 (. X20 X21)) (app_2 X20 X20 T8))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [ "X20", "X21" ], "exprvars": [] } }, "570": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "571": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "297": { "goal": [ { "clause": 1, "scope": 4, "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)" }, { "clause": 2, "scope": 4, "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X19"], "exprvars": [] } }, "452": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "299": { "goal": [{ "clause": 2, "scope": 4, "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X19"], "exprvars": [] } }, "453": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T51 (. T53 (. T54 T51)) T52)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "454": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "579": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T414 (. T416 (. T417 (. T418 (. T419 (. T420 (. T421 (. T422 (. T423 T414)))))))) T415)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "580": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "584": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T414 (. T416 T440) T415)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "585": { "goal": [ { "clause": 3, "scope": 16, "term": "(app_2 T414 (. T416 T440) T415)" }, { "clause": 4, "scope": 16, "term": "(app_2 T414 (. T416 T440) T415)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "586": { "goal": [{ "clause": 3, "scope": 16, "term": "(app_2 T414 (. T416 T440) T415)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "587": { "goal": [{ "clause": 4, "scope": 16, "term": "(app_2 T414 (. T416 T440) T415)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "588": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "589": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "502": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "503": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "504": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "505": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "506": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "509": { "goal": [ { "clause": 3, "scope": 12, "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" }, { "clause": 4, "scope": 12, "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 3, "to": 33, "label": "CASE" }, { "from": 33, "to": 36, "label": "ONLY EVAL with clause\ng(X14) :- ','(eq(X15, .(.(a, []), .(.(X16, []), []))), ','(eq(X17, .(.(X18, .(c, [])), .([], []))), ','(app_1(X15, X17, X19), ','(eq(X19, .(X20, X21)), app_2(X20, X20, X14))))).\nand substitutionT1 -> T6,\nX14 -> T6,\nT5 -> T6" }, { "from": 36, "to": 66, "label": "CASE" }, { "from": 66, "to": 140, "label": "ONLY EVAL with clause\neq(X34, X34).\nand substitutionX15 -> .(.(a, []), .(.(X36, []), [])),\nX34 -> .(.(a, []), .(.(X36, []), [])),\nX16 -> X36,\nX35 -> .(.(a, []), .(.(X36, []), []))" }, { "from": 140, "to": 142, "label": "CASE" }, { "from": 142, "to": 143, "label": "ONLY EVAL with clause\neq(X47, X47).\nand substitutionX17 -> .(.(X49, .(c, [])), .([], [])),\nX47 -> .(.(X49, .(c, [])), .([], [])),\nX18 -> X49,\nX48 -> .(.(X49, .(c, [])), .([], []))" }, { "from": 143, "to": 294, "label": "SPLIT 1" }, { "from": 143, "to": 295, "label": "SPLIT 2\nreplacements:X19 -> T7,\nT6 -> T8" }, { "from": 294, "to": 297, "label": "CASE" }, { "from": 295, "to": 375, "label": "CASE" }, { "from": 297, "to": 299, "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification" }, { "from": 299, "to": 319, "label": "ONLY EVAL with clause\napp_1(.(X71, X72), X73, .(X71, X74)) :- app_1(X72, X73, X74).\nand substitutionX71 -> .(a, []),\nX36 -> X75,\nX72 -> .(.(X75, []), []),\nX49 -> X76,\nX73 -> .(.(X76, .(c, [])), .([], [])),\nX74 -> X77,\nX19 -> .(.(a, []), X77)" }, { "from": 319, "to": 320, "label": "CASE" }, { "from": 320, "to": 321, "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification" }, { "from": 321, "to": 356, "label": "ONLY EVAL with clause\napp_1(.(X97, X98), X99, .(X97, X100)) :- app_1(X98, X99, X100).\nand substitutionX75 -> X101,\nX97 -> .(X101, []),\nX98 -> [],\nX76 -> X102,\nX99 -> .(.(X102, .(c, [])), .([], [])),\nX100 -> X103,\nX77 -> .(.(X101, []), X103)" }, { "from": 356, "to": 361, "label": "CASE" }, { "from": 361, "to": 364, "label": "PARALLEL" }, { "from": 361, "to": 365, "label": "PARALLEL" }, { "from": 364, "to": 371, "label": "ONLY EVAL with clause\napp_1([], X114, X114).\nand substitutionX102 -> X115,\nX114 -> .(.(X115, .(c, [])), .([], [])),\nX103 -> .(.(X115, .(c, [])), .([], []))" }, { "from": 365, "to": 373, "label": "BACKTRACK\nfor clause: app_1(.(X, Xs), Ys, .(X, Zs)) :- app_1(Xs, Ys, Zs)because of non-unification" }, { "from": 371, "to": 372, "label": "SUCCESS" }, { "from": 375, "to": 378, "label": "EVAL with clause\neq(X124, X124).\nand substitutionT7 -> .(T18, T17),\nX124 -> .(T18, T17),\nX20 -> T18,\nX21 -> T17,\nT15 -> .(T18, T17),\nT16 -> T18,\nT8 -> T19" }, { "from": 375, "to": 379, "label": "EVAL-BACKTRACK" }, { "from": 378, "to": 385, "label": "CASE" }, { "from": 385, "to": 386, "label": "PARALLEL" }, { "from": 385, "to": 387, "label": "PARALLEL" }, { "from": 386, "to": 388, "label": "EVAL with clause\napp_2([], X131, X131).\nand substitutionT18 -> [],\nX131 -> [],\nT19 -> []" }, { "from": 386, "to": 419, "label": "EVAL-BACKTRACK" }, { "from": 387, "to": 422, "label": "EVAL with clause\napp_2(.(X140, X141), X142, .(X140, X143)) :- app_2(X141, X142, X143).\nand substitutionX140 -> T31,\nX141 -> T29,\nT18 -> .(T31, T29),\nX142 -> .(T31, T29),\nX143 -> T30,\nT19 -> .(T31, T30),\nT27 -> T29,\nT28 -> T30,\nT26 -> T31" }, { "from": 387, "to": 424, "label": "EVAL-BACKTRACK" }, { "from": 388, "to": 420, "label": "SUCCESS" }, { "from": 422, "to": 425, "label": "CASE" }, { "from": 425, "to": 426, "label": "PARALLEL" }, { "from": 425, "to": 427, "label": "PARALLEL" }, { "from": 426, "to": 429, "label": "EVAL with clause\napp_2([], X150, X150).\nand substitutionT29 -> [],\nT31 -> T38,\nX150 -> .(T38, []),\nT30 -> .(T38, [])" }, { "from": 426, "to": 430, "label": "EVAL-BACKTRACK" }, { "from": 427, "to": 453, "label": "EVAL with clause\napp_2(.(X159, X160), X161, .(X159, X162)) :- app_2(X160, X161, X162).\nand substitutionX159 -> T54,\nX160 -> T51,\nT29 -> .(T54, T51),\nT31 -> T53,\nX161 -> .(T53, .(T54, T51)),\nX162 -> T52,\nT30 -> .(T54, T52),\nT48 -> T51,\nT50 -> T52,\nT49 -> T53,\nT47 -> T54" }, { "from": 427, "to": 454, "label": "EVAL-BACKTRACK" }, { "from": 429, "to": 452, "label": "SUCCESS" }, { "from": 453, "to": 471, "label": "CASE" }, { "from": 471, "to": 472, "label": "PARALLEL" }, { "from": 471, "to": 473, "label": "PARALLEL" }, { "from": 472, "to": 475, "label": "EVAL with clause\napp_2([], X169, X169).\nand substitutionT51 -> [],\nT53 -> T67,\nT54 -> T68,\nX169 -> .(T67, .(T68, [])),\nT52 -> .(T67, .(T68, []))" }, { "from": 472, "to": 476, "label": "EVAL-BACKTRACK" }, { "from": 473, "to": 483, "label": "EVAL with clause\napp_2(.(X178, X179), X180, .(X178, X181)) :- app_2(X179, X180, X181).\nand substitutionX178 -> T88,\nX179 -> T84,\nT51 -> .(T88, T84),\nT53 -> T86,\nT54 -> T87,\nX180 -> .(T86, .(T87, .(T88, T84))),\nX181 -> T85,\nT52 -> .(T88, T85),\nT80 -> T84,\nT83 -> T85,\nT81 -> T86,\nT82 -> T87,\nT79 -> T88" }, { "from": 473, "to": 484, "label": "EVAL-BACKTRACK" }, { "from": 475, "to": 477, "label": "SUCCESS" }, { "from": 483, "to": 488, "label": "CASE" }, { "from": 488, "to": 489, "label": "PARALLEL" }, { "from": 488, "to": 490, "label": "PARALLEL" }, { "from": 489, "to": 502, "label": "EVAL with clause\napp_2([], X188, X188).\nand substitutionT84 -> [],\nT86 -> T107,\nT87 -> T108,\nT88 -> T109,\nX188 -> .(T107, .(T108, .(T109, []))),\nT85 -> .(T107, .(T108, .(T109, [])))" }, { "from": 489, "to": 503, "label": "EVAL-BACKTRACK" }, { "from": 490, "to": 505, "label": "EVAL with clause\napp_2(.(X197, X198), X199, .(X197, X200)) :- app_2(X198, X199, X200).\nand substitutionX197 -> T133,\nX198 -> T128,\nT84 -> .(T133, T128),\nT86 -> T130,\nT87 -> T131,\nT88 -> T132,\nX199 -> .(T130, .(T131, .(T132, .(T133, T128)))),\nX200 -> T129,\nT85 -> .(T133, T129),\nT123 -> T128,\nT127 -> T129,\nT124 -> T130,\nT125 -> T131,\nT126 -> T132,\nT122 -> T133" }, { "from": 490, "to": 506, "label": "EVAL-BACKTRACK" }, { "from": 502, "to": 504, "label": "SUCCESS" }, { "from": 505, "to": 509, "label": "CASE" }, { "from": 509, "to": 510, "label": "PARALLEL" }, { "from": 509, "to": 511, "label": "PARALLEL" }, { "from": 510, "to": 514, "label": "EVAL with clause\napp_2([], X207, X207).\nand substitutionT128 -> [],\nT130 -> T158,\nT131 -> T159,\nT132 -> T160,\nT133 -> T161,\nX207 -> .(T158, .(T159, .(T160, .(T161, [])))),\nT129 -> .(T158, .(T159, .(T160, .(T161, []))))" }, { "from": 510, "to": 515, "label": "EVAL-BACKTRACK" }, { "from": 511, "to": 526, "label": "EVAL with clause\napp_2(.(X216, X217), X218, .(X216, X219)) :- app_2(X217, X218, X219).\nand substitutionX216 -> T189,\nX217 -> T183,\nT128 -> .(T189, T183),\nT130 -> T185,\nT131 -> T186,\nT132 -> T187,\nT133 -> T188,\nX218 -> .(T185, .(T186, .(T187, .(T188, .(T189, T183))))),\nX219 -> T184,\nT129 -> .(T189, T184),\nT177 -> T183,\nT182 -> T184,\nT178 -> T185,\nT179 -> T186,\nT180 -> T187,\nT181 -> T188,\nT176 -> T189" }, { "from": 511, "to": 527, "label": "EVAL-BACKTRACK" }, { "from": 514, "to": 516, "label": "SUCCESS" }, { "from": 526, "to": 531, "label": "CASE" }, { "from": 531, "to": 532, "label": "PARALLEL" }, { "from": 531, "to": 533, "label": "PARALLEL" }, { "from": 532, "to": 534, "label": "EVAL with clause\napp_2([], X226, X226).\nand substitutionT183 -> [],\nT185 -> T220,\nT186 -> T221,\nT187 -> T222,\nT188 -> T223,\nT189 -> T224,\nX226 -> .(T220, .(T221, .(T222, .(T223, .(T224, []))))),\nT184 -> .(T220, .(T221, .(T222, .(T223, .(T224, [])))))" }, { "from": 532, "to": 535, "label": "EVAL-BACKTRACK" }, { "from": 533, "to": 541, "label": "EVAL with clause\napp_2(.(X235, X236), X237, .(X235, X238)) :- app_2(X236, X237, X238).\nand substitutionX235 -> T256,\nX236 -> T249,\nT183 -> .(T256, T249),\nT185 -> T251,\nT186 -> T252,\nT187 -> T253,\nT188 -> T254,\nT189 -> T255,\nX237 -> .(T251, .(T252, .(T253, .(T254, .(T255, .(T256, T249)))))),\nX238 -> T250,\nT184 -> .(T256, T250),\nT242 -> T249,\nT248 -> T250,\nT243 -> T251,\nT244 -> T252,\nT245 -> T253,\nT246 -> T254,\nT247 -> T255,\nT241 -> T256" }, { "from": 533, "to": 542, "label": "EVAL-BACKTRACK" }, { "from": 534, "to": 536, "label": "SUCCESS" }, { "from": 541, "to": 549, "label": "CASE" }, { "from": 549, "to": 551, "label": "PARALLEL" }, { "from": 549, "to": 552, "label": "PARALLEL" }, { "from": 551, "to": 555, "label": "EVAL with clause\napp_2([], X245, X245).\nand substitutionT249 -> [],\nT251 -> T293,\nT252 -> T294,\nT253 -> T295,\nT254 -> T296,\nT255 -> T297,\nT256 -> T298,\nX245 -> .(T293, .(T294, .(T295, .(T296, .(T297, .(T298, [])))))),\nT250 -> .(T293, .(T294, .(T295, .(T296, .(T297, .(T298, []))))))" }, { "from": 551, "to": 556, "label": "EVAL-BACKTRACK" }, { "from": 552, "to": 560, "label": "EVAL with clause\napp_2(.(X254, X255), X256, .(X254, X257)) :- app_2(X255, X256, X257).\nand substitutionX254 -> T334,\nX255 -> T326,\nT249 -> .(T334, T326),\nT251 -> T328,\nT252 -> T329,\nT253 -> T330,\nT254 -> T331,\nT255 -> T332,\nT256 -> T333,\nX256 -> .(T328, .(T329, .(T330, .(T331, .(T332, .(T333, .(T334, T326))))))),\nX257 -> T327,\nT250 -> .(T334, T327),\nT318 -> T326,\nT325 -> T327,\nT319 -> T328,\nT320 -> T329,\nT321 -> T330,\nT322 -> T331,\nT323 -> T332,\nT324 -> T333,\nT317 -> T334" }, { "from": 552, "to": 561, "label": "EVAL-BACKTRACK" }, { "from": 555, "to": 557, "label": "SUCCESS" }, { "from": 560, "to": 562, "label": "CASE" }, { "from": 562, "to": 563, "label": "PARALLEL" }, { "from": 562, "to": 564, "label": "PARALLEL" }, { "from": 563, "to": 569, "label": "EVAL with clause\napp_2([], X264, X264).\nand substitutionT326 -> [],\nT328 -> T377,\nT329 -> T378,\nT330 -> T379,\nT331 -> T380,\nT332 -> T381,\nT333 -> T382,\nT334 -> T383,\nX264 -> .(T377, .(T378, .(T379, .(T380, .(T381, .(T382, .(T383, []))))))),\nT327 -> .(T377, .(T378, .(T379, .(T380, .(T381, .(T382, .(T383, [])))))))" }, { "from": 563, "to": 570, "label": "EVAL-BACKTRACK" }, { "from": 564, "to": 579, "label": "EVAL with clause\napp_2(.(X273, X274), X275, .(X273, X276)) :- app_2(X274, X275, X276).\nand substitutionX273 -> T423,\nX274 -> T414,\nT326 -> .(T423, T414),\nT328 -> T416,\nT329 -> T417,\nT330 -> T418,\nT331 -> T419,\nT332 -> T420,\nT333 -> T421,\nT334 -> T422,\nX275 -> .(T416, .(T417, .(T418, .(T419, .(T420, .(T421, .(T422, .(T423, T414)))))))),\nX276 -> T415,\nT327 -> .(T423, T415),\nT405 -> T414,\nT413 -> T415,\nT406 -> T416,\nT407 -> T417,\nT408 -> T418,\nT409 -> T419,\nT410 -> T420,\nT411 -> T421,\nT412 -> T422,\nT404 -> T423" }, { "from": 564, "to": 580, "label": "EVAL-BACKTRACK" }, { "from": 569, "to": 571, "label": "SUCCESS" }, { "from": 579, "to": 584, "label": "GENERALIZATION\nT440 <-- .(T417, .(T418, .(T419, .(T420, .(T421, .(T422, .(T423, T414)))))))" }, { "from": 584, "to": 585, "label": "CASE" }, { "from": 585, "to": 586, "label": "PARALLEL" }, { "from": 585, "to": 587, "label": "PARALLEL" }, { "from": 586, "to": 588, "label": "EVAL with clause\napp_2([], X285, X285).\nand substitutionT414 -> [],\nT416 -> T453,\nT440 -> T454,\nX285 -> .(T453, T454),\nT415 -> .(T453, T454)" }, { "from": 586, "to": 589, "label": "EVAL-BACKTRACK" }, { "from": 587, "to": 591, "label": "EVAL with clause\napp_2(.(X294, X295), X296, .(X294, X297)) :- app_2(X295, X296, X297).\nand substitutionX294 -> T465,\nX295 -> T470,\nT414 -> .(T465, T470),\nT416 -> T472,\nT440 -> T473,\nX296 -> .(T472, T473),\nX297 -> T471,\nT415 -> .(T465, T471),\nT466 -> T470,\nT469 -> T471,\nT467 -> T472,\nT468 -> T473" }, { "from": 587, "to": 592, "label": "EVAL-BACKTRACK" }, { "from": 588, "to": 590, "label": "SUCCESS" }, { "from": 591, "to": 584, "label": "INSTANCE with matching:\nT414 -> T470\nT416 -> T472\nT440 -> T473\nT415 -> T471" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Rules: f586_out -> f585_out :|: TRUE f587_out -> f585_out :|: TRUE f585_in -> f587_in :|: TRUE f585_in -> f586_in :|: TRUE f591_out -> f587_out :|: TRUE f587_in -> f592_in :|: TRUE f587_in -> f591_in :|: TRUE f592_out -> f587_out :|: TRUE f585_out -> f584_out :|: TRUE f584_in -> f585_in :|: TRUE f591_in -> f584_in :|: TRUE f584_out -> f591_out :|: TRUE f33_out -> f3_out :|: TRUE f3_in -> f33_in :|: TRUE f36_out -> f33_out :|: TRUE f33_in -> f36_in :|: TRUE f66_out -> f36_out :|: TRUE f36_in -> f66_in :|: TRUE f140_out -> f66_out :|: TRUE f66_in -> f140_in :|: TRUE f140_in -> f142_in :|: TRUE f142_out -> f140_out :|: TRUE f142_in -> f143_in :|: TRUE f143_out -> f142_out :|: TRUE f295_out -> f143_out :|: TRUE f143_in -> f294_in :|: TRUE f294_out -> f295_in :|: TRUE f375_out -> f295_out :|: TRUE f295_in -> f375_in :|: TRUE f375_in -> f378_in :|: TRUE f379_out -> f375_out :|: TRUE f375_in -> f379_in :|: TRUE f378_out -> f375_out :|: TRUE f378_in -> f385_in :|: TRUE f385_out -> f378_out :|: TRUE f385_in -> f387_in :|: TRUE f386_out -> f385_out :|: TRUE f385_in -> f386_in :|: TRUE f387_out -> f385_out :|: TRUE f387_in -> f422_in :|: TRUE f422_out -> f387_out :|: TRUE f387_in -> f424_in :|: TRUE f424_out -> f387_out :|: TRUE f422_in -> f425_in :|: TRUE f425_out -> f422_out :|: TRUE f425_in -> f426_in :|: TRUE f426_out -> f425_out :|: TRUE f425_in -> f427_in :|: TRUE f427_out -> f425_out :|: TRUE f427_in -> f454_in :|: TRUE f427_in -> f453_in :|: TRUE f453_out -> f427_out :|: TRUE f454_out -> f427_out :|: TRUE f453_in -> f471_in :|: TRUE f471_out -> f453_out :|: TRUE f472_out -> f471_out :|: TRUE f471_in -> f472_in :|: TRUE f473_out -> f471_out :|: TRUE f471_in -> f473_in :|: TRUE f473_in -> f483_in :|: TRUE f483_out -> f473_out :|: TRUE f473_in -> f484_in :|: TRUE f484_out -> f473_out :|: TRUE f483_in -> f488_in :|: TRUE f488_out -> f483_out :|: TRUE f488_in -> f490_in :|: TRUE f489_out -> f488_out :|: TRUE f488_in -> f489_in :|: TRUE f490_out -> f488_out :|: TRUE f490_in -> f506_in :|: TRUE f506_out -> f490_out :|: TRUE f490_in -> f505_in :|: TRUE f505_out -> f490_out :|: TRUE f505_in -> f509_in :|: TRUE f509_out -> f505_out :|: TRUE f509_in -> f511_in :|: TRUE f510_out -> f509_out :|: TRUE f509_in -> f510_in :|: TRUE f511_out -> f509_out :|: TRUE f511_in -> f527_in :|: TRUE f527_out -> f511_out :|: TRUE f511_in -> f526_in :|: TRUE f526_out -> f511_out :|: TRUE f526_in -> f531_in :|: TRUE f531_out -> f526_out :|: TRUE f533_out -> f531_out :|: TRUE f532_out -> f531_out :|: TRUE f531_in -> f532_in :|: TRUE f531_in -> f533_in :|: TRUE f542_out -> f533_out :|: TRUE f533_in -> f541_in :|: TRUE f541_out -> f533_out :|: TRUE f533_in -> f542_in :|: TRUE f541_in -> f549_in :|: TRUE f549_out -> f541_out :|: TRUE f552_out -> f549_out :|: TRUE f549_in -> f552_in :|: TRUE f549_in -> f551_in :|: TRUE f551_out -> f549_out :|: TRUE f560_out -> f552_out :|: TRUE f552_in -> f561_in :|: TRUE f561_out -> f552_out :|: TRUE f552_in -> f560_in :|: TRUE f562_out -> f560_out :|: TRUE f560_in -> f562_in :|: TRUE f562_in -> f563_in :|: TRUE f564_out -> f562_out :|: TRUE f562_in -> f564_in :|: TRUE f563_out -> f562_out :|: TRUE f580_out -> f564_out :|: TRUE f564_in -> f579_in :|: TRUE f579_out -> f564_out :|: TRUE f564_in -> f580_in :|: TRUE f579_in -> f584_in :|: TRUE f584_out -> f579_out :|: TRUE Start term: f3_in ---------------------------------------- (3) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (4) TRUE