/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern serialize0(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 113 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) TRUE (15) IRSwT (16) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (17) IRSwT (18) IntTRSCompressionProof [EQUIVALENT, 35 ms] (19) IRSwT (20) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (21) IRSwT (22) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms] (23) IRSwT (24) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 4 ms] (25) IRSwT (26) TempFilterProof [SOUND, 3 ms] (27) IRSwT (28) IRSwTToQDPProof [SOUND, 0 ms] (29) QDP (30) QDPSizeChangeProof [EQUIVALENT, 0 ms] (31) YES ---------------------------------------- (0) Obligation: Clauses: serialize0(L, R) :- ','(pairlists(L, R, A), ','(arrange0(A, T), numbered(T, 1, N))). pairlists(.(X, L), .(Y, R), .(pair(X, Y), A)) :- pairlists(L, R, A). pairlists([], [], []). arrange0(.(X, L), tree(T1, X, T2)) :- ','(split0(L, X, L1, L2), ','(arrange0(L1, T1), arrange0(L2, T2))). arrange0([], void). split0(.(pair(X1, N1), L), pair(X2, Y2), .(pair(X1, N1), L1), L2) :- ','(<(X1, X2), ','(!, split0(L, pair(X2, Y2), L1, L2))). split0(.(pair(X1, N1), L), pair(X2, N2), L1, L2) :- ','(=:=(X1, X2), ','(=(N1, N2), ','(!, split0(L, pair(X2, N2), L1, L2)))). split0(.(pair(X1, N1), L), pair(X2, Y2), L1, .(pair(X1, N1), L2)) :- ','(>(X1, X2), ','(!, split0(L, pair(X2, Y2), L1, L2))). split0([], X3, [], []). numbered(tree(T1, pair(X, N1), T2), N0, N) :- ','(numbered(T1, N0, N1), ','(is(N2, +(N1, 1)), numbered(T2, N2, N))). numbered(void, N, N). palin(.(65, .(66, .(76, .(69, .(32, .(87, .(65, .(83, .(32, .(73, .(32, .(69, .(82, .(69, .(32, .(73, .(32, .(83, .(65, .(87, .(32, .(69, .(76, .(66, .(65, [])))))))))))))))))))))))))). go(T, S) :- ','(time(X4), ','(palin(X), ','(serialize0(X, S), time(T)))). time(T) :- statistics(runtime, .(X5, .(T, []))). Query: serialize0(g,a) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 4, "program": { "directives": [], "clauses": [ [ "(serialize0 L R)", "(',' (pairlists L R A) (',' (arrange0 A T) (numbered T (1) N)))" ], [ "(pairlists (. X L) (. Y R) (. (pair X Y) A))", "(pairlists L R A)" ], [ "(pairlists ([]) ([]) ([]))", null ], [ "(arrange0 (. X L) (tree T1 X T2))", "(',' (split0 L X L1 L2) (',' (arrange0 L1 T1) (arrange0 L2 T2)))" ], [ "(arrange0 ([]) (void))", null ], [ "(split0 (. (pair X1 N1) L) (pair X2 Y2) (. (pair X1 N1) L1) L2)", "(',' (< X1 X2) (',' (!) (split0 L (pair X2 Y2) L1 L2)))" ], [ "(split0 (. (pair X1 N1) L) (pair X2 N2) L1 L2)", "(',' (=:= X1 X2) (',' (= N1 N2) (',' (!) (split0 L (pair X2 N2) L1 L2))))" ], [ "(split0 (. (pair X1 N1) L) (pair X2 Y2) L1 (. (pair X1 N1) L2))", "(',' (> X1 X2) (',' (!) (split0 L (pair X2 Y2) L1 L2)))" ], [ "(split0 ([]) X3 ([]) ([]))", null ], [ "(numbered (tree T1 (pair X N1) T2) N0 N)", "(',' (numbered T1 N0 N1) (',' (is N2 (+ N1 (1))) (numbered T2 N2 N)))" ], [ "(numbered (void) N N)", null ], [ "(palin (. (65) (. (66) (. (76) (. (69) (. (32) (. (87) (. (65) (. (83) (. (32) (. (73) (. (32) (. (69) (. (82) (. (69) (. (32) (. (73) (. (32) (. (83) (. (65) (. (87) (. (32) (. (69) (. (76) (. (66) (. (65) ([])))))))))))))))))))))))))))", null ], [ "(go T S)", "(',' (time X4) (',' (palin X) (',' (serialize0 X S) (time T))))" ], [ "(time T)", "(statistics (runtime) (. X5 (. T ([]))))" ] ] }, "graph": { "nodes": { "88": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5143": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5144": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5145": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5147": { "goal": [ { "clause": 9, "scope": 5, "term": "(numbered T53 (1) X23)" }, { "clause": 10, "scope": 5, "term": "(numbered T53 (1) X23)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X23"], "exprvars": [] } }, "type": "Nodes", "1851": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "5137": { "goal": [{ "clause": -1, "scope": -1, "term": "(arrange0 T193 X123)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X123"], "exprvars": [] } }, "4965": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> T178 T179) (',' (!_4) (split0 T180 (pair T179 T181) X293 X294)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [ "X293", "X294" ], "exprvars": [] } }, "4966": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": 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"nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T140"], "free": [ "X239", "X240" ], "exprvars": [] } }, "4953": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T139", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T140", "type": "PlainIntegerVariable" }, "operation": "=" }] }, "ground": [], "free": [], "exprvars": [ "T140", "T139" ] } }, "1848": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4954": { "goal": [{ "clause": -1, "scope": -1, "term": "(split0 T146 (pair T140 T147) X239 X240)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T140"], "free": [ "X239", "X240" ], "exprvars": [] } }, "86": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (< T105 T106) (',' (!_4) (split0 T107 (pair T106 T108) X185 X186)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [ "X185", "X186" ], "exprvars": [] } }, "87": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4957": { "goal": [{ "clause": 7, "scope": 4, "term": "(split0 T66 T67 X120 X121)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [ "X120", "X121" ], "exprvars": [] } } }, "edges": [ { "from": 4, "to": 5, "label": "CASE" }, { "from": 5, "to": 7, "label": "ONLY EVAL with clause\nserialize0(X19, X20) :- ','(pairlists(X19, X20, X21), ','(arrange0(X21, X22), numbered(X22, 1, X23))).\nand substitutionT3 -> T14,\nX19 -> T14,\nT4 -> T16,\nX20 -> T16,\nT15 -> T16" }, { "from": 7, "to": 9, "label": "SPLIT 1" }, { "from": 7, "to": 10, "label": "SPLIT 2\nnew knowledge:\nT14 is ground\nreplacements:X21 -> T21" }, { "from": 9, "to": 13, "label": "CASE" }, { "from": 10, "to": 52, "label": "SPLIT 1" }, { "from": 10, "to": 53, "label": "SPLIT 2\nreplacements:X22 -> T53" }, { "from": 13, "to": 15, "label": "PARALLEL" }, { "from": 13, "to": 16, "label": "PARALLEL" }, { "from": 15, "to": 21, "label": "EVAL with clause\npairlists(.(X60, X61), .(X62, X63), .(pair(X60, X62), X64)) :- pairlists(X61, X63, X64).\nand substitutionX60 -> T42,\nX61 -> T43,\nT14 -> .(T42, T43),\nX62 -> T44,\nX63 -> T46,\nT16 -> .(T44, T46),\nX64 -> X65,\nX21 -> .(pair(T42, T44), X65),\nT45 -> T46" }, { "from": 15, "to": 22, "label": "EVAL-BACKTRACK" }, { "from": 16, "to": 47, "label": "EVAL with clause\npairlists([], [], []).\nand substitutionT14 -> [],\nT16 -> [],\nX21 -> []" }, { "from": 16, "to": 48, "label": "EVAL-BACKTRACK" }, { "from": 21, "to": 9, "label": "INSTANCE with matching:\nT14 -> T43\nT16 -> T46\nX21 -> X65" }, { "from": 47, "to": 49, "label": "SUCCESS" }, { "from": 52, "to": 54, "label": "CASE" }, { "from": 53, "to": 5147, "label": "CASE" }, { "from": 54, "to": 57, "label": "PARALLEL" }, { "from": 54, "to": 58, "label": "PARALLEL" }, { "from": 57, "to": 68, "label": "EVAL with clause\narrange0(.(X116, X117), tree(X118, X116, X119)) :- ','(split0(X117, X116, X120, X121), ','(arrange0(X120, X118), arrange0(X121, X119))).\nand substitutionX116 -> T67,\nX117 -> T66,\nT21 -> .(T67, T66),\nX118 -> X122,\nX119 -> X123,\nX22 -> tree(X122, T67, X123),\nT65 -> T66,\nT64 -> T67" }, { "from": 57, "to": 69, "label": "EVAL-BACKTRACK" }, { "from": 58, "to": 5143, "label": "EVAL with clause\narrange0([], void).\nand substitutionT21 -> [],\nX22 -> void" }, { "from": 58, "to": 5144, "label": "EVAL-BACKTRACK" }, { "from": 68, "to": 72, "label": "SPLIT 1" }, { "from": 68, "to": 73, "label": "SPLIT 2\nreplacements:X120 -> T73,\nX121 -> T74" }, { "from": 72, "to": 74, "label": "CASE" }, { "from": 73, "to": 5136, "label": "SPLIT 1" }, { "from": 73, "to": 5137, "label": "SPLIT 2\nreplacements:X122 -> T192,\nT74 -> T193" }, { "from": 74, "to": 76, "label": "PARALLEL" }, { "from": 74, "to": 77, "label": "PARALLEL" }, { "from": 76, "to": 86, "label": "EVAL with clause\nsplit0(.(pair(X178, X179), X180), pair(X181, X182), .(pair(X178, X179), X183), X184) :- ','(<(X178, X181), ','(!_4, split0(X180, pair(X181, X182), X183, X184))).\nand substitutionX178 -> T105,\nX179 -> T101,\nX180 -> T107,\nT66 -> .(pair(T105, T101), T107),\nX181 -> T106,\nX182 -> T108,\nT67 -> pair(T106, T108),\nX183 -> X185,\nX120 -> .(pair(T105, T101), X185),\nX121 -> X186,\nX184 -> X186,\nT100 -> T105,\nT103 -> T106,\nT102 -> T107,\nT104 -> T108" }, { "from": 76, "to": 87, "label": "EVAL-BACKTRACK" }, { "from": 77, "to": 1743, "label": "PARALLEL" }, { "from": 77, "to": 1747, "label": "PARALLEL" }, { "from": 86, "to": 88, "label": "IS ERROR" }, { "from": 86, "to": 1388, "label": "ARITHCOMP SUCCESS" }, { "from": 86, "to": 1464, "label": "ARITHCOMP FAIL" }, { "from": 1388, "to": 1469, "label": "CUT" }, { "from": 1469, "to": 72, "label": "INSTANCE with matching:\nT66 -> T107\nT67 -> pair(T106, T108)\nX120 -> X185\nX121 -> X186" }, { "from": 1743, "to": 1844, "label": "EVAL with clause\nsplit0(.(pair(X232, X233), X234), pair(X235, X236), X237, X238) :- ','(=:=(X232, X235), ','(=(X233, X236), ','(!_4, split0(X234, pair(X235, X236), X237, X238)))).\nand substitutionX232 -> T139,\nX233 -> T141,\nX234 -> T143,\nT66 -> .(pair(T139, T141), T143),\nX235 -> T140,\nX236 -> T142,\nT67 -> pair(T140, T142),\nX120 -> X239,\nX237 -> X239,\nX121 -> X240,\nX238 -> X240,\nT134 -> T139,\nT137 -> T140,\nT135 -> T141,\nT138 -> T142,\nT136 -> T143" }, { "from": 1743, "to": 1848, "label": "EVAL-BACKTRACK" }, { "from": 1747, "to": 4957, "label": "PARALLEL" }, { "from": 1747, "to": 4958, "label": "PARALLEL" }, { "from": 1844, "to": 1851, "label": "IS ERROR" }, { "from": 1844, "to": 4950, "label": "ARITHCOMP SUCCESS" }, { "from": 1844, "to": 4951, "label": "ARITHCOMP FAIL" }, { "from": 4950, "to": 4952, "label": "UNIFY CASE with substitutionT141 -> T147,\nT142 -> T147,\nT143 -> T146,\nT145 -> T147" }, { "from": 4950, "to": 4953, "label": "UNIFY-BACKTRACK" }, { "from": 4952, "to": 4954, "label": "CUT" }, { "from": 4954, "to": 72, "label": "INSTANCE with matching:\nT66 -> T146\nT67 -> pair(T140, T147)\nX120 -> X239\nX121 -> X240" }, { "from": 4957, "to": 4965, "label": "EVAL with clause\nsplit0(.(pair(X286, X287), X288), pair(X289, X290), X291, .(pair(X286, X287), X292)) :- ','(>(X286, X289), ','(!_4, split0(X288, pair(X289, X290), X291, X292))).\nand substitutionX286 -> T178,\nX287 -> T174,\nX288 -> T180,\nT66 -> .(pair(T178, T174), T180),\nX289 -> T179,\nX290 -> T181,\nT67 -> pair(T179, T181),\nX120 -> X293,\nX291 -> X293,\nX292 -> X294,\nX121 -> .(pair(T178, T174), X294),\nT173 -> T178,\nT176 -> T179,\nT175 -> T180,\nT177 -> T181" }, { "from": 4957, "to": 4966, "label": "EVAL-BACKTRACK" }, { "from": 4958, "to": 5069, "label": "EVAL with clause\nsplit0([], X306, [], []).\nand substitutionT66 -> [],\nT67 -> T189,\nX306 -> T189,\nX120 -> [],\nX121 -> []" }, { "from": 4958, "to": 5070, "label": "EVAL-BACKTRACK" }, { "from": 4965, "to": 4967, "label": "IS ERROR" }, { "from": 4965, "to": 5058, "label": "ARITHCOMP SUCCESS" }, { "from": 4965, "to": 5059, "label": "ARITHCOMP FAIL" }, { "from": 5058, "to": 5060, "label": "CUT" }, { "from": 5060, "to": 72, "label": "INSTANCE with matching:\nT66 -> T180\nT67 -> pair(T179, T181)\nX120 -> X293\nX121 -> X294" }, { "from": 5069, "to": 5071, "label": "SUCCESS" }, { "from": 5136, "to": 52, "label": "INSTANCE with matching:\nT21 -> T73\nX22 -> X122" }, { "from": 5137, "to": 52, "label": "INSTANCE with matching:\nT21 -> T193\nX22 -> X123" }, { "from": 5143, "to": 5145, "label": "SUCCESS" }, { "from": 5147, "to": 5148, "label": "PARALLEL" }, { "from": 5147, "to": 5149, "label": "PARALLEL" }, { "from": 5148, "to": 5154, "label": "EVAL with clause\nnumbered(tree(X369, pair(X370, X371), X372), X373, X374) :- ','(numbered(X369, X373, X371), ','(is(X375, +(X371, 1)), numbered(X372, X375, X374))).\nand substitutionX369 -> T222,\nX370 -> T219,\nX371 -> T223,\nX372 -> T224,\nT53 -> tree(T222, pair(T219, T223), T224),\nX373 -> 1,\nX23 -> X376,\nX374 -> X376,\nT218 -> T222,\nT220 -> T223,\nT221 -> T224" }, { "from": 5148, "to": 5155, "label": "EVAL-BACKTRACK" }, { "from": 5149, "to": 5274, "label": "EVAL with clause\nnumbered(void, X558, X558).\nand substitutionT53 -> void,\nX558 -> 1,\nX23 -> 1" }, { "from": 5149, "to": 5275, "label": "EVAL-BACKTRACK" }, { "from": 5154, "to": 5156, "label": "SPLIT 1" }, { "from": 5154, "to": 5157, "label": "SPLIT 2\nnew knowledge:\nT230 is ground\nreplacements:T223 -> T230,\nT224 -> T231" }, { "from": 5156, "to": 5158, "label": "CASE" }, { "from": 5157, "to": 5221, "label": "IS ERROR" }, { "from": 5157, "to": 5222, "label": "\nX375 -> T388" }, { "from": 5158, "to": 5159, "label": "PARALLEL" }, { "from": 5158, "to": 5160, "label": "PARALLEL" }, { "from": 5159, "to": 5161, "label": "EVAL with clause\nnumbered(tree(X417, pair(X418, X419), X420), X421, X422) :- ','(numbered(X417, X421, X419), ','(is(X423, +(X419, 1)), numbered(X420, X423, X422))).\nand substitutionX417 -> T262,\nX418 -> T258,\nX419 -> T263,\nX420 -> T264,\nT222 -> tree(T262, pair(T258, T263), T264),\nX421 -> 1,\nT223 -> T265,\nX422 -> T265,\nT257 -> T262,\nT259 -> T263,\nT260 -> T264,\nT261 -> T265" }, { "from": 5159, "to": 5162, "label": "EVAL-BACKTRACK" }, { "from": 5160, "to": 5218, "label": "EVAL with clause\nnumbered(void, X547, X547).\nand substitutionT222 -> void,\nX547 -> 1,\nT223 -> 1" }, { "from": 5160, "to": 5219, "label": "EVAL-BACKTRACK" }, { "from": 5161, "to": 5163, "label": "SPLIT 1" }, { "from": 5161, "to": 5164, "label": "SPLIT 2\nnew knowledge:\nT271 is ground\nreplacements:T263 -> T271,\nT264 -> T272,\nT265 -> T273" }, { "from": 5163, "to": 5156, "label": "INSTANCE with matching:\nT222 -> T262\nT223 -> T263" }, { "from": 5164, "to": 5168, "label": "IS ERROR" }, { "from": 5164, "to": 5174, "label": "\nX423 -> T279" }, { "from": 5174, "to": 5176, "label": "CASE" }, { "from": 5176, "to": 5177, "label": "PARALLEL" }, { "from": 5176, "to": 5178, "label": "PARALLEL" }, { "from": 5177, "to": 5179, "label": "EVAL with clause\nnumbered(tree(X471, pair(X472, X473), X474), X475, X476) :- ','(numbered(X471, X475, X473), ','(is(X477, +(X473, 1)), numbered(X474, X477, X476))).\nand substitutionX471 -> T316,\nX472 -> T311,\nX473 -> T317,\nX474 -> T318,\nT272 -> tree(T316, pair(T311, T317), T318),\nT279 -> T314,\nX475 -> T314,\nT273 -> T319,\nX476 -> T319,\nT310 -> T316,\nT312 -> T317,\nT313 -> T318,\nT315 -> T319" }, { "from": 5177, "to": 5180, "label": "EVAL-BACKTRACK" }, { "from": 5178, "to": 5215, "label": "EVAL with clause\nnumbered(void, X544, X544).\nand substitutionT272 -> void,\nT279 -> T387,\nX544 -> T387,\nT273 -> T387" }, { "from": 5178, "to": 5216, "label": "EVAL-BACKTRACK" }, { "from": 5179, "to": 5186, "label": "SPLIT 1" }, { "from": 5179, "to": 5187, "label": "SPLIT 2\nnew knowledge:\nT314 is ground\nT326 is ground\nreplacements:T317 -> T326,\nT318 -> T327,\nT319 -> T328" }, { "from": 5186, "to": 5190, "label": "CASE" }, { "from": 5187, "to": 5213, "label": "IS ERROR" }, { "from": 5187, "to": 5214, "label": "\nX477 -> T378" }, { "from": 5190, "to": 5191, "label": "PARALLEL" }, { "from": 5190, "to": 5192, "label": "PARALLEL" }, { "from": 5191, "to": 5193, "label": "EVAL with clause\nnumbered(tree(X518, pair(X519, X520), X521), X522, X523) :- ','(numbered(X518, X522, X520), ','(is(X524, +(X520, 1)), numbered(X521, X524, X523))).\nand substitutionX518 -> T365,\nX519 -> T360,\nX520 -> T366,\nX521 -> T367,\nT316 -> tree(T365, pair(T360, T366), T367),\nT314 -> T363,\nX522 -> T363,\nT317 -> T368,\nX523 -> T368,\nT359 -> T365,\nT361 -> T366,\nT362 -> T367,\nT364 -> T368" }, { "from": 5191, "to": 5194, "label": "EVAL-BACKTRACK" }, { "from": 5192, "to": 5210, "label": "EVAL with clause\nnumbered(void, X534, X534).\nand substitutionT316 -> void,\nT314 -> T377,\nX534 -> T377,\nT317 -> T377" }, { "from": 5192, "to": 5211, "label": "EVAL-BACKTRACK" }, { "from": 5193, "to": 5179, "label": "INSTANCE with matching:\nT316 -> T365\nT314 -> T363\nT317 -> T366\nX477 -> X524\nT318 -> T367\nT319 -> T368" }, { "from": 5210, "to": 5212, "label": "SUCCESS" }, { "from": 5214, "to": 5174, "label": "INSTANCE with matching:\nT272 -> T327\nT279 -> T378\nT273 -> T328\nX423 -> X477" }, { "from": 5215, "to": 5217, "label": "SUCCESS" }, { "from": 5218, "to": 5220, "label": "SUCCESS" }, { "from": 5222, "to": 5186, "label": "INSTANCE with matching:\nT316 -> T231\nT314 -> T388\nT317 -> X376" }, { "from": 5274, "to": 5276, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) Complex Obligation (AND) ---------------------------------------- (3) Obligation: Rules: f5176_in(T279) -> f5177_in(T279) :|: TRUE f5177_out(x) -> f5176_out(x) :|: TRUE f5176_in(x1) -> f5178_in(x1) :|: TRUE f5178_out(x2) -> f5176_out(x2) :|: TRUE f5187_in(T326) -> f5214_in(T378, T326) :|: T378 = T326 + 1 f5214_out(x3, x4) -> f5187_out(x4) :|: TRUE f5187_in(x5) -> f5213_in :|: TRUE f5213_out -> f5187_out(x6) :|: TRUE f5174_out(x7, x8) -> f5214_out(x7, x9) :|: TRUE f5214_in(x10, x11) -> f5174_in(x10, x12) :|: TRUE f5190_out(T314) -> f5186_out(T314) :|: TRUE f5186_in(x13) -> f5190_in(x13) :|: TRUE f5179_in(x14) -> f5186_in(x14) :|: TRUE f5187_out(x15) -> f5179_out(x16) :|: TRUE f5186_out(x17) -> f5187_in(x18) :|: TRUE f5190_in(x19) -> f5192_in(x19) :|: TRUE f5191_out(x20) -> f5190_out(x20) :|: TRUE f5190_in(x21) -> f5191_in(x21) :|: TRUE f5192_out(x22) -> f5190_out(x22) :|: TRUE f5191_in(x23) -> f5194_in :|: TRUE f5191_in(T363) -> f5193_in(T363) :|: TRUE f5193_out(x24) -> f5191_out(x24) :|: TRUE f5194_out -> f5191_out(x25) :|: TRUE f5176_out(x26) -> f5174_out(x26, x27) :|: TRUE f5174_in(x28, x29) -> f5176_in(x28) :|: TRUE f5177_in(x30) -> f5180_in :|: TRUE f5180_out -> f5177_out(x31) :|: TRUE f5177_in(x32) -> f5179_in(x32) :|: TRUE f5179_out(x33) -> f5177_out(x33) :|: TRUE f5179_out(x34) -> f5193_out(x34) :|: TRUE f5193_in(x35) -> f5179_in(x35) :|: TRUE f5_out(T3) -> f4_out(T3) :|: TRUE f4_in(x36) -> f5_in(x36) :|: TRUE f7_out(T14) -> f5_out(T14) :|: TRUE f5_in(x37) -> f7_in(x37) :|: TRUE f7_in(x38) -> f9_in(x38) :|: TRUE f10_out -> f7_out(x39) :|: TRUE f9_out(x40) -> f10_in :|: TRUE f52_out -> f53_in :|: TRUE f10_in -> f52_in :|: TRUE f53_out -> f10_out :|: TRUE f5147_out -> f53_out :|: TRUE f53_in -> f5147_in :|: TRUE f5147_in -> f5149_in :|: TRUE f5148_out -> f5147_out :|: TRUE f5149_out -> f5147_out :|: TRUE f5147_in -> f5148_in :|: TRUE f5148_in -> f5154_in :|: TRUE f5148_in -> f5155_in :|: TRUE f5154_out -> f5148_out :|: TRUE f5155_out -> f5148_out :|: TRUE f5157_out(T230) -> f5154_out :|: TRUE f5156_out -> f5157_in(x41) :|: TRUE f5154_in -> f5156_in :|: TRUE f5156_in -> f5158_in :|: TRUE f5158_out -> f5156_out :|: TRUE f5158_in -> f5160_in :|: TRUE f5159_out -> f5158_out :|: TRUE f5158_in -> f5159_in :|: TRUE f5160_out -> f5158_out :|: TRUE f5159_in -> f5161_in :|: TRUE f5159_in -> f5162_in :|: TRUE f5161_out -> f5159_out :|: TRUE f5162_out -> f5159_out :|: TRUE f5161_in -> f5163_in :|: TRUE f5164_out(T271) -> f5161_out :|: TRUE f5163_out -> f5164_in(x42) :|: TRUE f5164_in(x43) -> f5168_in :|: TRUE f5174_out(x44, x45) -> f5164_out(x45) :|: TRUE f5168_out -> f5164_out(x46) :|: TRUE f5164_in(x47) -> f5174_in(x48, x47) :|: x48 = x47 + 1 f5221_out -> f5157_out(x49) :|: TRUE f5157_in(x50) -> f5221_in :|: TRUE f5157_in(x51) -> f5222_in(x52, x51) :|: x52 = x51 + 1 f5222_out(x53, x54) -> f5157_out(x54) :|: TRUE f5222_in(x55, x56) -> f5186_in(x55) :|: TRUE f5186_out(x57) -> f5222_out(x57, x58) :|: TRUE Start term: f4_in(T3) ---------------------------------------- (4) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (5) TRUE ---------------------------------------- (6) Obligation: Rules: f5158_in -> f5160_in :|: TRUE f5159_out -> f5158_out :|: TRUE f5158_in -> f5159_in :|: TRUE f5160_out -> f5158_out :|: TRUE f5179_in(T314) -> f5186_in(T314) :|: TRUE f5187_out(x) -> f5179_out(x1) :|: TRUE f5186_out(x2) -> f5187_in(x3) :|: TRUE f5190_in(x4) -> f5192_in(x4) :|: TRUE f5191_out(x5) -> f5190_out(x5) :|: TRUE f5190_in(x6) -> f5191_in(x6) :|: TRUE f5192_out(x7) -> f5190_out(x7) :|: TRUE f5191_in(x8) -> f5194_in :|: TRUE f5191_in(T363) -> f5193_in(T363) :|: TRUE f5193_out(x9) -> f5191_out(x9) :|: TRUE f5194_out -> f5191_out(x10) :|: TRUE f5177_in(T279) -> f5180_in :|: TRUE f5180_out -> f5177_out(x11) :|: TRUE f5177_in(x12) -> f5179_in(x12) :|: TRUE f5179_out(x13) -> f5177_out(x13) :|: TRUE f5156_in -> f5158_in :|: TRUE f5158_out -> f5156_out :|: TRUE f5190_out(x14) -> f5186_out(x14) :|: TRUE f5186_in(x15) -> f5190_in(x15) :|: TRUE f5178_in(x16) -> f5216_in :|: TRUE f5215_out -> f5178_out(T387) :|: TRUE f5216_out -> f5178_out(x17) :|: TRUE f5178_in(x18) -> f5215_in :|: TRUE f5161_in -> f5163_in :|: TRUE f5164_out(T271) -> f5161_out :|: TRUE f5163_out -> f5164_in(x19) :|: TRUE f5210_in -> f5210_out :|: TRUE f5187_in(T326) -> f5214_in(T378, T326) :|: T378 = T326 + 1 f5214_out(x20, x21) -> f5187_out(x21) :|: TRUE f5187_in(x22) -> f5213_in :|: TRUE f5213_out -> f5187_out(x23) :|: TRUE f5174_out(x24, x25) -> f5214_out(x24, x26) :|: TRUE f5214_in(x27, x28) -> f5174_in(x27, x29) :|: TRUE f5176_in(x30) -> f5177_in(x30) :|: TRUE f5177_out(x31) -> f5176_out(x31) :|: TRUE f5176_in(x32) -> f5178_in(x32) :|: TRUE f5178_out(x33) -> f5176_out(x33) :|: TRUE f5164_in(x34) -> f5168_in :|: TRUE f5174_out(x35, x36) -> f5164_out(x36) :|: TRUE f5168_out -> f5164_out(x37) :|: TRUE f5164_in(x38) -> f5174_in(x39, x38) :|: x39 = x38 + 1 f5159_in -> f5161_in :|: TRUE f5159_in -> f5162_in :|: TRUE f5161_out -> f5159_out :|: TRUE f5162_out -> f5159_out :|: TRUE f5215_in -> f5215_out :|: TRUE f5156_out -> f5163_out :|: TRUE f5163_in -> f5156_in :|: TRUE f5210_out -> f5192_out(T377) :|: TRUE f5192_in(x40) -> f5211_in :|: TRUE f5211_out -> f5192_out(x41) :|: TRUE f5192_in(x42) -> f5210_in :|: TRUE f5176_out(x43) -> f5174_out(x43, x44) :|: TRUE f5174_in(x45, x46) -> f5176_in(x45) :|: TRUE f5179_out(x47) -> f5193_out(x47) :|: TRUE f5193_in(x48) -> f5179_in(x48) :|: TRUE f5_out(T3) -> f4_out(T3) :|: TRUE f4_in(x49) -> f5_in(x49) :|: TRUE f7_out(T14) -> f5_out(T14) :|: TRUE f5_in(x50) -> f7_in(x50) :|: TRUE f7_in(x51) -> f9_in(x51) :|: TRUE f10_out -> f7_out(x52) :|: TRUE f9_out(x53) -> f10_in :|: TRUE f52_out -> f53_in :|: TRUE f10_in -> f52_in :|: TRUE f53_out -> f10_out :|: TRUE f5147_out -> f53_out :|: TRUE f53_in -> f5147_in :|: TRUE f5147_in -> f5149_in :|: TRUE f5148_out -> f5147_out :|: TRUE f5149_out -> f5147_out :|: TRUE f5147_in -> f5148_in :|: TRUE f5148_in -> f5154_in :|: TRUE f5148_in -> f5155_in :|: TRUE f5154_out -> f5148_out :|: TRUE f5155_out -> f5148_out :|: TRUE f5157_out(T230) -> f5154_out :|: TRUE f5156_out -> f5157_in(x54) :|: TRUE f5154_in -> f5156_in :|: TRUE Start term: f4_in(T3) ---------------------------------------- (7) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (8) TRUE ---------------------------------------- (9) Obligation: Rules: f86_in -> f1464_in(T105, T106) :|: T105 >= T106 f1464_out(x, x1) -> f86_out :|: x >= x1 f88_out -> f86_out :|: TRUE f1388_out(x2, x3) -> f86_out :|: x3 < x2 f86_in -> f1388_in(x4, x5) :|: x5 < x4 f86_in -> f88_in :|: TRUE f5058_in(T179, T178) -> f5060_in(T179) :|: TRUE f5060_out(x6) -> f5058_out(x6, x7) :|: TRUE f5060_in(x8) -> f72_in :|: TRUE f72_out -> f5060_out(x9) :|: TRUE f1469_in(x10) -> f72_in :|: TRUE f72_out -> f1469_out(x11) :|: TRUE f76_in -> f87_in :|: TRUE f87_out -> f76_out :|: TRUE f76_in -> f86_in :|: TRUE f86_out -> f76_out :|: TRUE f4950_in(T140, T139) -> f4952_in(T140) :|: TRUE f4950_in(x12, x13) -> f4953_in :|: TRUE f4952_out(x14) -> f4950_out(x14, x15) :|: TRUE f4953_out -> f4950_out(x16, x17) :|: TRUE f1747_in -> f4958_in :|: TRUE f4957_out -> f1747_out :|: TRUE f1747_in -> f4957_in :|: TRUE f4958_out -> f1747_out :|: TRUE f74_in -> f76_in :|: TRUE f77_out -> f74_out :|: TRUE f76_out -> f74_out :|: TRUE f74_in -> f77_in :|: TRUE f72_in -> f74_in :|: TRUE f74_out -> f72_out :|: TRUE f4954_out(x18) -> f4952_out(x18) :|: TRUE f4952_in(x19) -> f4954_in(x19) :|: TRUE f4957_in -> f4965_in :|: TRUE f4966_out -> f4957_out :|: TRUE f4957_in -> f4966_in :|: TRUE f4965_out -> f4957_out :|: TRUE f4954_in(x20) -> f72_in :|: TRUE f72_out -> f4954_out(x21) :|: TRUE f1388_in(x22, x23) -> f1469_in(x22) :|: TRUE f1469_out(x24) -> f1388_out(x24, x25) :|: TRUE f77_in -> f1743_in :|: TRUE f77_in -> f1747_in :|: TRUE f1747_out -> f77_out :|: TRUE f1743_out -> f77_out :|: TRUE f1844_in -> f1851_in :|: TRUE f1844_in -> f4950_in(x26, x27) :|: x27 = x26 f1851_out -> f1844_out :|: TRUE f1844_in -> f4951_in(x28, x29) :|: !(x29 = x28) f4950_out(x30, x31) -> f1844_out :|: x31 = x30 f4951_out(x32, x33) -> f1844_out :|: !(x33 = x32) f1743_in -> f1844_in :|: TRUE f1844_out -> f1743_out :|: TRUE f1743_in -> f1848_in :|: TRUE f1848_out -> f1743_out :|: TRUE f4965_in -> f4967_in :|: TRUE f5058_out(x34, x35) -> f4965_out :|: x35 > x34 f5059_out(x36, x37) -> f4965_out :|: x36 <= x37 f4965_in -> f5059_in(x38, x39) :|: x38 <= x39 f4965_in -> f5058_in(x40, x41) :|: x41 > x40 f4967_out -> f4965_out :|: TRUE f5_out(T3) -> f4_out(T3) :|: TRUE f4_in(x42) -> f5_in(x42) :|: TRUE f7_out(T14) -> f5_out(T14) :|: TRUE f5_in(x43) -> f7_in(x43) :|: TRUE f7_in(x44) -> f9_in(x44) :|: TRUE f10_out -> f7_out(x45) :|: TRUE f9_out(x46) -> f10_in :|: TRUE f52_out -> f53_in :|: TRUE f10_in -> f52_in :|: TRUE f53_out -> f10_out :|: TRUE f54_out -> f52_out :|: TRUE f52_in -> f54_in :|: TRUE f54_in -> f57_in :|: TRUE f58_out -> f54_out :|: TRUE f57_out -> f54_out :|: TRUE f54_in -> f58_in :|: TRUE f57_in -> f69_in :|: TRUE f69_out -> f57_out :|: TRUE f57_in -> f68_in :|: TRUE f68_out -> f57_out :|: TRUE f68_in -> f72_in :|: TRUE f72_out -> f73_in :|: TRUE f73_out -> f68_out :|: TRUE Start term: f4_in(T3) ---------------------------------------- (10) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (11) TRUE ---------------------------------------- (12) Obligation: Rules: f5058_in(T179, T178) -> f5060_in(T179) :|: TRUE f5060_out(x) -> f5058_out(x, x1) :|: TRUE f5060_in(x2) -> f72_in :|: TRUE f72_out -> f5060_out(x3) :|: TRUE f4950_in(T140, T139) -> f4952_in(T140) :|: TRUE f4950_in(x4, x5) -> f4953_in :|: TRUE f4952_out(x6) -> f4950_out(x6, x7) :|: TRUE f4953_out -> f4950_out(x8, x9) :|: TRUE f73_in -> f5136_in :|: TRUE f5136_out -> f5137_in :|: TRUE f5137_out -> f73_out :|: TRUE f1747_in -> f4958_in :|: TRUE f4957_out -> f1747_out :|: TRUE f1747_in -> f4957_in :|: TRUE f4958_out -> f1747_out :|: TRUE f4954_in(x10) -> f72_in :|: TRUE f72_out -> f4954_out(x11) :|: TRUE f1388_in(T106, T105) -> f1469_in(T106) :|: TRUE f1469_out(x12) -> f1388_out(x12, x13) :|: TRUE f77_in -> f1743_in :|: TRUE f77_in -> f1747_in :|: TRUE f1747_out -> f77_out :|: TRUE f1743_out -> f77_out :|: TRUE f57_in -> f69_in :|: TRUE f69_out -> f57_out :|: TRUE f57_in -> f68_in :|: TRUE f68_out -> f57_out :|: TRUE f1743_in -> f1844_in :|: TRUE f1844_out -> f1743_out :|: TRUE f1743_in -> f1848_in :|: TRUE f1848_out -> f1743_out :|: TRUE f4965_in -> f4967_in :|: TRUE f5058_out(x14, x15) -> f4965_out :|: x15 > x14 f5059_out(x16, x17) -> f4965_out :|: x16 <= x17 f4965_in -> f5059_in(x18, x19) :|: x18 <= x19 f4965_in -> f5058_in(x20, x21) :|: x21 > x20 f4967_out -> f4965_out :|: TRUE f86_in -> f1464_in(x22, x23) :|: x22 >= x23 f1464_out(x24, x25) -> f86_out :|: x24 >= x25 f88_out -> f86_out :|: TRUE f1388_out(x26, x27) -> f86_out :|: x27 < x26 f86_in -> f1388_in(x28, x29) :|: x29 < x28 f86_in -> f88_in :|: TRUE f1469_in(x30) -> f72_in :|: TRUE f72_out -> f1469_out(x31) :|: TRUE f76_in -> f87_in :|: TRUE f87_out -> f76_out :|: TRUE f76_in -> f86_in :|: TRUE f86_out -> f76_out :|: TRUE f74_in -> f76_in :|: TRUE f77_out -> f74_out :|: TRUE f76_out -> f74_out :|: TRUE f74_in -> f77_in :|: TRUE f72_in -> f74_in :|: TRUE f74_out -> f72_out :|: TRUE f4957_in -> f4965_in :|: TRUE f4966_out -> f4957_out :|: TRUE f4957_in -> f4966_in :|: TRUE f4965_out -> f4957_out :|: TRUE f4958_in -> f5070_in :|: TRUE f5070_out -> f4958_out :|: TRUE f5069_out -> f4958_out :|: TRUE f4958_in -> f5069_in :|: TRUE f4954_out(x32) -> f4952_out(x32) :|: TRUE f4952_in(x33) -> f4954_in(x33) :|: TRUE f54_in -> f57_in :|: TRUE f58_out -> f54_out :|: TRUE f57_out -> f54_out :|: TRUE f54_in -> f58_in :|: TRUE f5069_in -> f5069_out :|: TRUE f5136_in -> f52_in :|: TRUE f52_out -> f5136_out :|: TRUE f68_in -> f72_in :|: TRUE f72_out -> f73_in :|: TRUE f73_out -> f68_out :|: TRUE f54_out -> f52_out :|: TRUE f52_in -> f54_in :|: TRUE f1844_in -> f1851_in :|: TRUE f1844_in -> f4950_in(x34, x35) :|: x35 = x34 f1851_out -> f1844_out :|: TRUE f1844_in -> f4951_in(x36, x37) :|: !(x37 = x36) f4950_out(x38, x39) -> f1844_out :|: x39 = x38 f4951_out(x40, x41) -> f1844_out :|: !(x41 = x40) f5137_in -> f52_in :|: TRUE f52_out -> f5137_out :|: TRUE f5_out(T3) -> f4_out(T3) :|: TRUE f4_in(x42) -> f5_in(x42) :|: TRUE f7_out(T14) -> f5_out(T14) :|: TRUE f5_in(x43) -> f7_in(x43) :|: TRUE f7_in(x44) -> f9_in(x44) :|: TRUE f10_out -> f7_out(x45) :|: TRUE f9_out(x46) -> f10_in :|: TRUE f52_out -> f53_in :|: TRUE f10_in -> f52_in :|: TRUE f53_out -> f10_out :|: TRUE Start term: f4_in(T3) ---------------------------------------- (13) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: ---------------------------------------- (14) TRUE ---------------------------------------- (15) Obligation: Rules: f9_in(T14) -> f13_in(T14) :|: TRUE f13_out(x) -> f9_out(x) :|: TRUE f13_in(x1) -> f15_in(x1) :|: TRUE f13_in(x2) -> f16_in(x2) :|: TRUE f16_out(x3) -> f13_out(x3) :|: TRUE f15_out(x4) -> f13_out(x4) :|: TRUE f15_in(.(T42, T43)) -> f21_in(T43) :|: TRUE f22_out -> f15_out(x5) :|: TRUE f15_in(x6) -> f22_in :|: TRUE f21_out(x7) -> f15_out(.(x8, x7)) :|: TRUE f9_out(x9) -> f21_out(x9) :|: TRUE f21_in(x10) -> f9_in(x10) :|: TRUE f5_out(T3) -> f4_out(T3) :|: TRUE f4_in(x11) -> f5_in(x11) :|: TRUE f7_out(x12) -> f5_out(x12) :|: TRUE f5_in(x13) -> f7_in(x13) :|: TRUE f7_in(x14) -> f9_in(x14) :|: TRUE f10_out -> f7_out(x15) :|: TRUE f9_out(x16) -> f10_in :|: TRUE Start term: f4_in(T3) ---------------------------------------- (16) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f9_in(T14) -> f13_in(T14) :|: TRUE f13_in(x1) -> f15_in(x1) :|: TRUE f15_in(.(T42, T43)) -> f21_in(T43) :|: TRUE f21_in(x10) -> f9_in(x10) :|: TRUE ---------------------------------------- (17) Obligation: Rules: f9_in(T14) -> f13_in(T14) :|: TRUE f13_in(x1) -> f15_in(x1) :|: TRUE f15_in(.(T42, T43)) -> f21_in(T43) :|: TRUE f21_in(x10) -> f9_in(x10) :|: TRUE ---------------------------------------- (18) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (19) Obligation: Rules: f9_in(.(T42:0, T43:0)) -> f9_in(T43:0) :|: TRUE ---------------------------------------- (20) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (21) Obligation: Rules: f9_in(.(T42:0, T43:0)) -> f9_in(T43:0) :|: TRUE ---------------------------------------- (22) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f9_in(.(T42:0, T43:0)) -> f9_in(T43:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) f9_in(.(T42:0, T43:0)) -> f9_in(T43:0) :|: TRUE Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: .(x1, x2) -> .(x2) ---------------------------------------- (25) Obligation: Rules: f9_in(.(T43:0)) -> f9_in(T43:0) :|: TRUE ---------------------------------------- (26) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f9_in(VARIABLE) .(VARIABLE) Removed predefined arithmetic. ---------------------------------------- (27) Obligation: Rules: f9_in(.(T43:0)) -> f9_in(T43:0) ---------------------------------------- (28) IRSwTToQDPProof (SOUND) Removed the integers and created a QDP-Problem. ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: f9_in(.(T43:0)) -> f9_in(T43:0) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (30) 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: *f9_in(.(T43:0)) -> f9_in(T43:0) The graph contains the following edges 1 > 1 ---------------------------------------- (31) YES