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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern g(a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof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, 104 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": 2, "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": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "351": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "595": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T470 (. 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T31 T29) T30)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "451": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "572": { "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": [] } }, "331": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "452": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "573": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "574": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T414 (. T416 T440) T415)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "455": { "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": [] } }, "335": { "goal": [ { "clause": 3, "scope": 9, "term": "(app_2 T29 (. T31 T29) T30)" }, { "clause": 4, "scope": 9, "term": "(app_2 T29 (. T31 T29) T30)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "456": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "336": { "goal": [{ "clause": 3, "scope": 9, "term": "(app_2 T29 (. T31 T29) T30)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "578": { "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": [] } }, "337": { "goal": [{ "clause": 4, "scope": 9, "term": "(app_2 T29 (. T31 T29) T30)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "579": { "goal": [{ "clause": 3, "scope": 16, "term": "(app_2 T414 (. T416 T440) T415)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "339": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "580": { "goal": [{ "clause": 4, "scope": 16, "term": "(app_2 T414 (. T416 T440) T415)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "340": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "342": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "500": { "goal": [{ "clause": 3, "scope": 12, "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "501": { "goal": [{ "clause": 4, "scope": 12, "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "589": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "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": [] } }, "349": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T51 (. T53 (. T54 T51)) T52)" }], "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": [] } }, "508": { "goal": [{ "clause": -1, "scope": -1, "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "509": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 2, "to": 5, "label": "CASE" }, { "from": 5, "to": 38, "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": 38, "to": 40, "label": "CASE" }, { "from": 40, "to": 42, "label": "ONLY EVAL with clause\neq(X34, X34).\nand substitutionX15 -> .(.(a, []), .(.(X36, []), [])),\nX34 -> .(.(a, []), .(.(X36, []), [])),\nX16 -> X36,\nX35 -> .(.(a, []), .(.(X36, []), []))" }, { "from": 42, "to": 46, "label": "CASE" }, { "from": 46, "to": 249, "label": "ONLY EVAL with clause\neq(X47, X47).\nand substitutionX17 -> .(.(X49, .(c, [])), .([], [])),\nX47 -> .(.(X49, .(c, [])), .([], [])),\nX18 -> X49,\nX48 -> .(.(X49, .(c, [])), .([], []))" }, { "from": 249, "to": 252, "label": "SPLIT 1" }, { "from": 249, "to": 253, "label": "SPLIT 2\nreplacements:X19 -> T7,\nT6 -> T8" }, { "from": 252, "to": 254, "label": "CASE" }, { "from": 253, "to": 307, "label": "CASE" }, { "from": 254, "to": 255, "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification" }, { "from": 255, "to": 259, "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": 259, "to": 260, "label": "CASE" }, { "from": 260, "to": 261, "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification" }, { "from": 261, "to": 264, "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": 264, "to": 265, "label": "CASE" }, { "from": 265, "to": 275, "label": "PARALLEL" }, { "from": 265, "to": 277, "label": "PARALLEL" }, { "from": 275, "to": 292, "label": "ONLY EVAL with clause\napp_1([], X114, X114).\nand substitutionX102 -> X115,\nX114 -> .(.(X115, .(c, [])), .([], [])),\nX103 -> .(.(X115, .(c, [])), .([], []))" }, { "from": 277, "to": 300, "label": "BACKTRACK\nfor clause: app_1(.(X, Xs), Ys, .(X, Zs)) :- app_1(Xs, Ys, Zs)because of non-unification" }, { "from": 292, "to": 293, "label": "SUCCESS" }, { "from": 307, "to": 313, "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": 307, "to": 315, "label": "EVAL-BACKTRACK" }, { "from": 313, "to": 317, "label": "CASE" }, { "from": 317, "to": 321, "label": "PARALLEL" }, { "from": 317, "to": 322, "label": "PARALLEL" }, { "from": 321, "to": 325, "label": "EVAL with clause\napp_2([], X131, X131).\nand substitutionT18 -> [],\nX131 -> [],\nT19 -> []" }, { "from": 321, "to": 326, "label": "EVAL-BACKTRACK" }, { "from": 322, "to": 330, "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": 322, "to": 331, "label": "EVAL-BACKTRACK" }, { "from": 325, "to": 327, "label": "SUCCESS" }, { "from": 330, "to": 335, "label": "CASE" }, { "from": 335, "to": 336, "label": "PARALLEL" }, { "from": 335, "to": 337, "label": "PARALLEL" }, { "from": 336, "to": 339, "label": "EVAL with clause\napp_2([], X150, X150).\nand substitutionT29 -> [],\nT31 -> T38,\nX150 -> .(T38, []),\nT30 -> .(T38, [])" }, { "from": 336, "to": 340, "label": "EVAL-BACKTRACK" }, { "from": 337, "to": 349, "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": 337, "to": 351, "label": "EVAL-BACKTRACK" }, { "from": 339, "to": 342, "label": "SUCCESS" }, { "from": 349, "to": 364, "label": "CASE" }, { "from": 364, "to": 371, "label": "PARALLEL" }, { "from": 364, "to": 374, "label": "PARALLEL" }, { "from": 371, "to": 387, "label": "EVAL with clause\napp_2([], X169, X169).\nand substitutionT51 -> [],\nT53 -> T67,\nT54 -> T68,\nX169 -> .(T67, .(T68, [])),\nT52 -> .(T67, .(T68, []))" }, { "from": 371, "to": 389, "label": "EVAL-BACKTRACK" }, { "from": 374, "to": 400, "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": 374, "to": 401, "label": "EVAL-BACKTRACK" }, { "from": 387, "to": 391, "label": "SUCCESS" }, { "from": 400, "to": 407, "label": "CASE" }, { "from": 407, "to": 448, "label": "PARALLEL" }, { "from": 407, "to": 449, "label": "PARALLEL" }, { "from": 448, "to": 450, "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": 448, "to": 451, "label": "EVAL-BACKTRACK" }, { "from": 449, "to": 455, "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": 449, "to": 456, "label": "EVAL-BACKTRACK" }, { "from": 450, "to": 452, "label": "SUCCESS" }, { "from": 455, "to": 498, "label": "CASE" }, { "from": 498, "to": 500, "label": "PARALLEL" }, { "from": 498, "to": 501, "label": "PARALLEL" }, { "from": 500, "to": 502, "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": 500, "to": 503, "label": "EVAL-BACKTRACK" }, { "from": 501, "to": 508, "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": 501, "to": 509, "label": "EVAL-BACKTRACK" }, { "from": 502, "to": 504, "label": "SUCCESS" }, { "from": 508, "to": 511, "label": "CASE" }, { "from": 511, "to": 524, "label": "PARALLEL" }, { "from": 511, "to": 525, "label": "PARALLEL" }, { "from": 524, "to": 528, "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": 524, "to": 529, "label": "EVAL-BACKTRACK" }, { "from": 525, "to": 537, "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": 525, "to": 538, "label": "EVAL-BACKTRACK" }, { "from": 528, "to": 530, "label": "SUCCESS" }, { "from": 537, "to": 539, "label": "CASE" }, { "from": 539, "to": 540, "label": "PARALLEL" }, { "from": 539, "to": 541, "label": "PARALLEL" }, { "from": 540, "to": 546, "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": 540, "to": 547, "label": "EVAL-BACKTRACK" }, { "from": 541, "to": 553, "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": 541, "to": 554, "label": "EVAL-BACKTRACK" }, { "from": 546, "to": 548, "label": "SUCCESS" }, { "from": 553, "to": 566, "label": "CASE" }, { "from": 566, "to": 567, "label": "PARALLEL" }, { "from": 566, "to": 568, "label": "PARALLEL" }, { "from": 567, "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": 567, "to": 570, "label": "EVAL-BACKTRACK" }, { "from": 568, "to": 572, "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": 568, "to": 573, "label": "EVAL-BACKTRACK" }, { "from": 569, "to": 571, "label": "SUCCESS" }, { "from": 572, "to": 574, "label": "GENERALIZATION\nT440 <-- .(T417, .(T418, .(T419, .(T420, .(T421, .(T422, .(T423, T414)))))))" }, { "from": 574, "to": 578, "label": "CASE" }, { "from": 578, "to": 579, "label": "PARALLEL" }, { "from": 578, "to": 580, "label": "PARALLEL" }, { "from": 579, "to": 589, "label": "EVAL with clause\napp_2([], X285, X285).\nand substitutionT414 -> [],\nT416 -> T453,\nT440 -> T454,\nX285 -> .(T453, T454),\nT415 -> .(T453, T454)" }, { "from": 579, "to": 590, "label": "EVAL-BACKTRACK" }, { "from": 580, "to": 595, "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": 580, "to": 596, "label": "EVAL-BACKTRACK" }, { "from": 589, "to": 591, "label": "SUCCESS" }, { "from": 595, "to": 574, "label": "INSTANCE with matching:\nT414 -> T470\nT416 -> T472\nT440 -> T473\nT415 -> T471" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Rules: f595_out -> f580_out :|: TRUE f580_in -> f595_in :|: TRUE f580_in -> f596_in :|: TRUE f596_out -> f580_out :|: TRUE f578_out -> f574_out :|: TRUE f574_in -> f578_in :|: TRUE f595_in -> f574_in :|: TRUE f574_out -> f595_out :|: TRUE f578_in -> f580_in :|: TRUE f580_out -> f578_out :|: TRUE f578_in -> f579_in :|: TRUE f579_out -> f578_out :|: TRUE f2_in -> f5_in :|: TRUE f5_out -> f2_out :|: TRUE f38_out -> f5_out :|: TRUE f5_in -> f38_in :|: TRUE f38_in -> f40_in :|: TRUE f40_out -> f38_out :|: TRUE f42_out -> f40_out :|: TRUE f40_in -> f42_in :|: TRUE f42_in -> f46_in :|: TRUE f46_out -> f42_out :|: TRUE f249_out -> f46_out :|: TRUE f46_in -> f249_in :|: TRUE f252_out -> f253_in :|: TRUE f249_in -> f252_in :|: TRUE f253_out -> f249_out :|: TRUE f253_in -> f307_in :|: TRUE f307_out -> f253_out :|: TRUE f307_in -> f315_in :|: TRUE f313_out -> f307_out :|: TRUE f307_in -> f313_in :|: TRUE f315_out -> f307_out :|: TRUE f313_in -> f317_in :|: TRUE f317_out -> f313_out :|: TRUE f317_in -> f321_in :|: TRUE f321_out -> f317_out :|: TRUE f317_in -> f322_in :|: TRUE f322_out -> f317_out :|: TRUE f322_in -> f331_in :|: TRUE f331_out -> f322_out :|: TRUE f330_out -> f322_out :|: TRUE f322_in -> f330_in :|: TRUE f335_out -> f330_out :|: TRUE f330_in -> f335_in :|: TRUE f337_out -> f335_out :|: TRUE f335_in -> f336_in :|: TRUE f336_out -> f335_out :|: TRUE f335_in -> f337_in :|: TRUE f337_in -> f349_in :|: TRUE f349_out -> f337_out :|: TRUE f337_in -> f351_in :|: TRUE f351_out -> f337_out :|: TRUE f349_in -> f364_in :|: TRUE f364_out -> f349_out :|: TRUE f364_in -> f374_in :|: TRUE f364_in -> f371_in :|: TRUE f371_out -> f364_out :|: TRUE f374_out -> f364_out :|: TRUE f374_in -> f401_in :|: TRUE f374_in -> f400_in :|: TRUE f401_out -> f374_out :|: TRUE f400_out -> f374_out :|: TRUE f400_in -> f407_in :|: TRUE f407_out -> f400_out :|: TRUE f448_out -> f407_out :|: TRUE f407_in -> f448_in :|: TRUE f449_out -> f407_out :|: TRUE f407_in -> f449_in :|: TRUE f456_out -> f449_out :|: TRUE f449_in -> f456_in :|: TRUE f449_in -> f455_in :|: TRUE f455_out -> f449_out :|: TRUE f498_out -> f455_out :|: TRUE f455_in -> f498_in :|: TRUE f498_in -> f500_in :|: TRUE f498_in -> f501_in :|: TRUE f500_out -> f498_out :|: TRUE f501_out -> f498_out :|: TRUE f501_in -> f508_in :|: TRUE f501_in -> f509_in :|: TRUE f509_out -> f501_out :|: TRUE f508_out -> f501_out :|: TRUE f508_in -> f511_in :|: TRUE f511_out -> f508_out :|: TRUE f511_in -> f524_in :|: TRUE f525_out -> f511_out :|: TRUE f524_out -> f511_out :|: TRUE f511_in -> f525_in :|: TRUE f525_in -> f537_in :|: TRUE f537_out -> f525_out :|: TRUE f538_out -> f525_out :|: TRUE f525_in -> f538_in :|: TRUE f537_in -> f539_in :|: TRUE f539_out -> f537_out :|: TRUE f539_in -> f540_in :|: TRUE f541_out -> f539_out :|: TRUE f540_out -> f539_out :|: TRUE f539_in -> f541_in :|: TRUE f553_out -> f541_out :|: TRUE f541_in -> f554_in :|: TRUE f541_in -> f553_in :|: TRUE f554_out -> f541_out :|: TRUE f553_in -> f566_in :|: TRUE f566_out -> f553_out :|: TRUE f567_out -> f566_out :|: TRUE f568_out -> f566_out :|: TRUE f566_in -> f568_in :|: TRUE f566_in -> f567_in :|: TRUE f573_out -> f568_out :|: TRUE f572_out -> f568_out :|: TRUE f568_in -> f572_in :|: TRUE f568_in -> f573_in :|: TRUE f572_in -> f574_in :|: TRUE f574_out -> f572_out :|: TRUE Start term: f2_in ---------------------------------------- (3) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (4) TRUE