/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern sum(a,g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 72 ms] (2) IRSwT (3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 29 ms] (6) IRSwT (7) IRSFormatTransformerProof [EQUIVALENT, 1 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 33 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 12 ms] (18) YES ---------------------------------------- (0) Obligation: Clauses: sum(X, Y, Z) :- ','(=:=(X, 0), is(Z, Y)). sum(X, Y, Z) :- ','(<(X, 0), sum(+(X, 1), -(Y, 1), Z)). sum(X, Y, Z) :- ','(>(X, 0), sum(-(X, 1), +(Y, 1), Z)). Query: sum(a,g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 1, "program": { "directives": [], "clauses": [ [ "(sum X Y Z)", "(',' (=:= X (0)) (is Z Y))" ], [ "(sum X Y Z)", "(',' (< X (0)) (sum (+ X (1)) (- Y (1)) Z))" ], [ "(sum X Y Z)", "(',' (> X (0)) (sum (- X (1)) (+ Y (1)) Z))" ] ] }, "graph": { "nodes": { "type": "Nodes", "1932": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (< (+ (- T158 (1)) (1)) (0)) (sum (+ (+ (- T158 (1)) (1)) (1)) (- (- (+ T159 (1)) (1)) (1)) T160))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T125", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T125", "type": "PlainIntegerVariable" }, { "type": 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"relations": [] }, "ground": [ "T91", "T92" ], "free": [], "exprvars": [] } }, "1853": { "goal": [{ "clause": -1, "scope": -1, "term": "(sum (+ (- T125 (1)) (1)) (- (+ T126 (1)) (1)) T127)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T125", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T125", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" } ] }, "ground": [ "T126", "T125", "T127" ], "free": [], 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}, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T93", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" } ] }, "ground": [ "T167", "T168", "T169" ], "free": [], "exprvars": [ "T125", "T167", "T93" ] } }, "10": { "goal": [ { "clause": 1, "scope": 1, "term": "(sum T1 T2 T3)" }, { "clause": 2, "scope": 1, "term": "(sum T1 T2 T3)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T2", "T3" ], "free": [], "exprvars": [] } }, "13": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (=:= T21 (0)) (is T20 T19))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { 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}, "operation": ">=" }] }, "ground": [ "T40", "T39", "T38" ], "free": [], "exprvars": ["T40"] } }, "1866": { "goal": [ { "clause": 1, "scope": 4, "term": "(sum (+ (- T125 (1)) (1)) (- (+ T126 (1)) (1)) T127)" }, { "clause": 2, "scope": 4, "term": "(sum (+ (- T125 (1)) (1)) (- (+ T126 (1)) (1)) T127)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T125", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "arguments": [ { "name": "T125", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "type": 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{ "name": "T125", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" }, { "lhs": { "name": "T93", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T93", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" } ] }, "ground": [ "T143", "T144", "T145" ], "free": [], "exprvars": [ "T125", "T143", "T93" ] } }, "1703": { "goal": [{ "clause": 0, "scope": 2, "term": "(sum (+ T40 (1)) (- T38 (1)) T39)" }], "kb": { "nonunifying": [], 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"1794": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "arguments": [ { "name": "T109", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "=" }, { "lhs": { "name": "T112", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T110", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T109", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": 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"type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T109", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T109", "T111", "T110" ], "free": [], "exprvars": [ "T109", "T110", "T93" ] } }, "1759": { "goal": [ { "clause": 0, "scope": 3, "term": "(sum (- T93 (1)) (+ T91 (1)) T92)" }, { "clause": 1, "scope": 3, "term": "(sum (- T93 (1)) (+ T91 (1)) T92)" }, { "clause": 2, "scope": 3, "term": "(sum (- T93 (1)) (+ T91 (1)) T92)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }] }, "ground": [ "T92", "T91", "T93" ], "free": [], "exprvars": ["T93"] } }, "1714": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (< (+ T71 (1)) (0)) (sum (+ (+ T71 (1)) (1)) (- (- T72 (1)) (1)) T73))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" } ] }, "ground": [ "T71", "T72", "T73" ], "free": [], "exprvars": [ "T40", "T71" ] } }, "1713": { "goal": [{ "clause": 2, "scope": 2, "term": "(sum (+ T40 (1)) (- T38 (1)) T39)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" }] }, "ground": [ "T40", "T39", "T38" ], "free": [], "exprvars": ["T40"] } }, "1764": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (=:= (- T109 (1)) (0)) (is T111 (+ T110 (1))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T109", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T109", "T110", "T111" ], "free": [], "exprvars": [ "T109", "T93" ] } }, "1685": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1684": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (< T40 (0)) (sum (+ T40 (1)) (- T38 (1)) T39))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T38", "T39" ], "free": [], "exprvars": [] } }, "1761": { "goal": [ { "clause": 1, "scope": 3, "term": "(sum (- T93 (1)) (+ T91 (1)) T92)" }, { "clause": 2, "scope": 3, "term": "(sum (- T93 (1)) (+ T91 (1)) T92)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }] }, "ground": [ "T92", "T91", "T93" ], "free": [], "exprvars": ["T93"] } }, "1760": { "goal": [{ "clause": 0, "scope": 3, "term": "(sum (- T93 (1)) (+ T91 (1)) T92)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }] }, "ground": [ "T92", "T91", "T93" ], "free": [], "exprvars": ["T93"] } }, "1728": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> (+ T80 (1)) (0)) (sum (- (+ T80 (1)) (1)) (+ (- T81 (1)) (1)) T82))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "<" } ] }, "ground": [ "T80", "T81", "T82" ], "free": [], "exprvars": [ "T80", "T40" ] } }, "1769": { "goal": [{ "clause": -1, "scope": -1, "term": "(is T111 (+ T110 (1)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "arguments": [ { "name": "T109", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T109", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T93", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T109", "T111", "T110" ], "free": [], "exprvars": [ "T109", "T93" ] } } }, "edges": [ { "from": 1, "to": 5, "label": "CASE" }, { "from": 5, "to": 8, "label": "PARALLEL" }, { "from": 5, "to": 10, "label": "PARALLEL" }, { "from": 8, "to": 13, "label": "ONLY EVAL with clause\nsum(X13, X14, X15) :- ','(=:=(X13, 0), is(X15, X14)).\nand substitutionT1 -> T21,\nX13 -> T21,\nT2 -> T19,\nX14 -> T19,\nT3 -> T20,\nX15 -> T20,\nT18 -> T21" }, { "from": 10, "to": 1677, "label": "PARALLEL" }, { "from": 10, "to": 1678, "label": "PARALLEL" }, { "from": 13, "to": 14, "label": "IS ERROR" }, { "from": 13, "to": 1671, "label": "ARITHCOMP SUCCESS" }, { "from": 13, "to": 1672, "label": "ARITHCOMP FAIL" }, { "from": 1671, "to": 1673, "label": "IS ERROR" }, { "from": 1671, "to": 1674, "label": "\nT20 -> T22" }, { "from": 1671, "to": 1675, "label": "IS FAIL" }, { "from": 1674, "to": 1676, "label": "SUCCESS" }, { "from": 1677, "to": 1684, "label": "ONLY EVAL with clause\nsum(X28, X29, X30) :- ','(<(X28, 0), sum(+(X28, 1), -(X29, 1), X30)).\nand substitutionT1 -> T40,\nX28 -> T40,\nT2 -> T38,\nX29 -> T38,\nT3 -> T39,\nX30 -> T39,\nT37 -> T40" }, { "from": 1678, "to": 1732, "label": "ONLY EVAL with clause\nsum(X79, X80, X81) :- ','(>(X79, 0), sum(-(X79, 1), +(X80, 1), X81)).\nand substitutionT1 -> T93,\nX79 -> T93,\nT2 -> T91,\nX80 -> T91,\nT3 -> T92,\nX81 -> T92,\nT90 -> T93" }, { "from": 1684, "to": 1685, "label": "IS ERROR" }, { "from": 1684, "to": 1700, "label": "ARITHCOMP SUCCESS" }, { "from": 1684, "to": 1701, "label": "ARITHCOMP FAIL" }, { "from": 1700, "to": 1702, "label": "CASE" }, { "from": 1702, "to": 1703, "label": "PARALLEL" }, { "from": 1702, "to": 1704, "label": "PARALLEL" }, { "from": 1703, "to": 1705, "label": "ONLY EVAL with clause\nsum(X46, X47, X48) :- ','(=:=(X46, 0), is(X48, X47)).\nand substitutionT40 -> T56,\nX46 -> +(T56, 1),\nT38 -> T57,\nX47 -> -(T57, 1),\nT39 -> T58,\nX48 -> T58" }, { "from": 1704, "to": 1712, "label": "PARALLEL" }, { "from": 1704, "to": 1713, "label": "PARALLEL" }, { "from": 1712, "to": 1714, "label": "ONLY EVAL with clause\nsum(X61, X62, X63) :- ','(<(X61, 0), sum(+(X61, 1), -(X62, 1), X63)).\nand substitutionT40 -> T71,\nX61 -> +(T71, 1),\nT38 -> T72,\nX62 -> -(T72, 1),\nT39 -> T73,\nX63 -> T73" }, { "from": 1713, "to": 1728, "label": "ONLY EVAL with clause\nsum(X70, X71, X72) :- ','(>(X70, 0), sum(-(X70, 1), +(X71, 1), X72)).\nand substitutionT40 -> T80,\nX70 -> +(T80, 1),\nT38 -> T81,\nX71 -> -(T81, 1),\nT39 -> T82,\nX72 -> T82" }, { "from": 1732, "to": 1733, "label": "IS ERROR" }, { "from": 1732, "to": 1755, "label": "ARITHCOMP SUCCESS" }, { "from": 1732, "to": 1756, "label": "ARITHCOMP FAIL" }, { "from": 1755, "to": 1759, "label": "CASE" }, { "from": 1759, "to": 1760, "label": "PARALLEL" }, { "from": 1759, "to": 1761, "label": "PARALLEL" }, { "from": 1760, "to": 1764, "label": "ONLY EVAL with clause\nsum(X97, X98, X99) :- ','(=:=(X97, 0), is(X99, X98)).\nand substitutionT93 -> T109,\nX97 -> -(T109, 1),\nT91 -> T110,\nX98 -> +(T110, 1),\nT92 -> T111,\nX99 -> T111" }, { "from": 1761, "to": 1795, "label": "PARALLEL" }, { "from": 1761, "to": 1796, "label": "PARALLEL" }, { "from": 1764, "to": 1769, "label": "ARITHCOMP SUCCESS" }, { "from": 1764, "to": 1772, "label": "ARITHCOMP FAIL" }, { "from": 1769, "to": 1773, "label": "IS ERROR" }, { "from": 1769, "to": 1775, "label": "\nT111 -> T112" }, { "from": 1769, "to": 1793, "label": "IS FAIL" }, { "from": 1775, "to": 1794, "label": "SUCCESS" }, { "from": 1795, "to": 1797, "label": "ONLY EVAL with clause\nsum(X112, X113, X114) :- ','(<(X112, 0), sum(+(X112, 1), -(X113, 1), X114)).\nand substitutionT93 -> T125,\nX112 -> -(T125, 1),\nT91 -> T126,\nX113 -> +(T126, 1),\nT92 -> T127,\nX114 -> T127" }, { "from": 1796, "to": 1943, "label": "ONLY EVAL with clause\nsum(X163, X164, X165) :- ','(>(X163, 0), sum(-(X163, 1), +(X164, 1), X165)).\nand substitutionT93 -> T176,\nX163 -> -(T176, 1),\nT91 -> T177,\nX164 -> +(T177, 1),\nT92 -> T178,\nX165 -> T178" }, { "from": 1797, "to": 1853, "label": "ARITHCOMP SUCCESS" }, { "from": 1797, "to": 1854, "label": "ARITHCOMP FAIL" }, { "from": 1853, "to": 1864, "label": "CASE" }, { "from": 1864, "to": 1865, "label": "PARALLEL" }, { "from": 1864, "to": 1866, "label": "PARALLEL" }, { "from": 1865, "to": 1869, "label": "ONLY EVAL with clause\nsum(X130, X131, X132) :- ','(=:=(X130, 0), is(X132, X131)).\nand substitutionT125 -> T143,\nX130 -> +(-(T143, 1), 1),\nT126 -> T144,\nX131 -> -(+(T144, 1), 1),\nT127 -> T145,\nX132 -> T145" }, { "from": 1866, "to": 1930, "label": "PARALLEL" }, { "from": 1866, "to": 1931, "label": "PARALLEL" }, { "from": 1930, "to": 1932, "label": "ONLY EVAL with clause\nsum(X145, X146, X147) :- ','(<(X145, 0), sum(+(X145, 1), -(X146, 1), X147)).\nand substitutionT125 -> T158,\nX145 -> +(-(T158, 1), 1),\nT126 -> T159,\nX146 -> -(+(T159, 1), 1),\nT127 -> T160,\nX147 -> T160" }, { "from": 1931, "to": 1939, "label": "ONLY EVAL with clause\nsum(X154, X155, X156) :- ','(>(X154, 0), sum(-(X154, 1), +(X155, 1), X156)).\nand substitutionT125 -> T167,\nX154 -> +(-(T167, 1), 1),\nT126 -> T168,\nX155 -> -(+(T168, 1), 1),\nT127 -> T169,\nX156 -> T169" }, { "from": 1943, "to": 2028, "label": "ARITHCOMP SUCCESS" }, { "from": 1943, "to": 2029, "label": "ARITHCOMP FAIL" }, { "from": 2028, "to": 1755, "label": "INSTANCE with matching:\nT93 -> -(T176, 1)\nT91 -> +(T177, 1)\nT92 -> T178" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Rules: f1759_in(T93, T91, T92) -> f1761_in(T93, T91, T92) :|: TRUE f1760_out(x, x1, x2) -> f1759_out(x, x1, x2) :|: TRUE f1761_out(x3, x4, x5) -> f1759_out(x3, x4, x5) :|: TRUE f1759_in(x6, x7, x8) -> f1760_in(x6, x7, x8) :|: TRUE f1755_out(T176 - 1, T177 + 1, T178) -> f2028_out(T176, T177, T178) :|: TRUE f2028_in(x9, x10, x11) -> f1755_in(x9 - 1, x10 + 1, x11) :|: TRUE f1761_in(x12, x13, x14) -> f1795_in(x12, x13, x14) :|: TRUE f1795_out(x15, x16, x17) -> f1761_out(x15, x16, x17) :|: TRUE f1796_out(x18, x19, x20) -> f1761_out(x18, x19, x20) :|: TRUE f1761_in(x21, x22, x23) -> f1796_in(x21, x22, x23) :|: TRUE f1759_out(x24, x25, x26) -> f1755_out(x24, x25, x26) :|: TRUE f1755_in(x27, x28, x29) -> f1759_in(x27, x28, x29) :|: TRUE f2029_out(x30, x31, x32) -> f1943_out(x31, x30, x32) :|: x31 - 1 <= 0 f2028_out(x33, x34, x35) -> f1943_out(x33, x34, x35) :|: x33 - 1 > 0 f1943_in(x36, x37, x38) -> f2028_in(x36, x37, x38) :|: x36 - 1 > 0 f1943_in(x39, x40, x41) -> f2029_in(x40, x39, x41) :|: x39 - 1 <= 0 f1943_out(x42, x43, x44) -> f1796_out(x42, x43, x44) :|: TRUE f1796_in(x45, x46, x47) -> f1943_in(x45, x46, x47) :|: TRUE f5_out(T2, T3) -> f1_out(T2, T3) :|: TRUE f1_in(x48, x49) -> f5_in(x48, x49) :|: TRUE f5_in(x50, x51) -> f8_in(x50, x51) :|: TRUE f8_out(x52, x53) -> f5_out(x52, x53) :|: TRUE f5_in(x54, x55) -> f10_in(x54, x55) :|: TRUE f10_out(x56, x57) -> f5_out(x56, x57) :|: TRUE f10_in(x58, x59) -> f1677_in(x58, x59) :|: TRUE f1677_out(x60, x61) -> f10_out(x60, x61) :|: TRUE f10_in(x62, x63) -> f1678_in(x62, x63) :|: TRUE f1678_out(x64, x65) -> f10_out(x64, x65) :|: TRUE f1678_in(x66, x67) -> f1732_in(x66, x67) :|: TRUE f1732_out(x68, x69) -> f1678_out(x68, x69) :|: TRUE f1733_out -> f1732_out(x70, x71) :|: TRUE f1755_out(x72, x73, x74) -> f1732_out(x73, x74) :|: x72 > 0 f1756_out(x75, x76, x77) -> f1732_out(x76, x75) :|: x77 <= 0 f1732_in(x78, x79) -> f1755_in(x80, x78, x79) :|: x80 > 0 f1732_in(x81, x82) -> f1733_in :|: TRUE f1732_in(x83, x84) -> f1756_in(x84, x83, x85) :|: x85 <= 0 Start term: f1_in(T2, T3) ---------------------------------------- (3) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f1759_in(T93, T91, T92) -> f1761_in(T93, T91, T92) :|: TRUE f2028_in(x9, x10, x11) -> f1755_in(x9 - 1, x10 + 1, x11) :|: TRUE f1761_in(x21, x22, x23) -> f1796_in(x21, x22, x23) :|: TRUE f1755_in(x27, x28, x29) -> f1759_in(x27, x28, x29) :|: TRUE f1943_in(x36, x37, x38) -> f2028_in(x36, x37, x38) :|: x36 - 1 > 0 f1796_in(x45, x46, x47) -> f1943_in(x45, x46, x47) :|: TRUE ---------------------------------------- (4) Obligation: Rules: f1759_in(T93, T91, T92) -> f1761_in(T93, T91, T92) :|: TRUE f2028_in(x9, x10, x11) -> f1755_in(x9 - 1, x10 + 1, x11) :|: TRUE f1761_in(x21, x22, x23) -> f1796_in(x21, x22, x23) :|: TRUE f1755_in(x27, x28, x29) -> f1759_in(x27, x28, x29) :|: TRUE f1943_in(x36, x37, x38) -> f2028_in(x36, x37, x38) :|: x36 - 1 > 0 f1796_in(x45, x46, x47) -> f1943_in(x45, x46, x47) :|: TRUE ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f1943_in(x36:0, x37:0, x38:0) -> f1943_in(x36:0 - 1, x37:0 + 1, x38:0) :|: x36:0 > 1 ---------------------------------------- (7) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (8) Obligation: Rules: f1943_in(x36:0, x37:0, x38:0) -> f1943_in(arith, arith1, x38:0) :|: x36:0 > 1 && arith = x36:0 - 1 && arith1 = x37:0 + 1 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1943_in(x36:0, x37:0, x38:0) -> f1943_in(arith, arith1, x38:0) :|: x36:0 > 1 && arith = x36:0 - 1 && arith1 = x37:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) f1943_in(x36:0, x37:0, x38:0) -> f1943_in(arith, arith1, x38:0) :|: x36:0 > 1 && arith = x36:0 - 1 && arith1 = x37:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f1943_in(x36:0:0, x37:0:0, x38:0:0) -> f1943_in(x36:0:0 - 1, x37:0:0 + 1, x38:0:0) :|: x36:0:0 > 1 ---------------------------------------- (13) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1943_in(x1, x2, x3) -> f1943_in(x1) ---------------------------------------- (14) Obligation: Rules: f1943_in(x36:0:0) -> f1943_in(x36:0:0 - 1) :|: x36:0:0 > 1 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1943_in(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f1943_in(x36:0:0) -> f1943_in(c) :|: c = x36:0:0 - 1 && x36:0:0 > 1 ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1943_in(x)] = x The following rules are decreasing: f1943_in(x36:0:0) -> f1943_in(c) :|: c = x36:0:0 - 1 && x36:0:0 > 1 The following rules are bounded: f1943_in(x36:0:0) -> f1943_in(c) :|: c = x36:0:0 - 1 && x36:0:0 > 1 ---------------------------------------- (18) YES