/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern goal(g,a,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 218 ms] (2) AND (3) IRSwT (4) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (5) TRUE (6) IRSwT (7) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (8) TRUE (9) IRSwT (10) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (11) TRUE (12) IRSwT (13) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 32 ms] (16) IRSwT (17) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (18) IRSwT (19) IRSwTTerminationDigraphProof [EQUIVALENT, 6 ms] (20) IRSwT (21) TempFilterProof [SOUND, 4 ms] (22) IRSwT (23) IRSwTToQDPProof [SOUND, 0 ms] (24) QDP (25) QDPSizeChangeProof [EQUIVALENT, 0 ms] (26) YES ---------------------------------------- (0) Obligation: Clauses: goal(A, B, C) :- ','(s2t(A, T), tapplast(T, B, C)). tapplast(L, X, Last) :- ','(tappend(L, node(nil, X, nil), LX), tlast(Last, LX)). tlast(X, node(nil, X, nil)). tlast(X, node(L, X1, X2)) :- tlast(X, L). tlast(X, node(X3, X4, R)) :- tlast(X, R). tappend(nil, Y, Z) :- ','(!, eq(Y, Z)). tappend(T, T1, node(T1, X, T2)) :- ','(left(T, nil), ','(right(T, T2), value(T, X))). tappend(T, T2, node(T1, X, T2)) :- ','(left(T, T1), ','(right(T, nil), value(T, X))). tappend(T, T3, node(U, X, T2)) :- ','(left(T, T1), ','(right(T, T2), ','(value(T, X), tappend(T1, T3, U)))). tappend(T, T1, node(T1, X, U)) :- ','(left(T, T1), ','(right(T, T2), ','(value(T, X), tappend(T2, T3, U)))). s2t(0, L) :- ','(!, eq(L, nil)). s2t(X, node(T, X5, T)) :- ','(p(X, P), s2t(P, T)). s2t(X, node(nil, X6, T)) :- ','(p(X, P), s2t(P, T)). s2t(X, node(T, X7, nil)) :- ','(p(X, P), s2t(P, T)). s2t(X, node(nil, X8, nil)). left(nil, nil). left(node(L, X9, X10), L). right(nil, nil). right(node(X11, X12, R), R). value(nil, nil). value(node(X13, X, X14), X). p(0, 0). p(s(X), X). eq(X, X). Query: goal(g,a,a) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 2, "program": { "directives": [], "clauses": [ [ "(goal A B C)", "(',' (s2t A T) (tapplast T B C))" ], [ "(tapplast L X Last)", "(',' (tappend L (node (nil) X (nil)) LX) (tlast Last LX))" ], [ "(tlast X (node (nil) X (nil)))", null ], [ "(tlast X (node L X1 X2))", "(tlast X L)" ], [ "(tlast X (node X3 X4 R))", "(tlast X R)" ], [ "(tappend (nil) Y Z)", "(',' (!) (eq Y Z))" ], [ "(tappend T T1 (node T1 X T2))", "(',' (left T (nil)) (',' (right T T2) (value T X)))" ], [ "(tappend T T2 (node T1 X T2))", "(',' (left T T1) (',' (right T (nil)) (value T X)))" ], [ "(tappend T T3 (node U X T2))", "(',' (left T T1) (',' (right T T2) (',' (value T X) (tappend T1 T3 U))))" ], [ "(tappend T T1 (node T1 X U))", "(',' (left T T1) (',' (right T T2) (',' (value T X) (tappend T2 T3 U))))" ], [ "(s2t (0) L)", "(',' (!) (eq L (nil)))" ], [ "(s2t X (node T X5 T))", "(',' (p X P) (s2t P T))" ], [ "(s2t X (node (nil) X6 T))", "(',' (p X P) (s2t P T))" ], [ "(s2t X (node T X7 (nil)))", "(',' (p X P) (s2t P T))" ], [ "(s2t X (node (nil) X8 (nil)))", null ], [ "(left (nil) (nil))", null ], [ "(left (node L X9 X10) L)", null ], [ "(right (nil) (nil))", null ], [ "(right (node X11 X12 R) R)", null ], [ "(value (nil) (nil))", null ], [ "(value (node X13 X X14) X)", null ], [ "(p (0) (0))", null ], [ "(p (s X) X)", null ], [ "(eq X X)", null ] ] }, "graph": { "nodes": { "111": { "goal": [ { "clause": 12, "scope": 2, "term": "(s2t T15 X27)" }, { "clause": 13, "scope": 2, "term": "(s2t T15 X27)" }, { "clause": 14, "scope": 2, "term": "(s2t T15 X27)" } ], "kb": { "nonunifying": [[ "(s2t T15 X27)", "(s2t (0) X36)" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T15"], "free": [ "X27", "X36" ], "exprvars": [] } }, "2309": { "goal": [{ "clause": 4, "scope": 54, "term": "(tlast T69 T68)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2308": { "goal": [{ "clause": 3, "scope": 54, "term": "(tlast T69 T68)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "10": { "goal": [{ "clause": -1, "scope": -1, "term": "(s2t T15 X27)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T15"], "free": ["X27"], "exprvars": [] } }, "11": { "goal": [{ "clause": -1, "scope": -1, "term": "(tapplast T20 T18 T19)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "12": { "goal": [ { "clause": 10, "scope": 2, "term": "(s2t T15 X27)" }, { "clause": 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"free": [ "X27", "X36" ], "exprvars": [] } }, "1322": { "goal": [ { "clause": 5, "scope": 23, "term": "(tappend (nil) (node (nil) T179 (nil)) X378)" }, { "clause": 6, "scope": 23, "term": "(tappend (nil) (node (nil) T179 (nil)) X378)" }, { "clause": 7, "scope": 23, "term": "(tappend (nil) (node (nil) T179 (nil)) X378)" }, { "clause": 8, "scope": 23, "term": "(tappend (nil) (node (nil) T179 (nil)) X378)" }, { "clause": 9, "scope": 23, "term": "(tappend (nil) (node (nil) T179 (nil)) X378)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X378"], "exprvars": [] } } }, "edges": [ { "from": 2, "to": 3, "label": "CASE" }, { "from": 3, "to": 9, "label": "ONLY EVAL with clause\ngoal(X24, X25, X26) :- ','(s2t(X24, X27), tapplast(X27, X25, X26)).\nand substitutionT4 -> T15,\nX24 -> T15,\nT5 -> T18,\nX25 -> T18,\nT6 -> T19,\nX26 -> T19,\nT16 -> T18,\nT17 -> T19" }, { "from": 9, "to": 10, "label": "SPLIT 1" }, { "from": 9, "to": 11, "label": "SPLIT 2\nnew knowledge:\nT15 is ground\nreplacements:X27 -> T20" }, { "from": 10, "to": 12, "label": "CASE" }, { "from": 11, "to": 973, "label": "CASE" }, { "from": 12, "to": 15, "label": "EVAL with clause\ns2t(0, X36) :- ','(!_2, eq(X36, nil)).\nand substitutionT15 -> 0,\nX27 -> X37,\nX36 -> X37" }, { "from": 12, "to": 16, "label": "EVAL-BACKTRACK" }, { "from": 15, "to": 100, "label": "CUT" }, { "from": 16, "to": 104, "label": "PARALLEL" }, { "from": 16, "to": 111, "label": "PARALLEL" }, { "from": 100, "to": 101, "label": "CASE" }, { "from": 101, "to": 102, "label": "ONLY EVAL with clause\neq(X42, X42).\nand substitutionX37 -> nil,\nX42 -> nil,\nX43 -> nil" }, { "from": 102, "to": 103, "label": "SUCCESS" }, { "from": 104, "to": 321, "label": "ONLY EVAL with clause\ns2t(X70, node(X71, X72, X71)) :- ','(p(X70, X73), s2t(X73, X71)).\nand substitutionT15 -> T25,\nX70 -> T25,\nX71 -> X74,\nX72 -> X75,\nX27 -> node(X74, X75, X74)" }, { "from": 111, "to": 372, "label": "PARALLEL" }, { "from": 111, "to": 373, "label": "PARALLEL" }, { "from": 321, "to": 322, "label": "CASE" }, { "from": 322, "to": 324, "label": "BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T25, X27), s2t(0, X36))" }, { "from": 324, "to": 326, "label": "EVAL with clause\np(s(X80), X80).\nand substitutionX80 -> T28,\nT25 -> s(T28),\nX73 -> T28" }, { "from": 324, "to": 328, "label": "EVAL-BACKTRACK" }, { "from": 326, "to": 10, "label": "INSTANCE with matching:\nT15 -> T28\nX27 -> X74" }, { "from": 372, "to": 374, "label": "ONLY EVAL with clause\ns2t(X109, node(nil, X110, X111)) :- ','(p(X109, X112), s2t(X112, X111)).\nand substitutionT15 -> T33,\nX109 -> T33,\nX110 -> X113,\nX111 -> X114,\nX27 -> node(nil, X113, X114)" }, { "from": 373, "to": 519, "label": "PARALLEL" }, { "from": 373, "to": 530, "label": "PARALLEL" }, { "from": 374, "to": 375, "label": "CASE" }, { "from": 375, "to": 376, "label": "BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T33, X27), s2t(0, X36))" }, { "from": 376, "to": 377, "label": "EVAL with clause\np(s(X119), X119).\nand substitutionX119 -> T36,\nT33 -> s(T36),\nX112 -> T36" }, { "from": 376, "to": 378, "label": "EVAL-BACKTRACK" }, { "from": 377, "to": 10, "label": "INSTANCE with matching:\nT15 -> T36\nX27 -> X114" }, { "from": 519, "to": 668, "label": "ONLY EVAL with clause\ns2t(X148, node(X149, X150, nil)) :- ','(p(X148, X151), s2t(X151, X149)).\nand substitutionT15 -> T41,\nX148 -> T41,\nX149 -> X152,\nX150 -> X153,\nX27 -> node(X152, X153, nil)" }, { "from": 530, "to": 971, "label": "ONLY EVAL with clause\ns2t(X167, node(nil, X168, nil)).\nand substitutionT15 -> T47,\nX167 -> T47,\nX168 -> X169,\nX27 -> node(nil, X169, nil)" }, { "from": 668, "to": 734, "label": "CASE" }, { "from": 734, "to": 751, "label": "BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T41, X27), s2t(0, X36))" }, { "from": 751, "to": 840, "label": "EVAL with clause\np(s(X158), X158).\nand substitutionX158 -> T44,\nT41 -> s(T44),\nX151 -> T44" }, { "from": 751, "to": 862, "label": "EVAL-BACKTRACK" }, { "from": 840, "to": 10, "label": "INSTANCE with matching:\nT15 -> T44\nX27 -> X152" }, { "from": 971, "to": 972, "label": "SUCCESS" }, { "from": 973, "to": 989, "label": "ONLY EVAL with clause\ntapplast(X184, X185, X186) :- ','(tappend(X184, node(nil, X185, nil), X187), tlast(X186, X187)).\nand substitutionT20 -> T64,\nX184 -> T64,\nT18 -> T65,\nX185 -> T65,\nT19 -> T66,\nX186 -> T66,\nT61 -> T64,\nT62 -> T65,\nT63 -> T66" }, { "from": 989, "to": 993, "label": "SPLIT 1" }, { "from": 989, "to": 994, "label": "SPLIT 2\nreplacements:X187 -> T68,\nT66 -> T69" }, { "from": 993, "to": 999, "label": "CASE" }, { "from": 994, "to": 2272, "label": "CASE" }, { "from": 999, "to": 1002, "label": "EVAL with clause\ntappend(nil, X200, X201) :- ','(!_8, eq(X200, X201)).\nand substitutionT64 -> nil,\nT65 -> T74,\nX200 -> node(nil, T74, nil),\nX187 -> X202,\nX201 -> X202,\nT73 -> T74" }, { "from": 999, "to": 1003, "label": "EVAL-BACKTRACK" }, { "from": 1002, "to": 1006, "label": "CUT" }, { "from": 1003, "to": 1027, "label": "PARALLEL" }, { "from": 1003, "to": 1028, "label": "PARALLEL" }, { "from": 1006, "to": 1009, "label": "CASE" }, { "from": 1009, "to": 1021, "label": "ONLY EVAL with clause\neq(X205, X205).\nand substitutionT74 -> T77,\nX205 -> node(nil, T77, nil),\nX202 -> node(nil, T77, nil)" }, { "from": 1021, "to": 1022, "label": "SUCCESS" }, { "from": 1027, "to": 1031, "label": "ONLY EVAL with clause\ntappend(X230, X231, node(X231, X232, X233)) :- ','(left(X230, nil), ','(right(X230, X233), value(X230, X232))).\nand substitutionT64 -> T90,\nX230 -> T90,\nT65 -> T89,\nX231 -> node(nil, T89, nil),\nX232 -> X234,\nX233 -> X235,\nX187 -> node(node(nil, T89, nil), X234, X235),\nT88 -> T90" }, { "from": 1028, "to": 1083, "label": "PARALLEL" }, { "from": 1028, "to": 1085, "label": "PARALLEL" }, { "from": 1031, "to": 1034, "label": "CASE" }, { "from": 1034, "to": 1035, "label": "PARALLEL" }, { "from": 1034, "to": 1036, "label": "PARALLEL" }, { "from": 1035, "to": 1037, "label": "EVAL with clause\nleft(nil, nil).\nand substitutionT90 -> nil" }, { "from": 1035, "to": 1038, "label": "EVAL-BACKTRACK" }, { "from": 1036, "to": 1057, "label": "EVAL with clause\nleft(node(X248, X249, X250), X248).\nand substitutionX248 -> nil,\nX249 -> T100,\nX250 -> T101,\nT90 -> node(nil, T100, T101),\nT97 -> nil,\nT98 -> T100,\nT99 -> T101" }, { "from": 1036, "to": 1058, "label": "EVAL-BACKTRACK" }, { "from": 1037, "to": 1040, "label": "CASE" }, { "from": 1040, "to": 1041, "label": "PARALLEL" }, { "from": 1040, "to": 1042, "label": "PARALLEL" }, { "from": 1041, "to": 1043, "label": "ONLY EVAL with clause\nright(nil, nil).\nand substitutionX235 -> nil" }, { "from": 1042, "to": 1054, "label": "BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification" }, { "from": 1043, "to": 1044, "label": "CASE" }, { "from": 1044, "to": 1045, "label": "PARALLEL" }, { "from": 1044, "to": 1046, "label": "PARALLEL" }, { "from": 1045, "to": 1047, "label": "ONLY EVAL with clause\nvalue(nil, nil).\nand substitutionX234 -> nil" }, { "from": 1046, "to": 1052, "label": "BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification" }, { "from": 1047, "to": 1048, "label": "SUCCESS" }, { "from": 1057, "to": 1059, "label": "CASE" }, { "from": 1059, "to": 1060, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 1060, "to": 1063, "label": "ONLY EVAL with clause\nright(node(X257, X258, X259), X259).\nand substitutionX257 -> nil,\nT100 -> T110,\nX258 -> T110,\nT101 -> T111,\nX259 -> T111,\nX235 -> T111,\nT108 -> T110,\nT109 -> T111" }, { "from": 1063, "to": 1064, "label": "CASE" }, { "from": 1064, "to": 1065, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 1065, "to": 1069, "label": "ONLY EVAL with clause\nvalue(node(X266, X267, X268), X267).\nand substitutionX266 -> nil,\nT110 -> T116,\nX267 -> T116,\nT111 -> T117,\nX268 -> T117,\nX234 -> T116" }, { "from": 1069, "to": 1071, "label": "SUCCESS" }, { "from": 1083, "to": 1091, "label": "ONLY EVAL with clause\ntappend(X293, X294, node(X295, X296, X294)) :- ','(left(X293, X295), ','(right(X293, nil), value(X293, X296))).\nand substitutionT64 -> T130,\nX293 -> T130,\nT65 -> T129,\nX294 -> node(nil, T129, nil),\nX295 -> X297,\nX296 -> X298,\nX187 -> node(X297, X298, node(nil, T129, nil)),\nT128 -> T130" }, { "from": 1085, "to": 1154, "label": "PARALLEL" }, { "from": 1085, "to": 1155, "label": "PARALLEL" }, { "from": 1091, "to": 1092, "label": "CASE" }, { "from": 1092, "to": 1093, "label": "PARALLEL" }, { "from": 1092, "to": 1094, "label": "PARALLEL" }, { "from": 1093, "to": 1095, "label": "EVAL with clause\nleft(nil, nil).\nand substitutionT130 -> nil,\nX297 -> nil" }, { "from": 1093, "to": 1096, "label": "EVAL-BACKTRACK" }, { "from": 1094, "to": 1113, "label": "EVAL with clause\nleft(node(X311, X312, X313), X311).\nand substitutionX311 -> T140,\nX312 -> T141,\nX313 -> T142,\nT130 -> node(T140, T141, T142),\nX297 -> T140,\nT137 -> T140,\nT138 -> T141,\nT139 -> T142" }, { "from": 1094, "to": 1115, "label": "EVAL-BACKTRACK" }, { "from": 1095, "to": 1097, "label": "CASE" }, { "from": 1097, "to": 1100, "label": "PARALLEL" }, { "from": 1097, "to": 1101, "label": "PARALLEL" }, { "from": 1100, "to": 1103, "label": "ONLY EVAL with clause\nright(nil, nil).\nand substitution" }, { "from": 1101, "to": 1112, "label": "BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification" }, { "from": 1103, "to": 1104, "label": "CASE" }, { "from": 1104, "to": 1105, "label": "PARALLEL" }, { "from": 1104, "to": 1106, "label": "PARALLEL" }, { "from": 1105, "to": 1107, "label": "ONLY EVAL with clause\nvalue(nil, nil).\nand substitutionX298 -> nil" }, { "from": 1106, "to": 1109, "label": "BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification" }, { "from": 1107, "to": 1108, "label": "SUCCESS" }, { "from": 1113, "to": 1117, "label": "CASE" }, { "from": 1117, "to": 1118, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 1118, "to": 1119, "label": "EVAL with clause\nright(node(X320, X321, X322), X322).\nand substitutionT140 -> T152,\nX320 -> T152,\nT141 -> T153,\nX321 -> T153,\nT142 -> nil,\nX322 -> nil,\nT151 -> nil,\nT149 -> T152,\nT150 -> T153" }, { "from": 1118, "to": 1120, "label": "EVAL-BACKTRACK" }, { "from": 1119, "to": 1121, "label": "CASE" }, { "from": 1121, "to": 1122, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 1122, "to": 1137, "label": "ONLY EVAL with clause\nvalue(node(X329, X330, X331), X330).\nand substitutionT152 -> T158,\nX329 -> T158,\nT153 -> T159,\nX330 -> T159,\nX331 -> nil,\nX298 -> T159" }, { "from": 1137, "to": 1138, "label": "SUCCESS" }, { "from": 1154, "to": 1166, "label": "ONLY EVAL with clause\ntappend(X372, X373, node(X374, X375, X376)) :- ','(left(X372, X377), ','(right(X372, X376), ','(value(X372, X375), tappend(X377, X373, X374)))).\nand substitutionT64 -> T176,\nX372 -> T176,\nT65 -> T177,\nX373 -> node(nil, T177, nil),\nX374 -> X378,\nX375 -> X379,\nX376 -> X380,\nX187 -> node(X378, X379, X380),\nT174 -> T176,\nT175 -> T177" }, { "from": 1155, "to": 1847, "label": "ONLY EVAL with clause\ntappend(X483, X484, node(X484, X485, X486)) :- ','(left(X483, X484), ','(right(X483, X487), ','(value(X483, X485), tappend(X487, X488, X486)))).\nand substitutionT64 -> T251,\nX483 -> T251,\nT65 -> T252,\nX484 -> node(nil, T252, nil),\nX485 -> X489,\nX486 -> X490,\nX187 -> node(node(nil, T252, nil), X489, X490),\nT249 -> T251,\nT250 -> T252" }, { "from": 1166, "to": 1167, "label": "CASE" }, { "from": 1167, "to": 1168, "label": "PARALLEL" }, { "from": 1167, "to": 1169, "label": "PARALLEL" }, { "from": 1168, "to": 1170, "label": "EVAL with clause\nleft(nil, nil).\nand substitutionT176 -> nil,\nX377 -> nil,\nT177 -> T179" }, { "from": 1168, "to": 1171, "label": "EVAL-BACKTRACK" }, { "from": 1169, "to": 1589, "label": "EVAL with clause\nleft(node(X429, X430, X431), X429).\nand substitutionX429 -> T204,\nX430 -> T205,\nX431 -> T206,\nT176 -> node(T204, T205, T206),\nX377 -> T204,\nT201 -> T204,\nT202 -> T205,\nT203 -> T206,\nT177 -> T207" }, { "from": 1169, "to": 1591, "label": "EVAL-BACKTRACK" }, { "from": 1170, "to": 1279, "label": "CASE" }, { "from": 1279, "to": 1295, "label": "PARALLEL" }, { "from": 1279, "to": 1296, "label": "PARALLEL" }, { "from": 1295, "to": 1308, "label": "ONLY EVAL with clause\nright(nil, nil).\nand substitutionX380 -> nil" }, { "from": 1296, "to": 1517, "label": "BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification" }, { "from": 1308, "to": 1309, "label": "CASE" }, { "from": 1309, "to": 1311, "label": "PARALLEL" }, { "from": 1309, "to": 1312, "label": "PARALLEL" }, { "from": 1311, "to": 1314, "label": "ONLY EVAL with clause\nvalue(nil, nil).\nand substitutionX379 -> nil" }, { "from": 1312, "to": 1516, "label": "BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification" }, { "from": 1314, "to": 1322, "label": "CASE" }, { "from": 1322, "to": 1370, "label": "ONLY EVAL with clause\ntappend(nil, X411, X412) :- ','(!_23, eq(X411, X412)).\nand substitutionT179 -> T191,\nX411 -> node(nil, T191, nil),\nX378 -> X413,\nX412 -> X413,\nT190 -> T191" }, { "from": 1370, "to": 1372, "label": "CUT" }, { "from": 1372, "to": 1512, "label": "CASE" }, { "from": 1512, "to": 1514, "label": "ONLY EVAL with clause\neq(X416, X416).\nand substitutionT191 -> T194,\nX416 -> node(nil, T194, nil),\nX413 -> node(nil, T194, nil)" }, { "from": 1514, "to": 1515, "label": "SUCCESS" }, { "from": 1589, "to": 1606, "label": "CASE" }, { "from": 1606, "to": 1609, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 1609, "to": 1787, "label": "ONLY EVAL with clause\nright(node(X444, X445, X446), X446).\nand substitutionT204 -> T223,\nX444 -> T223,\nT205 -> T224,\nX445 -> T224,\nT206 -> T225,\nX446 -> T225,\nX380 -> T225,\nT220 -> T223,\nT221 -> T224,\nT222 -> T225,\nT207 -> T226" }, { "from": 1787, "to": 1788, "label": "CASE" }, { "from": 1788, "to": 1789, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 1789, "to": 1790, "label": "ONLY EVAL with clause\nvalue(node(X459, X460, X461), X460).\nand substitutionT223 -> T240,\nX459 -> T240,\nT224 -> T238,\nX460 -> T238,\nT225 -> T239,\nX461 -> T239,\nX379 -> T238,\nT237 -> T240,\nT226 -> T241" }, { "from": 1790, "to": 993, "label": "INSTANCE with matching:\nT64 -> T240\nT65 -> T241\nX187 -> X378" }, { "from": 1847, "to": 1848, "label": "CASE" }, { "from": 1848, "to": 1849, "label": "BACKTRACK\nfor clause: left(nil, nil)because of non-unification" }, { "from": 1849, "to": 1859, "label": "EVAL with clause\nleft(node(X501, X502, X503), X501).\nand substitutionX501 -> node(nil, T267, nil),\nX502 -> T265,\nX503 -> T266,\nT251 -> node(node(nil, T267, nil), T265, T266),\nT252 -> T267,\nT261 -> node(nil, T267, nil),\nT262 -> T265,\nT263 -> T266,\nT264 -> T267" }, { "from": 1849, "to": 1860, "label": "EVAL-BACKTRACK" }, { "from": 1859, "to": 1861, "label": "CASE" }, { "from": 1861, "to": 1862, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 1862, "to": 1879, "label": "ONLY EVAL with clause\nright(node(X518, X519, X520), X520).\nand substitutionT267 -> T282,\nX518 -> node(nil, T282, nil),\nT265 -> T280,\nX519 -> T280,\nT266 -> T281,\nX520 -> T281,\nX487 -> T281,\nT278 -> T280,\nT279 -> T281,\nT277 -> T282" }, { "from": 1879, "to": 1880, "label": "CASE" }, { "from": 1880, "to": 1881, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 1881, "to": 1882, "label": "ONLY EVAL with clause\nvalue(node(X535, X536, X537), X536).\nand substitutionT282 -> T290,\nX535 -> node(nil, T290, nil),\nT280 -> T291,\nX536 -> T291,\nT281 -> T293,\nX537 -> T293,\nX489 -> T291,\nT292 -> T293" }, { "from": 1882, "to": 1942, "label": "CASE" }, { "from": 1942, "to": 1948, "label": "EVAL with clause\ntappend(nil, X550, X551) :- ','(!_30, eq(X550, X551)).\nand substitutionT293 -> nil,\nX488 -> X552,\nX550 -> X552,\nX490 -> X553,\nX551 -> X553" }, { "from": 1942, "to": 1949, "label": "EVAL-BACKTRACK" }, { "from": 1948, "to": 1950, "label": "CUT" }, { "from": 1949, "to": 1958, "label": "PARALLEL" }, { "from": 1949, "to": 1959, "label": "PARALLEL" }, { "from": 1950, "to": 1951, "label": "CASE" }, { "from": 1951, "to": 1952, "label": "ONLY EVAL with clause\neq(X558, X558).\nand substitutionX552 -> X559,\nX558 -> X559,\nX553 -> X559" }, { "from": 1952, "to": 1953, "label": "SUCCESS" }, { "from": 1958, "to": 1988, "label": "ONLY EVAL with clause\ntappend(X588, X589, node(X589, X590, X591)) :- ','(left(X588, nil), ','(right(X588, X591), value(X588, X590))).\nand substitutionT293 -> T301,\nX588 -> T301,\nX488 -> X592,\nX589 -> X592,\nX590 -> X593,\nX591 -> X594,\nX490 -> node(X592, X593, X594),\nT300 -> T301" }, { "from": 1959, "to": 2042, "label": "PARALLEL" }, { "from": 1959, "to": 2043, "label": "PARALLEL" }, { "from": 1988, "to": 1991, "label": "CASE" }, { "from": 1991, "to": 1993, "label": "PARALLEL" }, { "from": 1991, "to": 1995, "label": "PARALLEL" }, { "from": 1993, "to": 1996, "label": "EVAL with clause\nleft(nil, nil).\nand substitutionT301 -> nil" }, { "from": 1993, "to": 1997, "label": "EVAL-BACKTRACK" }, { "from": 1995, "to": 2015, "label": "EVAL with clause\nleft(node(X607, X608, X609), X607).\nand substitutionX607 -> nil,\nX608 -> T311,\nX609 -> T312,\nT301 -> node(nil, T311, T312),\nT308 -> nil,\nT309 -> T311,\nT310 -> T312" }, { "from": 1995, "to": 2016, "label": "EVAL-BACKTRACK" }, { "from": 1996, "to": 1998, "label": "CASE" }, { "from": 1998, "to": 1999, "label": "PARALLEL" }, { "from": 1998, "to": 2000, "label": "PARALLEL" }, { "from": 1999, "to": 2002, "label": "ONLY EVAL with clause\nright(nil, nil).\nand substitutionX594 -> nil" }, { "from": 2000, "to": 2010, "label": "BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification" }, { "from": 2002, "to": 2003, "label": "CASE" }, { "from": 2003, "to": 2004, "label": "PARALLEL" }, { "from": 2003, "to": 2005, "label": "PARALLEL" }, { "from": 2004, "to": 2007, "label": "ONLY EVAL with clause\nvalue(nil, nil).\nand substitutionX593 -> nil" }, { "from": 2005, "to": 2009, "label": "BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification" }, { "from": 2007, "to": 2008, "label": "SUCCESS" }, { "from": 2015, "to": 2017, "label": "CASE" }, { "from": 2017, "to": 2018, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 2018, "to": 2022, "label": "ONLY EVAL with clause\nright(node(X616, X617, X618), X618).\nand substitutionX616 -> nil,\nT311 -> T321,\nX617 -> T321,\nT312 -> T322,\nX618 -> T322,\nX594 -> T322,\nT319 -> T321,\nT320 -> T322" }, { "from": 2022, "to": 2023, "label": "CASE" }, { "from": 2023, "to": 2024, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 2024, "to": 2027, "label": "ONLY EVAL with clause\nvalue(node(X625, X626, X627), X626).\nand substitutionX625 -> nil,\nT321 -> T327,\nX626 -> T327,\nT322 -> T328,\nX627 -> T328,\nX593 -> T327" }, { "from": 2027, "to": 2028, "label": "SUCCESS" }, { "from": 2042, "to": 2046, "label": "ONLY EVAL with clause\ntappend(X656, X657, node(X658, X659, X657)) :- ','(left(X656, X658), ','(right(X656, nil), value(X656, X659))).\nand substitutionT293 -> T336,\nX656 -> T336,\nX488 -> X660,\nX657 -> X660,\nX658 -> X661,\nX659 -> X662,\nX490 -> node(X661, X662, X660),\nT335 -> T336" }, { "from": 2043, "to": 2133, "label": "PARALLEL" }, { "from": 2043, "to": 2134, "label": "PARALLEL" }, { "from": 2046, "to": 2047, "label": "CASE" }, { "from": 2047, "to": 2048, "label": "PARALLEL" }, { "from": 2047, "to": 2049, "label": "PARALLEL" }, { "from": 2048, "to": 2050, "label": "EVAL with clause\nleft(nil, nil).\nand substitutionT336 -> nil,\nX661 -> nil" }, { "from": 2048, "to": 2051, "label": "EVAL-BACKTRACK" }, { "from": 2049, "to": 2080, "label": "EVAL with clause\nleft(node(X675, X676, X677), X675).\nand substitutionX675 -> T346,\nX676 -> T347,\nX677 -> T348,\nT336 -> node(T346, T347, T348),\nX661 -> T346,\nT343 -> T346,\nT344 -> T347,\nT345 -> T348" }, { "from": 2049, "to": 2081, "label": "EVAL-BACKTRACK" }, { "from": 2050, "to": 2052, "label": "CASE" }, { "from": 2052, "to": 2053, "label": "PARALLEL" }, { "from": 2052, "to": 2054, "label": "PARALLEL" }, { "from": 2053, "to": 2055, "label": "ONLY EVAL with clause\nright(nil, nil).\nand substitution" }, { "from": 2054, "to": 2071, "label": "BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification" }, { "from": 2055, "to": 2056, "label": "CASE" }, { "from": 2056, "to": 2057, "label": "PARALLEL" }, { "from": 2056, "to": 2058, "label": "PARALLEL" }, { "from": 2057, "to": 2061, "label": "ONLY EVAL with clause\nvalue(nil, nil).\nand substitutionX662 -> nil" }, { "from": 2058, "to": 2067, "label": "BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification" }, { "from": 2061, "to": 2062, "label": "SUCCESS" }, { "from": 2080, "to": 2082, "label": "CASE" }, { "from": 2082, "to": 2083, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 2083, "to": 2088, "label": "EVAL with clause\nright(node(X684, X685, X686), X686).\nand substitutionT346 -> T358,\nX684 -> T358,\nT347 -> T359,\nX685 -> T359,\nT348 -> nil,\nX686 -> nil,\nT357 -> nil,\nT355 -> T358,\nT356 -> T359" }, { "from": 2083, "to": 2089, "label": "EVAL-BACKTRACK" }, { "from": 2088, "to": 2090, "label": "CASE" }, { "from": 2090, "to": 2130, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 2130, "to": 2131, "label": "ONLY EVAL with clause\nvalue(node(X693, X694, X695), X694).\nand substitutionT358 -> T364,\nX693 -> T364,\nT359 -> T365,\nX694 -> T365,\nX695 -> nil,\nX662 -> T365" }, { "from": 2131, "to": 2132, "label": "SUCCESS" }, { "from": 2133, "to": 2135, "label": "ONLY EVAL with clause\ntappend(X742, X743, node(X744, X745, X746)) :- ','(left(X742, X747), ','(right(X742, X746), ','(value(X742, X745), tappend(X747, X743, X744)))).\nand substitutionT293 -> T373,\nX742 -> T373,\nX488 -> X748,\nX743 -> X748,\nX744 -> X749,\nX745 -> X750,\nX746 -> X751,\nX490 -> node(X749, X750, X751),\nT372 -> T373" }, { "from": 2134, "to": 2237, "label": "ONLY EVAL with clause\ntappend(X875, X876, node(X876, X877, X878)) :- ','(left(X875, X876), ','(right(X875, X879), ','(value(X875, X877), tappend(X879, X880, X878)))).\nand substitutionT293 -> T416,\nX875 -> T416,\nX488 -> X881,\nX876 -> X881,\nX877 -> X882,\nX878 -> X883,\nX490 -> node(X881, X882, X883),\nT415 -> T416" }, { "from": 2135, "to": 2136, "label": "CASE" }, { "from": 2136, "to": 2137, "label": "PARALLEL" }, { "from": 2136, "to": 2138, "label": "PARALLEL" }, { "from": 2137, "to": 2139, "label": "EVAL with clause\nleft(nil, nil).\nand substitutionT373 -> nil,\nX747 -> nil" }, { "from": 2137, "to": 2140, "label": "EVAL-BACKTRACK" }, { "from": 2138, "to": 2200, "label": "EVAL with clause\nleft(node(X814, X815, X816), X814).\nand substitutionX814 -> T383,\nX815 -> T384,\nX816 -> T385,\nT373 -> node(T383, T384, T385),\nX747 -> T383,\nT380 -> T383,\nT381 -> T384,\nT382 -> T385" }, { "from": 2138, "to": 2201, "label": "EVAL-BACKTRACK" }, { "from": 2139, "to": 2142, "label": "CASE" }, { "from": 2142, "to": 2144, "label": "PARALLEL" }, { "from": 2142, "to": 2145, "label": "PARALLEL" }, { "from": 2144, "to": 2150, "label": "ONLY EVAL with clause\nright(nil, nil).\nand substitutionX751 -> nil" }, { "from": 2145, "to": 2199, "label": "BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification" }, { "from": 2150, "to": 2152, "label": "CASE" }, { "from": 2152, "to": 2155, "label": "PARALLEL" }, { "from": 2152, "to": 2156, "label": "PARALLEL" }, { "from": 2155, "to": 2158, "label": "ONLY EVAL with clause\nvalue(nil, nil).\nand substitutionX750 -> nil" }, { "from": 2156, "to": 2198, "label": "BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification" }, { "from": 2158, "to": 2190, "label": "CASE" }, { "from": 2190, "to": 2191, "label": "ONLY EVAL with clause\ntappend(nil, X792, X793) :- ','(!_45, eq(X792, X793)).\nand substitutionX748 -> X794,\nX792 -> X794,\nX749 -> X795,\nX793 -> X795" }, { "from": 2191, "to": 2192, "label": "CUT" }, { "from": 2192, "to": 2195, "label": "CASE" }, { "from": 2195, "to": 2196, "label": "ONLY EVAL with clause\neq(X800, X800).\nand substitutionX794 -> X801,\nX800 -> X801,\nX795 -> X801" }, { "from": 2196, "to": 2197, "label": "SUCCESS" }, { "from": 2200, "to": 2203, "label": "CASE" }, { "from": 2203, "to": 2204, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 2204, "to": 2214, "label": "ONLY EVAL with clause\nright(node(X831, X832, X833), X833).\nand substitutionT383 -> T398,\nX831 -> T398,\nT384 -> T399,\nX832 -> T399,\nT385 -> T400,\nX833 -> T400,\nX751 -> T400,\nT395 -> T398,\nT396 -> T399,\nT397 -> T400" }, { "from": 2214, "to": 2216, "label": "CASE" }, { "from": 2216, "to": 2232, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 2232, "to": 2234, "label": "ONLY EVAL with clause\nvalue(node(X848, X849, X850), X849).\nand substitutionT398 -> T411,\nX848 -> T411,\nT399 -> T409,\nX849 -> T409,\nT400 -> T410,\nX850 -> T410,\nX750 -> T409,\nT408 -> T411" }, { "from": 2234, "to": 1882, "label": "INSTANCE with matching:\nT293 -> T411\nX488 -> X748\nX490 -> X749" }, { "from": 2237, "to": 2240, "label": "CASE" }, { "from": 2240, "to": 2241, "label": "PARALLEL" }, { "from": 2240, "to": 2242, "label": "PARALLEL" }, { "from": 2241, "to": 2243, "label": "EVAL with clause\nleft(nil, nil).\nand substitutionT416 -> nil,\nX881 -> nil" }, { "from": 2241, "to": 2244, "label": "EVAL-BACKTRACK" }, { "from": 2242, "to": 2255, "label": "EVAL with clause\nleft(node(X928, X929, X930), X928).\nand substitutionX928 -> T426,\nX929 -> T427,\nX930 -> T428,\nT416 -> node(T426, T427, T428),\nX881 -> T426,\nT423 -> T426,\nT424 -> T427,\nT425 -> T428" }, { "from": 2242, "to": 2256, "label": "EVAL-BACKTRACK" }, { "from": 2243, "to": 2245, "label": "CASE" }, { "from": 2245, "to": 2246, "label": "PARALLEL" }, { "from": 2245, "to": 2247, "label": "PARALLEL" }, { "from": 2246, "to": 2248, "label": "ONLY EVAL with clause\nright(nil, nil).\nand substitutionX879 -> nil" }, { "from": 2247, "to": 2254, "label": "BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification" }, { "from": 2248, "to": 2249, "label": "CASE" }, { "from": 2249, "to": 2250, "label": "PARALLEL" }, { "from": 2249, "to": 2251, "label": "PARALLEL" }, { "from": 2250, "to": 2252, "label": "ONLY EVAL with clause\nvalue(nil, nil).\nand substitutionX882 -> nil" }, { "from": 2251, "to": 2253, "label": "BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification" }, { "from": 2252, "to": 2158, "label": "INSTANCE with matching:\nX748 -> X880\nX749 -> X883" }, { "from": 2255, "to": 2257, "label": "CASE" }, { "from": 2257, "to": 2258, "label": "BACKTRACK\nfor clause: right(nil, nil)because of non-unification" }, { "from": 2258, "to": 2263, "label": "ONLY EVAL with clause\nright(node(X945, X946, X947), X947).\nand substitutionT426 -> T441,\nX945 -> T441,\nT427 -> T442,\nX946 -> T442,\nT428 -> T443,\nX947 -> T443,\nX879 -> T443,\nT438 -> T441,\nT439 -> T442,\nT440 -> T443" }, { "from": 2263, "to": 2264, "label": "CASE" }, { "from": 2264, "to": 2265, "label": "BACKTRACK\nfor clause: value(nil, nil)because of non-unification" }, { "from": 2265, "to": 2269, "label": "ONLY EVAL with clause\nvalue(node(X962, X963, X964), X963).\nand substitutionT441 -> T451,\nX962 -> T451,\nT442 -> T452,\nX963 -> T452,\nT443 -> T454,\nX964 -> T454,\nX882 -> T452,\nT453 -> T454" }, { "from": 2269, "to": 1882, "label": "INSTANCE with matching:\nT293 -> T454\nX488 -> X880\nX490 -> X883" }, { "from": 2272, "to": 2273, "label": "PARALLEL" }, { "from": 2272, "to": 2274, "label": "PARALLEL" }, { "from": 2273, "to": 2275, "label": "EVAL with clause\ntlast(X975, node(nil, X975, nil)).\nand substitutionT69 -> T461,\nX975 -> T461,\nT68 -> node(nil, T461, nil)" }, { "from": 2273, "to": 2276, "label": "EVAL-BACKTRACK" }, { "from": 2274, "to": 2308, "label": "PARALLEL" }, { "from": 2274, "to": 2309, "label": "PARALLEL" }, { "from": 2275, "to": 2277, "label": "SUCCESS" }, { "from": 2308, "to": 2325, "label": "EVAL with clause\ntlast(X992, node(X993, X994, X995)) :- tlast(X992, X993).\nand substitutionT69 -> T482,\nX992 -> T482,\nX993 -> T483,\nX994 -> T480,\nX995 -> T481,\nT68 -> node(T483, T480, T481),\nT478 -> T482,\nT479 -> T483" }, { "from": 2308, "to": 2326, "label": "EVAL-BACKTRACK" }, { "from": 2309, "to": 2327, "label": "EVAL with clause\ntlast(X1006, node(X1007, X1008, X1009)) :- tlast(X1006, X1009).\nand substitutionT69 -> T498,\nX1006 -> T498,\nX1007 -> T495,\nX1008 -> T496,\nX1009 -> T499,\nT68 -> node(T495, T496, T499),\nT494 -> T498,\nT497 -> T499" }, { "from": 2309, "to": 2328, "label": "EVAL-BACKTRACK" }, { "from": 2325, "to": 994, "label": "INSTANCE with matching:\nT69 -> T482\nT68 -> T483" }, { "from": 2327, "to": 994, "label": "INSTANCE with matching:\nT69 -> T498\nT68 -> T499" } ], "type": "Graph" } } ---------------------------------------- (2) Complex Obligation (AND) ---------------------------------------- (3) Obligation: Rules: f2203_out -> f2200_out :|: TRUE f2200_in -> f2203_in :|: TRUE f2204_in -> f2214_in :|: TRUE f2214_out -> f2204_out :|: TRUE f2258_out -> f2257_out :|: TRUE f2257_in -> f2258_in :|: TRUE f2216_out -> f2214_out :|: TRUE f2214_in -> f2216_in :|: TRUE f2237_in -> f2240_in :|: TRUE f2240_out -> f2237_out :|: TRUE f2241_out -> f2240_out :|: TRUE f2242_out -> f2240_out :|: TRUE f2240_in -> f2242_in :|: TRUE f2240_in -> f2241_in :|: TRUE f2138_in -> f2201_in :|: TRUE f2200_out -> f2138_out :|: TRUE f2201_out -> f2138_out :|: TRUE f2138_in -> f2200_in :|: TRUE f2234_out -> f2232_out :|: TRUE f2232_in -> f2234_in :|: TRUE f2136_in -> f2138_in :|: TRUE f2136_in -> f2137_in :|: TRUE f2137_out -> f2136_out :|: TRUE f2138_out -> f2136_out :|: TRUE f2043_in -> f2133_in :|: TRUE f2133_out -> f2043_out :|: TRUE f2134_out -> f2043_out :|: TRUE f2043_in -> f2134_in :|: TRUE f2242_in -> f2256_in :|: TRUE f2256_out -> f2242_out :|: TRUE f2242_in -> f2255_in :|: TRUE f2255_out -> f2242_out :|: TRUE f2232_out -> f2216_out :|: TRUE f2216_in -> f2232_in :|: TRUE f2264_in -> f2265_in :|: TRUE f2265_out -> f2264_out :|: TRUE f2135_in -> f2136_in :|: TRUE f2136_out -> f2135_out :|: TRUE f2134_in -> f2237_in :|: TRUE f2237_out -> f2134_out :|: TRUE f2135_out -> f2133_out :|: TRUE f2133_in -> f2135_in :|: TRUE f2234_in -> f1882_in :|: TRUE f1882_out -> f2234_out :|: TRUE f2269_in -> f1882_in :|: TRUE f1882_out -> f2269_out :|: TRUE f1949_in -> f1959_in :|: TRUE f1959_out -> f1949_out :|: TRUE f1949_in -> f1958_in :|: TRUE f1958_out -> f1949_out :|: TRUE f2204_out -> f2203_out :|: TRUE f2203_in -> f2204_in :|: TRUE f2255_in -> f2257_in :|: TRUE f2257_out -> f2255_out :|: TRUE f2269_out -> f2265_out :|: TRUE f2265_in -> f2269_in :|: TRUE f2263_out -> f2258_out :|: TRUE f2258_in -> f2263_in :|: TRUE f2042_out -> f1959_out :|: TRUE f2043_out -> f1959_out :|: TRUE f1959_in -> f2042_in :|: TRUE f1959_in -> f2043_in :|: TRUE f1949_out -> f1942_out :|: TRUE f1942_in -> f1948_in :|: TRUE f1942_in -> f1949_in :|: TRUE f1948_out -> f1942_out :|: TRUE f2263_in -> f2264_in :|: TRUE f2264_out -> f2263_out :|: TRUE f1882_in -> f1942_in :|: TRUE f1942_out -> f1882_out :|: TRUE f2_in(T4) -> f3_in(T4) :|: TRUE f3_out(x) -> f2_out(x) :|: TRUE f9_out(T15) -> f3_out(T15) :|: TRUE f3_in(x1) -> f9_in(x1) :|: TRUE f9_in(x2) -> f10_in(x2) :|: TRUE f10_out(x3) -> f11_in :|: TRUE f11_out -> f9_out(x4) :|: TRUE f11_in -> f973_in :|: TRUE f973_out -> f11_out :|: TRUE f989_out -> f973_out :|: TRUE f973_in -> f989_in :|: TRUE f989_in -> f993_in :|: TRUE f993_out -> f994_in :|: TRUE f994_out -> f989_out :|: TRUE f993_in -> f999_in :|: TRUE f999_out -> f993_out :|: TRUE f999_in -> f1002_in :|: TRUE f1002_out -> f999_out :|: TRUE f1003_out -> f999_out :|: TRUE f999_in -> f1003_in :|: TRUE f1003_in -> f1027_in :|: TRUE f1003_in -> f1028_in :|: TRUE f1028_out -> f1003_out :|: TRUE f1027_out -> f1003_out :|: TRUE f1028_in -> f1085_in :|: TRUE f1085_out -> f1028_out :|: TRUE f1083_out -> f1028_out :|: TRUE f1028_in -> f1083_in :|: TRUE f1085_in -> f1155_in :|: TRUE f1155_out -> f1085_out :|: TRUE f1085_in -> f1154_in :|: TRUE f1154_out -> f1085_out :|: TRUE f1155_in -> f1847_in :|: TRUE f1847_out -> f1155_out :|: TRUE f1847_in -> f1848_in :|: TRUE f1848_out -> f1847_out :|: TRUE f1848_in -> f1849_in :|: TRUE f1849_out -> f1848_out :|: TRUE f1849_in -> f1860_in :|: TRUE f1849_in -> f1859_in :|: TRUE f1860_out -> f1849_out :|: TRUE f1859_out -> f1849_out :|: TRUE f1859_in -> f1861_in :|: TRUE f1861_out -> f1859_out :|: TRUE f1862_out -> f1861_out :|: TRUE f1861_in -> f1862_in :|: TRUE f1862_in -> f1879_in :|: TRUE f1879_out -> f1862_out :|: TRUE f1880_out -> f1879_out :|: TRUE f1879_in -> f1880_in :|: TRUE f1881_out -> f1880_out :|: TRUE f1880_in -> f1881_in :|: TRUE f1881_in -> f1882_in :|: TRUE f1882_out -> f1881_out :|: TRUE Start term: f2_in(T4) ---------------------------------------- (4) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (5) TRUE ---------------------------------------- (6) Obligation: Rules: f994_out -> f2325_out :|: TRUE f2325_in -> f994_in :|: TRUE f2327_in -> f994_in :|: TRUE f994_out -> f2327_out :|: TRUE f994_in -> f2272_in :|: TRUE f2272_out -> f994_out :|: TRUE f2309_in -> f2328_in :|: TRUE f2327_out -> f2309_out :|: TRUE f2309_in -> f2327_in :|: TRUE f2328_out -> f2309_out :|: TRUE f2274_out -> f2272_out :|: TRUE f2273_out -> f2272_out :|: TRUE f2272_in -> f2274_in :|: TRUE f2272_in -> f2273_in :|: TRUE f2308_out -> f2274_out :|: TRUE f2309_out -> f2274_out :|: TRUE f2274_in -> f2308_in :|: TRUE f2274_in -> f2309_in :|: TRUE f2325_out -> f2308_out :|: TRUE f2326_out -> f2308_out :|: TRUE f2308_in -> f2325_in :|: TRUE f2308_in -> f2326_in :|: TRUE f2_in(T4) -> f3_in(T4) :|: TRUE f3_out(x) -> f2_out(x) :|: TRUE f9_out(T15) -> f3_out(T15) :|: TRUE f3_in(x1) -> f9_in(x1) :|: TRUE f9_in(x2) -> f10_in(x2) :|: TRUE f10_out(x3) -> f11_in :|: TRUE f11_out -> f9_out(x4) :|: TRUE f11_in -> f973_in :|: TRUE f973_out -> f11_out :|: TRUE f989_out -> f973_out :|: TRUE f973_in -> f989_in :|: TRUE f989_in -> f993_in :|: TRUE f993_out -> f994_in :|: TRUE f994_out -> f989_out :|: TRUE Start term: f2_in(T4) ---------------------------------------- (7) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (8) TRUE ---------------------------------------- (9) Obligation: Rules: f1606_in -> f1609_in :|: TRUE f1609_out -> f1606_out :|: TRUE f1787_in -> f1788_in :|: TRUE f1788_out -> f1787_out :|: TRUE f1589_in -> f1606_in :|: TRUE f1606_out -> f1589_out :|: TRUE f1168_out -> f1167_out :|: TRUE f1169_out -> f1167_out :|: TRUE f1167_in -> f1168_in :|: TRUE f1167_in -> f1169_in :|: TRUE f1154_in -> f1166_in :|: TRUE f1166_out -> f1154_out :|: TRUE f1085_in -> f1155_in :|: TRUE f1155_out -> f1085_out :|: TRUE f1085_in -> f1154_in :|: TRUE f1154_out -> f1085_out :|: TRUE f1003_in -> f1027_in :|: TRUE f1003_in -> f1028_in :|: TRUE f1028_out -> f1003_out :|: TRUE f1027_out -> f1003_out :|: TRUE f1788_in -> f1789_in :|: TRUE f1789_out -> f1788_out :|: TRUE f1790_out -> f1789_out :|: TRUE f1789_in -> f1790_in :|: TRUE f999_in -> f1002_in :|: TRUE f1002_out -> f999_out :|: TRUE f1003_out -> f999_out :|: TRUE f999_in -> f1003_in :|: TRUE f993_out -> f1790_out :|: TRUE f1790_in -> f993_in :|: TRUE f1787_out -> f1609_out :|: TRUE f1609_in -> f1787_in :|: TRUE f1169_in -> f1591_in :|: TRUE f1591_out -> f1169_out :|: TRUE f1169_in -> f1589_in :|: TRUE f1589_out -> f1169_out :|: TRUE f1167_out -> f1166_out :|: TRUE f1166_in -> f1167_in :|: TRUE f993_in -> f999_in :|: TRUE f999_out -> f993_out :|: TRUE f1028_in -> f1085_in :|: TRUE f1085_out -> f1028_out :|: TRUE f1083_out -> f1028_out :|: TRUE f1028_in -> f1083_in :|: TRUE f2_in(T4) -> f3_in(T4) :|: TRUE f3_out(x) -> f2_out(x) :|: TRUE f9_out(T15) -> f3_out(T15) :|: TRUE f3_in(x1) -> f9_in(x1) :|: TRUE f9_in(x2) -> f10_in(x2) :|: TRUE f10_out(x3) -> f11_in :|: TRUE f11_out -> f9_out(x4) :|: TRUE f11_in -> f973_in :|: TRUE f973_out -> f11_out :|: TRUE f989_out -> f973_out :|: TRUE f973_in -> f989_in :|: TRUE f989_in -> f993_in :|: TRUE f993_out -> f994_in :|: TRUE f994_out -> f989_out :|: TRUE Start term: f2_in(T4) ---------------------------------------- (10) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (11) TRUE ---------------------------------------- (12) Obligation: Rules: f375_out(T33) -> f374_out(T33) :|: TRUE f374_in(x) -> f375_in(x) :|: TRUE f321_out(T25) -> f104_out(T25) :|: TRUE f104_in(x1) -> f321_in(x1) :|: TRUE f372_in(x2) -> f374_in(x2) :|: TRUE f374_out(x3) -> f372_out(x3) :|: TRUE f12_in(0) -> f15_in :|: TRUE f12_in(T15) -> f16_in(T15) :|: TRUE f15_out -> f12_out(0) :|: TRUE f16_out(x4) -> f12_out(x4) :|: TRUE f840_in(T44) -> f10_in(T44) :|: TRUE f10_out(x5) -> f840_out(x5) :|: TRUE f326_in(T28) -> f10_in(T28) :|: TRUE f10_out(x6) -> f326_out(x6) :|: TRUE f111_in(x7) -> f373_in(x7) :|: TRUE f372_out(x8) -> f111_out(x8) :|: TRUE f373_out(x9) -> f111_out(x9) :|: TRUE f111_in(x10) -> f372_in(x10) :|: TRUE f377_in(T36) -> f10_in(T36) :|: TRUE f10_out(x11) -> f377_out(x11) :|: TRUE f668_in(T41) -> f734_in(T41) :|: TRUE f734_out(x12) -> f668_out(x12) :|: TRUE f16_in(x13) -> f111_in(x13) :|: TRUE f104_out(x14) -> f16_out(x14) :|: TRUE f111_out(x15) -> f16_out(x15) :|: TRUE f16_in(x16) -> f104_in(x16) :|: TRUE f751_in(x17) -> f862_in :|: TRUE f751_in(s(x18)) -> f840_in(x18) :|: TRUE f862_out -> f751_out(x19) :|: TRUE f840_out(x20) -> f751_out(s(x20)) :|: TRUE f377_out(x21) -> f376_out(s(x21)) :|: TRUE f376_in(s(x22)) -> f377_in(x22) :|: TRUE f378_out -> f376_out(x23) :|: TRUE f376_in(x24) -> f378_in :|: TRUE f326_out(x25) -> f324_out(s(x25)) :|: TRUE f324_in(s(x26)) -> f326_in(x26) :|: TRUE f324_in(x27) -> f328_in :|: TRUE f328_out -> f324_out(x28) :|: TRUE f519_out(x29) -> f373_out(x29) :|: TRUE f373_in(x30) -> f530_in(x30) :|: TRUE f373_in(x31) -> f519_in(x31) :|: TRUE f530_out(x32) -> f373_out(x32) :|: TRUE f322_in(x33) -> f324_in(x33) :|: TRUE f324_out(x34) -> f322_out(x34) :|: TRUE f322_out(x35) -> f321_out(x35) :|: TRUE f321_in(x36) -> f322_in(x36) :|: TRUE f10_in(x37) -> f12_in(x37) :|: TRUE f12_out(x38) -> f10_out(x38) :|: TRUE f734_in(x39) -> f751_in(x39) :|: TRUE f751_out(x40) -> f734_out(x40) :|: TRUE f376_out(x41) -> f375_out(x41) :|: TRUE f375_in(x42) -> f376_in(x42) :|: TRUE f668_out(x43) -> f519_out(x43) :|: TRUE f519_in(x44) -> f668_in(x44) :|: TRUE f2_in(T4) -> f3_in(T4) :|: TRUE f3_out(x45) -> f2_out(x45) :|: TRUE f9_out(x46) -> f3_out(x46) :|: TRUE f3_in(x47) -> f9_in(x47) :|: TRUE f9_in(x48) -> f10_in(x48) :|: TRUE f10_out(x49) -> f11_in :|: TRUE f11_out -> f9_out(x50) :|: TRUE Start term: f2_in(T4) ---------------------------------------- (13) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f374_in(x) -> f375_in(x) :|: TRUE f104_in(x1) -> f321_in(x1) :|: TRUE f372_in(x2) -> f374_in(x2) :|: TRUE f12_in(T15) -> f16_in(T15) :|: TRUE f840_in(T44) -> f10_in(T44) :|: TRUE f326_in(T28) -> f10_in(T28) :|: TRUE f111_in(x7) -> f373_in(x7) :|: TRUE f111_in(x10) -> f372_in(x10) :|: TRUE f377_in(T36) -> f10_in(T36) :|: TRUE f668_in(T41) -> f734_in(T41) :|: TRUE f16_in(x13) -> f111_in(x13) :|: TRUE f16_in(x16) -> f104_in(x16) :|: TRUE f751_in(s(x18)) -> f840_in(x18) :|: TRUE f376_in(s(x22)) -> f377_in(x22) :|: TRUE f324_in(s(x26)) -> f326_in(x26) :|: TRUE f373_in(x31) -> f519_in(x31) :|: TRUE f322_in(x33) -> f324_in(x33) :|: TRUE f321_in(x36) -> f322_in(x36) :|: TRUE f10_in(x37) -> f12_in(x37) :|: TRUE f734_in(x39) -> f751_in(x39) :|: TRUE f375_in(x42) -> f376_in(x42) :|: TRUE f519_in(x44) -> f668_in(x44) :|: TRUE ---------------------------------------- (14) Obligation: Rules: f374_in(x) -> f375_in(x) :|: TRUE f104_in(x1) -> f321_in(x1) :|: TRUE f372_in(x2) -> f374_in(x2) :|: TRUE f12_in(T15) -> f16_in(T15) :|: TRUE f840_in(T44) -> f10_in(T44) :|: TRUE f326_in(T28) -> f10_in(T28) :|: TRUE f111_in(x7) -> f373_in(x7) :|: TRUE f111_in(x10) -> f372_in(x10) :|: TRUE f377_in(T36) -> f10_in(T36) :|: TRUE f668_in(T41) -> f734_in(T41) :|: TRUE f16_in(x13) -> f111_in(x13) :|: TRUE f16_in(x16) -> f104_in(x16) :|: TRUE f751_in(s(x18)) -> f840_in(x18) :|: TRUE f376_in(s(x22)) -> f377_in(x22) :|: TRUE f324_in(s(x26)) -> f326_in(x26) :|: TRUE f373_in(x31) -> f519_in(x31) :|: TRUE f322_in(x33) -> f324_in(x33) :|: TRUE f321_in(x36) -> f322_in(x36) :|: TRUE f10_in(x37) -> f12_in(x37) :|: TRUE f734_in(x39) -> f751_in(x39) :|: TRUE f375_in(x42) -> f376_in(x42) :|: TRUE f519_in(x44) -> f668_in(x44) :|: TRUE ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: f12_in(s(x18:0)) -> f12_in(x18:0) :|: TRUE ---------------------------------------- (17) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (18) Obligation: Rules: f12_in(s(x18:0)) -> f12_in(x18:0) :|: TRUE ---------------------------------------- (19) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f12_in(s(x18:0)) -> f12_in(x18:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f12_in(s(x18:0)) -> f12_in(x18:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f12_in(VARIABLE) s(VARIABLE) Removed predefined arithmetic. ---------------------------------------- (22) Obligation: Rules: f12_in(s(x18:0)) -> f12_in(x18:0) ---------------------------------------- (23) IRSwTToQDPProof (SOUND) Removed the integers and created a QDP-Problem. ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: f12_in(s(x18:0)) -> f12_in(x18:0) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (25) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *f12_in(s(x18:0)) -> f12_in(x18:0) The graph contains the following edges 1 > 1 ---------------------------------------- (26) YES