/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern between(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 92 ms] (2) TRIPLES (3) TPisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Clauses: between(I, J, J) :- >=(J, I). between(I, J, K) :- ','(>(J, I), ','(is(J1, -(J, 1)), between(I, J1, K))). Query: between(g,g,a) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 3, "program": { "directives": [], "clauses": [ [ "(between I J J)", "(>= J I)" ], [ "(between I J K)", "(',' (> J I) (',' (is J1 (- J (1))) (between I J1 K)))" ] ] }, "graph": { "nodes": { "type": "Nodes", "1657": { "goal": [ { "clause": -1, "scope": -1, "term": "(true)" }, { "clause": 1, "scope": 1, "term": "(between T6 T7 T3)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }] }, "ground": [ "T6", "T7" ], "free": [], "exprvars": [ "T6", "T7" ] } }, "1777": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> T63 T62) (',' (is X60 (- T63 (1))) (between T62 X60 T65)))" }], "kb": { 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"T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T7", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T7", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T62", "T63" ], "free": ["X60"], "exprvars": [ "T41", "T63", "T6", "T40", "T62", "T7", "T44" ] } }, "1794": { "goal": [], "kb": { "nonunifying": [], 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{ "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T69", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T70", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T70", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T70", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T70", "T91", "T92" ], "free": [ "X3", "X4", "X88" ], "exprvars": [ "T70", "T92", "T69", "T91", "T73" ] } }, "1819": { "goal": [{ "clause": -1, "scope": -1, "term": "(between T69 T73 T72)" }], "kb": { "nonunifying": [[ "(between T69 T70 T3)", "(between X3 X4 X4)" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T73", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T70", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T69", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T70", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T70", "T69", "T73" ], "free": [ "X3", "X4", "X67" ], "exprvars": [ "T70", "T69", "T73" ] } }, "1719": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T12", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T11", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T12", "type": "PlainIntegerVariable" }, "operation": "<" }, { 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"type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T12", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T12", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T12", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T11", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T12", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T12", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T12", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T12", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T7", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T7", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T24", "T25" ], "free": [], "exprvars": [ "T25", "T24", "T6", "T12", "T7", "T11", "T15" ] } }, "1817": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X67 (- T70 (1))) (between T69 X67 T72))" }], 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"type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T40", "T44" ], "free": [], "exprvars": [ "T41", "T6", "T40", "T7", "T44" ] } }, "1820": { "goal": [ { "clause": 0, "scope": 4, "term": "(between T69 T73 T72)" }, { "clause": 1, "scope": 4, "term": "(between T69 T73 T72)" } ], "kb": { "nonunifying": [[ "(between T69 T70 T3)", "(between X3 X4 X4)" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T73", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T70", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T69", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T70", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T70", "T69", "T73" ], "free": [ "X3", "X4" ], "exprvars": [ "T70", "T69", "T73" ] } }, "1842": { "goal": [{ "clause": 0, "scope": 4, "term": "(between T69 T73 T72)" }], "kb": { "nonunifying": [[ "(between T69 T70 T3)", "(between X3 X4 X4)" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T73", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T70", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T69", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T70", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T70", "T69", "T73" ], "free": [ "X3", "X4" ], "exprvars": [ "T70", "T69", "T73" ] } }, "3": { "goal": [{ "clause": -1, "scope": -1, "term": "(between T1 T2 T3)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1", "T2" ], "free": [], "exprvars": [] } }, "1720": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> T34 T33) (',' (is X32 (- T34 (1))) (between T33 X32 T36)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T12", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T12", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T12", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T11", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T12", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T12", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T12", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T12", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T7", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T7", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T33", "T34" ], "free": ["X32"], "exprvars": [ "T6", "T12", "T34", "T7", "T11", "T33", "T15" ] } }, "1764": { "goal": [ { "clause": 0, "scope": 3, "term": "(between T40 T44 T43)" }, { "clause": 1, "scope": 3, "term": "(between T40 T44 T43)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T44", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T41", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": 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}, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T41", "T40", "T44" ], "free": ["X39"], "exprvars": [ "T41", "T6", "T40", "T7", "T44" ] } }, "5": { "goal": [ { "clause": 0, "scope": 1, "term": "(between T1 T2 T3)" }, { "clause": 1, "scope": 1, "term": "(between T1 T2 T3)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T1", "T2" ], "free": [], "exprvars": [] } }, "1663": { "goal": [{ "clause": 1, "scope": 1, "term": "(between T6 T7 T3)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }] }, "ground": [ "T6", "T7" ], "free": [], "exprvars": [ "T6", "T7" ] } }, "1762": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": ">=" } ] }, "ground": [ "T41", "T40" ], "free": ["X39"], "exprvars": [ "T41", "T6", "T40", "T7" ] } }, "1761": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X39 (- T41 (1))) (between T40 X39 T43))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": 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"<=" }, { "lhs": { "name": "T11", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T12", "type": "PlainIntegerVariable" }, "operation": ">=" } ] }, "ground": [ "T12", "T11" ], "free": ["X11"], "exprvars": [ "T6", "T12", "T7", "T11" ] } }, "9": { "goal": [ { "clause": -1, "scope": -1, "term": "(>= T7 T6)" }, { "clause": 1, "scope": 1, "term": "(between T6 T7 T3)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T6", "T7" ], "free": [], "exprvars": [] } }, "1708": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X11 (- T12 (1))) (between T11 X11 T14))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T11", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T12", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T12", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T12", "T11" ], "free": ["X11"], "exprvars": [ "T6", "T12", "T7", "T11" ] } }, "1768": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T44", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T41", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T6", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T7", "type": "PlainIntegerVariable" }, "operation": ">" }, { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [], "free": [], "exprvars": [ "T41", "T6", "T40", "T7", "T44" ] } }, "1845": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T73", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T70", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T69", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T70", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [], "free": [], "exprvars": [ "T70", "T69", "T73" ] } } }, "edges": [ { "from": 3, "to": 5, "label": "CASE" }, { "from": 5, "to": 9, "label": "EVAL with clause\nbetween(X3, X4, X4) :- >=(X4, X3).\nand substitutionT1 -> T6,\nX3 -> T6,\nT2 -> T7,\nX4 -> T7,\nT3 -> T7" }, { "from": 5, "to": 10, "label": "EVAL-BACKTRACK" }, { "from": 9, "to": 11, "label": "IS ERROR" }, { "from": 9, "to": 1657, "label": "ARITHCOMP SUCCESS" }, { "from": 9, "to": 1663, "label": "ARITHCOMP FAIL" }, { "from": 10, "to": 1790, "label": "ONLY EVAL with clause\nbetween(X64, X65, X66) :- ','(>(X65, X64), ','(is(X67, -(X65, 1)), between(X64, X67, X66))).\nand substitutionT1 -> T69,\nX64 -> T69,\nT2 -> T70,\nX65 -> T70,\nT3 -> T72,\nX66 -> T72,\nT71 -> T72" }, { "from": 1657, "to": 1664, "label": "SUCCESS" }, { "from": 1663, "to": 1737, "label": "ONLY EVAL with clause\nbetween(X36, X37, X38) :- ','(>(X37, X36), ','(is(X39, -(X37, 1)), between(X36, X39, X38))).\nand substitutionT6 -> T40,\nX36 -> T40,\nT7 -> T41,\nX37 -> T41,\nT3 -> T43,\nX38 -> T43,\nT42 -> T43" }, { "from": 1664, "to": 1666, "label": "ONLY EVAL with clause\nbetween(X8, X9, X10) :- ','(>(X9, X8), ','(is(X11, -(X9, 1)), between(X8, X11, X10))).\nand substitutionT6 -> T11,\nX8 -> T11,\nT7 -> T12,\nX9 -> T12,\nT3 -> T14,\nX10 -> T14,\nT13 -> T14" }, { "from": 1666, "to": 1708, "label": "ARITHCOMP SUCCESS" }, { "from": 1666, "to": 1709, "label": "ARITHCOMP FAIL" }, { "from": 1708, "to": 1713, "label": "\nX11 -> T15" }, { "from": 1713, "to": 1715, "label": "CASE" }, { "from": 1715, "to": 1716, "label": "PARALLEL" }, { "from": 1715, "to": 1717, "label": "PARALLEL" }, { "from": 1716, "to": 1718, "label": "EVAL with clause\nbetween(X20, X21, X21) :- >=(X21, X20).\nand substitutionT11 -> T24,\nX20 -> T24,\nT15 -> T25,\nX21 -> T25,\nT14 -> T25" }, { "from": 1716, "to": 1719, "label": "EVAL-BACKTRACK" }, { "from": 1717, "to": 1720, "label": "ONLY EVAL with clause\nbetween(X29, X30, X31) :- ','(>(X30, X29), ','(is(X32, -(X30, 1)), between(X29, X32, X31))).\nand substitutionT11 -> T33,\nX29 -> T33,\nT15 -> T34,\nX30 -> T34,\nT14 -> T36,\nX31 -> T36,\nT35 -> T36" }, { "from": 1737, "to": 1761, "label": "ARITHCOMP SUCCESS" }, { "from": 1737, "to": 1762, "label": "ARITHCOMP FAIL" }, { "from": 1761, "to": 1763, "label": "\nX39 -> T44" }, { "from": 1763, "to": 1764, "label": "CASE" }, { "from": 1764, "to": 1765, "label": "PARALLEL" }, { "from": 1764, "to": 1766, "label": "PARALLEL" }, { "from": 1765, "to": 1767, "label": "EVAL with clause\nbetween(X48, X49, X49) :- >=(X49, X48).\nand substitutionT40 -> T53,\nX48 -> T53,\nT44 -> T54,\nX49 -> T54,\nT43 -> T54" }, { "from": 1765, "to": 1768, "label": "EVAL-BACKTRACK" }, { "from": 1766, "to": 1777, "label": "ONLY EVAL with clause\nbetween(X57, X58, X59) :- ','(>(X58, X57), ','(is(X60, -(X58, 1)), between(X57, X60, X59))).\nand substitutionT40 -> T62,\nX57 -> T62,\nT44 -> T63,\nX58 -> T63,\nT43 -> T65,\nX59 -> T65,\nT64 -> T65" }, { "from": 1790, "to": 1794, "label": "IS ERROR" }, { "from": 1790, "to": 1817, "label": "ARITHCOMP SUCCESS" }, { "from": 1790, "to": 1818, "label": "ARITHCOMP FAIL" }, { "from": 1817, "to": 1819, "label": "\nX67 -> T73" }, { "from": 1819, "to": 1820, "label": "CASE" }, { "from": 1820, "to": 1842, "label": "PARALLEL" }, { "from": 1820, "to": 1843, "label": "PARALLEL" }, { "from": 1842, "to": 1844, "label": "EVAL with clause\nbetween(X76, X77, X77) :- >=(X77, X76).\nand substitutionT69 -> T82,\nX76 -> T82,\nT73 -> T83,\nX77 -> T83,\nT72 -> T83" }, { "from": 1842, "to": 1845, "label": "EVAL-BACKTRACK" }, { "from": 1843, "to": 1870, "label": "ONLY EVAL with clause\nbetween(X85, X86, X87) :- ','(>(X86, X85), ','(is(X88, -(X86, 1)), between(X85, X88, X87))).\nand substitutionT69 -> T91,\nX85 -> T91,\nT73 -> T92,\nX86 -> T92,\nT72 -> T94,\nX87 -> T94,\nT93 -> T94" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Triples: Clauses: Afs: ---------------------------------------- (3) TPisEmptyProof (EQUIVALENT) There are no more dependency triples. Hence, the dependency triple problem trivially terminates. ---------------------------------------- (4) YES