/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern fib(a,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 123 ms] (2) IRSwT (3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 48 ms] (6) IRSwT (7) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 23 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT (13) TempFilterProof [SOUND, 32 ms] (14) IntTRS (15) PolynomialOrderProcessor [EQUIVALENT, 11 ms] (16) YES ---------------------------------------- (0) Obligation: Clauses: fib(X, Y) :- ','(<(X, 2), =(Y, 1)). fib(X, Y) :- ','(>=(X, 2), ','(fib(-(X, 1), F1), ','(fib(-(X, 2), F2), is(Y, +(F1, F2))))). Query: fib(a,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 3, "program": { "directives": [], "clauses": [ [ "(fib X Y)", "(',' (< X (2)) (= Y (1)))" ], [ "(fib X Y)", "(',' (>= X (2)) (',' (fib (- X (1)) F1) (',' (fib (- X (2)) F2) (is Y (+ F1 F2)))))" ] ] }, "graph": { "nodes": { "2551": { "goal": [{ "clause": -1, "scope": -1, "term": "(is X214 (+ T92 T95))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T92", "T95" ], "free": ["X214"], "exprvars": [] } }, "2793": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T140", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T64", "type": "PlainIntegerVariable" }, { "name": "T67", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }] }, "ground": [], "free": [], "exprvars": [ "T64", "T140", "T67" ] } }, 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-> T22,\nT21 -> T23" }, { "from": 11, "to": 12, "label": "IS ERROR" }, { "from": 11, "to": 1923, "label": "ARITHCOMP SUCCESS" }, { "from": 11, "to": 1924, "label": "ARITHCOMP FAIL" }, { "from": 1923, "to": 1925, "label": "UNIFY CASE with substitutionT14 -> 1" }, { "from": 1923, "to": 1926, "label": "UNIFY-BACKTRACK" }, { "from": 1925, "to": 1930, "label": "SUCCESS" }, { "from": 2075, "to": 2076, "label": "IS ERROR" }, { "from": 2075, "to": 2084, "label": "ARITHCOMP SUCCESS" }, { "from": 2075, "to": 2085, "label": "ARITHCOMP FAIL" }, { "from": 2084, "to": 2086, "label": "SPLIT 1" }, { "from": 2084, "to": 2087, "label": "SPLIT 2\nnew knowledge:\nT23 is ground\nT25 is ground\nreplacements:X19 -> T25" }, { "from": 2086, "to": 2088, "label": "CASE" }, { "from": 2087, "to": 2801, "label": "SPLIT 1" }, { "from": 2087, "to": 2802, "label": "SPLIT 2\nnew knowledge:\nT23 is ground\nT144 is ground\nreplacements:X20 -> T144" }, { "from": 2088, "to": 2092, "label": "PARALLEL" }, { "from": 2088, "to": 2093, "label": "PARALLEL" }, { "from": 2092, "to": 2094, "label": "ONLY EVAL with clause\nfib(X39, X40) :- ','(<(X39, 2), =(X40, 1)).\nand substitutionT23 -> T31,\nX39 -> -(T31, 1),\nX19 -> X41,\nX40 -> X41" }, { "from": 2093, "to": 2150, "label": "ONLY EVAL with clause\nfib(X50, X51) :- ','(>=(X50, 2), ','(fib(-(X50, 1), X52), ','(fib(-(X50, 2), X53), is(X51, +(X52, X53))))).\nand substitutionT23 -> T34,\nX50 -> -(T34, 1),\nX19 -> X54,\nX51 -> X54" }, { "from": 2094, "to": 2146, "label": "ARITHCOMP SUCCESS" }, { "from": 2094, "to": 2147, "label": "ARITHCOMP FAIL" }, { "from": 2146, "to": 2148, "label": "UNIFY SUCCESS with substitutionX41 -> 1" }, { "from": 2148, "to": 2149, "label": "SUCCESS" }, { "from": 2150, "to": 2167, "label": "ARITHCOMP SUCCESS" }, { "from": 2150, "to": 2168, "label": "ARITHCOMP FAIL" }, { "from": 2167, "to": 2169, "label": "SPLIT 1" }, { "from": 2167, "to": 2170, "label": "SPLIT 2\nnew knowledge:\nT34 is ground\nT36 is ground\nreplacements:X52 -> T36" }, { "from": 2169, "to": 2086, "label": "INSTANCE with matching:\nT23 -> -(T34, 1)\nX19 -> X52" }, { "from": 2170, "to": 2181, "label": "SPLIT 1" }, { "from": 2170, "to": 2182, "label": "SPLIT 2\nnew knowledge:\nT34 is ground\nT39 is ground\nreplacements:X53 -> T39" }, { "from": 2181, "to": 2183, "label": "CASE" }, { "from": 2182, "to": 2797, "label": "IS ERROR" }, { "from": 2182, "to": 2798, "label": "\nX54 -> T142" }, { "from": 2183, "to": 2184, "label": "PARALLEL" }, { "from": 2183, "to": 2185, "label": "PARALLEL" }, { "from": 2184, "to": 2186, "label": "ONLY EVAL with clause\nfib(X79, X80) :- ','(<(X79, 2), =(X80, 1)).\nand substitutionT34 -> T45,\nX79 -> -(-(T45, 1), 2),\nX53 -> X81,\nX80 -> X81" }, { "from": 2185, "to": 2195, "label": "ONLY EVAL with clause\nfib(X90, X91) :- ','(>=(X90, 2), ','(fib(-(X90, 1), X92), ','(fib(-(X90, 2), X93), is(X91, +(X92, X93))))).\nand substitutionT34 -> T48,\nX90 -> -(-(T48, 1), 2),\nX53 -> X94,\nX91 -> X94" }, { "from": 2186, "to": 2187, "label": "IS ERROR" }, { "from": 2186, "to": 2191, "label": "ARITHCOMP SUCCESS" }, { "from": 2186, "to": 2192, "label": "ARITHCOMP FAIL" }, { "from": 2191, "to": 2193, "label": "UNIFY SUCCESS with substitutionX81 -> 1" }, { "from": 2193, "to": 2194, "label": "SUCCESS" }, { "from": 2195, "to": 2196, "label": "IS ERROR" }, { "from": 2195, "to": 2214, "label": "ARITHCOMP SUCCESS" }, { "from": 2195, "to": 2215, "label": "ARITHCOMP FAIL" }, { "from": 2214, "to": 2216, "label": "SPLIT 1" }, { "from": 2214, "to": 2217, "label": "SPLIT 2\nnew knowledge:\nT48 is ground\nT50 is ground\nreplacements:X92 -> T50" }, { "from": 2216, "to": 2086, "label": "INSTANCE with matching:\nT23 -> -(-(T48, 1), 2)\nX19 -> X92" }, { "from": 2217, "to": 2226, "label": "SPLIT 1" }, { "from": 2217, "to": 2227, "label": "SPLIT 2\nnew knowledge:\nT48 is ground\nT53 is ground\nreplacements:X93 -> T53" }, { "from": 2226, "to": 2228, "label": "CASE" }, { "from": 2227, "to": 2794, "label": "IS ERROR" }, { "from": 2227, "to": 2795, "label": "\nX94 -> T141" }, { "from": 2228, "to": 2229, "label": "PARALLEL" }, { "from": 2228, "to": 2230, "label": "PARALLEL" }, { "from": 2229, "to": 2231, "label": "ONLY EVAL with clause\nfib(X119, X120) :- ','(<(X119, 2), =(X120, 1)).\nand substitutionT48 -> T59,\nX119 -> -(-(-(T59, 1), 2), 2),\nX93 -> X121,\nX120 -> X121" }, { "from": 2230, "to": 2244, "label": "ONLY EVAL with clause\nfib(X130, X131) :- ','(>=(X130, 2), ','(fib(-(X130, 1), X132), ','(fib(-(X130, 2), X133), is(X131, +(X132, X133))))).\nand substitutionT48 -> T62,\nX130 -> -(-(-(T62, 1), 2), 2),\nX93 -> X134,\nX131 -> X134" }, { "from": 2231, "to": 2232, "label": "IS ERROR" }, { "from": 2231, "to": 2240, "label": "ARITHCOMP SUCCESS" }, { "from": 2231, "to": 2241, "label": "ARITHCOMP FAIL" }, { "from": 2240, "to": 2242, "label": "UNIFY SUCCESS with substitutionX121 -> 1" }, { "from": 2242, "to": 2243, "label": "SUCCESS" }, { "from": 2244, "to": 2245, "label": "IS ERROR" }, { "from": 2244, "to": 2256, "label": "ARITHCOMP SUCCESS" }, { "from": 2244, "to": 2257, "label": "ARITHCOMP FAIL" }, { "from": 2256, "to": 2258, "label": "SPLIT 1" }, { "from": 2256, "to": 2259, "label": "SPLIT 2\nnew knowledge:\nT62 is ground\nT64 is ground\nreplacements:X132 -> T64" }, { "from": 2258, "to": 2086, "label": "INSTANCE with matching:\nT23 -> -(-(-(T62, 1), 2), 2)\nX19 -> X132" }, { "from": 2259, "to": 2264, "label": "SPLIT 1" }, { "from": 2259, "to": 2265, "label": "SPLIT 2\nnew knowledge:\nT62 is ground\nT67 is ground\nreplacements:X133 -> T67" }, { "from": 2264, "to": 2266, "label": "CASE" }, { "from": 2265, "to": 2791, "label": "IS ERROR" }, { "from": 2265, "to": 2792, "label": "\nX134 -> T140" }, { "from": 2266, "to": 2267, "label": "PARALLEL" }, { "from": 2266, "to": 2268, "label": "PARALLEL" }, { "from": 2267, "to": 2269, "label": "ONLY EVAL with clause\nfib(X159, X160) :- ','(<(X159, 2), =(X160, 1)).\nand substitutionT62 -> T73,\nX159 -> -(-(-(-(T73, 1), 2), 2), 2),\nX133 -> X161,\nX160 -> X161" }, { "from": 2268, "to": 2292, "label": "ONLY EVAL with clause\nfib(X170, X171) :- ','(>=(X170, 2), ','(fib(-(X170, 1), X172), ','(fib(-(X170, 2), X173), is(X171, +(X172, X173))))).\nand substitutionT62 -> T76,\nX170 -> -(-(-(-(T76, 1), 2), 2), 2),\nX133 -> X174,\nX171 -> X174" }, { "from": 2269, "to": 2270, "label": "IS ERROR" }, { "from": 2269, "to": 2288, "label": "ARITHCOMP SUCCESS" }, { "from": 2269, "to": 2289, "label": "ARITHCOMP FAIL" }, { "from": 2288, "to": 2290, "label": "UNIFY SUCCESS with substitutionX161 -> 1" }, { "from": 2290, "to": 2291, "label": "SUCCESS" }, { "from": 2292, "to": 2293, "label": "IS ERROR" }, { "from": 2292, "to": 2405, "label": "ARITHCOMP SUCCESS" }, { "from": 2292, "to": 2406, "label": "ARITHCOMP FAIL" }, { "from": 2405, "to": 2407, "label": "SPLIT 1" }, { "from": 2405, "to": 2408, "label": "SPLIT 2\nnew knowledge:\nT76 is ground\nT78 is ground\nreplacements:X172 -> T78" }, { "from": 2407, "to": 2086, "label": "INSTANCE with matching:\nT23 -> -(-(-(-(T76, 1), 2), 2), 2)\nX19 -> X172" }, { "from": 2408, "to": 2441, "label": "SPLIT 1" }, { "from": 2408, "to": 2442, "label": "SPLIT 2\nnew knowledge:\nT76 is ground\nT81 is ground\nreplacements:X173 -> T81" }, { "from": 2441, "to": 2443, "label": "CASE" }, { "from": 2442, "to": 2788, "label": "IS ERROR" }, { "from": 2442, "to": 2789, "label": "\nX174 -> T139" }, { "from": 2443, "to": 2490, "label": "PARALLEL" }, { "from": 2443, "to": 2491, "label": "PARALLEL" }, { "from": 2490, "to": 2492, "label": "ONLY EVAL with clause\nfib(X199, X200) :- ','(<(X199, 2), =(X200, 1)).\nand substitutionT76 -> T87,\nX199 -> -(-(-(-(-(T87, 1), 2), 2), 2), 2),\nX173 -> X201,\nX200 -> X201" }, { "from": 2491, "to": 2530, "label": "ONLY EVAL with clause\nfib(X210, X211) :- ','(>=(X210, 2), ','(fib(-(X210, 1), X212), ','(fib(-(X210, 2), X213), is(X211, +(X212, X213))))).\nand substitutionT76 -> T90,\nX210 -> -(-(-(-(-(T90, 1), 2), 2), 2), 2),\nX173 -> X214,\nX211 -> X214" }, { "from": 2492, "to": 2493, "label": "IS ERROR" }, { "from": 2492, "to": 2524, "label": "ARITHCOMP SUCCESS" }, { "from": 2492, "to": 2525, "label": "ARITHCOMP FAIL" }, { "from": 2524, "to": 2526, "label": "UNIFY SUCCESS with substitutionX201 -> 1" }, { "from": 2526, "to": 2527, "label": "SUCCESS" }, { "from": 2530, "to": 2531, "label": "IS ERROR" }, { "from": 2530, "to": 2544, "label": "ARITHCOMP SUCCESS" }, { "from": 2530, "to": 2545, "label": "ARITHCOMP FAIL" }, { "from": 2544, "to": 2548, "label": "SPLIT 1" }, { "from": 2544, "to": 2549, "label": "SPLIT 2\nnew knowledge:\nT90 is ground\nT92 is ground\nreplacements:X212 -> T92" }, { "from": 2548, "to": 2086, "label": "INSTANCE with matching:\nT23 -> -(-(-(-(-(T90, 1), 2), 2), 2), 2)\nX19 -> X212" }, { "from": 2549, "to": 2550, "label": "SPLIT 1" }, { "from": 2549, "to": 2551, "label": "SPLIT 2\nnew knowledge:\nT90 is ground\nT95 is ground\nreplacements:X213 -> T95" }, { "from": 2550, "to": 2552, "label": "CASE" }, { "from": 2551, "to": 2785, "label": "IS ERROR" }, { "from": 2551, "to": 2786, "label": "\nX214 -> T138" }, { "from": 2552, "to": 2553, "label": "PARALLEL" }, { "from": 2552, "to": 2554, "label": "PARALLEL" }, { "from": 2553, "to": 2555, "label": "ONLY EVAL with clause\nfib(X239, X240) :- ','(<(X239, 2), =(X240, 1)).\nand substitutionT90 -> T101,\nX239 -> -(-(-(-(-(-(T101, 1), 2), 2), 2), 2), 2),\nX213 -> X241,\nX240 -> X241" }, { "from": 2554, "to": 2564, "label": "ONLY EVAL with clause\nfib(X250, X251) :- ','(>=(X250, 2), ','(fib(-(X250, 1), X252), ','(fib(-(X250, 2), X253), is(X251, +(X252, X253))))).\nand substitutionT90 -> T104,\nX250 -> -(-(-(-(-(-(T104, 1), 2), 2), 2), 2), 2),\nX213 -> X254,\nX251 -> X254" }, { "from": 2555, "to": 2556, "label": "IS ERROR" }, { "from": 2555, "to": 2560, "label": "ARITHCOMP SUCCESS" }, { "from": 2555, "to": 2561, "label": "ARITHCOMP FAIL" }, { "from": 2560, "to": 2562, "label": "UNIFY SUCCESS with substitutionX241 -> 1" }, { "from": 2562, "to": 2563, "label": "SUCCESS" }, { "from": 2564, "to": 2565, "label": "IS ERROR" }, { "from": 2564, "to": 2610, "label": "ARITHCOMP SUCCESS" }, { "from": 2564, "to": 2611, "label": "ARITHCOMP FAIL" }, { "from": 2610, "to": 2612, "label": "SPLIT 1" }, { "from": 2610, "to": 2613, "label": "SPLIT 2\nnew knowledge:\nT104 is ground\nT106 is ground\nreplacements:X252 -> T106" }, { "from": 2612, "to": 2086, "label": "INSTANCE with matching:\nT23 -> -(-(-(-(-(-(T104, 1), 2), 2), 2), 2), 2)\nX19 -> X252" }, { "from": 2613, "to": 2687, "label": "SPLIT 1" }, { "from": 2613, "to": 2688, "label": "SPLIT 2\nnew knowledge:\nT104 is ground\nT109 is ground\nreplacements:X253 -> T109" }, { "from": 2687, "to": 2689, "label": "CASE" }, { "from": 2688, "to": 2782, "label": "IS ERROR" }, { "from": 2688, "to": 2783, "label": "\nX254 -> T137" }, { "from": 2689, "to": 2690, "label": "PARALLEL" }, { "from": 2689, "to": 2691, "label": "PARALLEL" }, { "from": 2690, "to": 2692, "label": "ONLY EVAL with clause\nfib(X279, X280) :- ','(<(X279, 2), =(X280, 1)).\nand substitutionT104 -> T115,\nX279 -> -(-(-(-(-(-(-(T115, 1), 2), 2), 2), 2), 2), 2),\nX253 -> X281,\nX280 -> X281" }, { "from": 2691, "to": 2717, "label": "ONLY EVAL with clause\nfib(X290, X291) :- ','(>=(X290, 2), ','(fib(-(X290, 1), X292), ','(fib(-(X290, 2), X293), is(X291, +(X292, X293))))).\nand substitutionT104 -> T118,\nX290 -> -(-(-(-(-(-(-(T118, 1), 2), 2), 2), 2), 2), 2),\nX253 -> X294,\nX291 -> X294" }, { "from": 2692, "to": 2693, "label": "IS ERROR" }, { "from": 2692, "to": 2713, "label": "ARITHCOMP SUCCESS" }, { "from": 2692, "to": 2714, "label": "ARITHCOMP FAIL" }, { "from": 2713, "to": 2715, "label": "UNIFY SUCCESS with substitutionX281 -> 1" }, { "from": 2715, "to": 2716, "label": "SUCCESS" }, { "from": 2717, "to": 2718, "label": "IS ERROR" }, { "from": 2717, "to": 2730, "label": "ARITHCOMP SUCCESS" }, { "from": 2717, "to": 2731, "label": "ARITHCOMP FAIL" }, { "from": 2730, "to": 2739, "label": "GENERALIZATION\nT120 <-- -(-(-(-(-(-(-(T118, 1), 2), 2), 2), 2), 2), 2)\n\nNew Knowledge:\nT120 is ground" }, { "from": 2739, "to": 2740, "label": "SPLIT 1" }, { "from": 2739, "to": 2741, "label": "SPLIT 2\nnew knowledge:\nT120 is ground\nT122 is ground\nreplacements:X292 -> T122" }, { "from": 2740, "to": 2086, "label": "INSTANCE with matching:\nT23 -> T120\nX19 -> X292" }, { "from": 2741, "to": 2750, "label": "SPLIT 1" }, { "from": 2741, "to": 2751, "label": "SPLIT 2\nnew knowledge:\nT120 is ground\nT125 is ground\nreplacements:X293 -> T125" }, { "from": 2750, "to": 2752, "label": "CASE" }, { "from": 2751, "to": 2779, "label": "IS ERROR" }, { "from": 2751, "to": 2780, "label": "\nX294 -> T136" }, { "from": 2752, "to": 2753, "label": "PARALLEL" }, { "from": 2752, "to": 2754, "label": "PARALLEL" }, { "from": 2753, "to": 2755, "label": "ONLY EVAL with clause\nfib(X322, X323) :- ','(<(X322, 2), =(X323, 1)).\nand substitutionT120 -> T131,\nX322 -> -(T131, 2),\nX293 -> X324,\nX323 -> X324" }, { "from": 2754, "to": 2767, "label": "ONLY EVAL with clause\nfib(X333, X334) :- ','(>=(X333, 2), ','(fib(-(X333, 1), X335), ','(fib(-(X333, 2), X336), is(X334, +(X335, X336))))).\nand substitutionT120 -> T134,\nX333 -> -(T134, 2),\nX293 -> X337,\nX334 -> X337" }, { "from": 2755, "to": 2756, "label": "IS ERROR" }, { "from": 2755, "to": 2763, "label": "ARITHCOMP SUCCESS" }, { "from": 2755, "to": 2764, "label": "ARITHCOMP FAIL" }, { "from": 2763, "to": 2765, "label": "UNIFY SUCCESS with substitutionX324 -> 1" }, { "from": 2765, "to": 2766, "label": "SUCCESS" }, { "from": 2767, "to": 2768, "label": "IS ERROR" }, { "from": 2767, "to": 2777, "label": "ARITHCOMP SUCCESS" }, { "from": 2767, "to": 2778, "label": "ARITHCOMP FAIL" }, { "from": 2777, "to": 2739, "label": "INSTANCE with matching:\nT120 -> -(T134, 2)\nX292 -> X335\nX293 -> X336\nX294 -> X337" }, { "from": 2780, "to": 2781, "label": "SUCCESS" }, { "from": 2783, "to": 2784, "label": "SUCCESS" }, { "from": 2786, "to": 2787, "label": "SUCCESS" }, { "from": 2789, "to": 2790, "label": "SUCCESS" }, { "from": 2792, "to": 2793, "label": "SUCCESS" }, { "from": 2795, "to": 2796, "label": "SUCCESS" }, { "from": 2798, "to": 2799, "label": "SUCCESS" }, { "from": 2801, "to": 2750, "label": "INSTANCE with matching:\nT120 -> T23\nX293 -> X20" }, { "from": 2802, "to": 2803, "label": "IS ERROR" }, { "from": 2802, "to": 2805, "label": "\nT22 -> T146" }, { "from": 2802, "to": 2806, "label": "IS FAIL" }, { "from": 2805, "to": 2808, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Rules: f2792_in(T64, T67, T140) -> f2792_out(T64, T67, T140) :|: TRUE f2086_out(T62 - 1 - 2 - 2) -> f2258_out(T62) :|: TRUE f2258_in(x) -> f2086_in(x - 1 - 2 - 2) :|: TRUE f2086_out(T48 - 1 - 2) -> f2216_out(T48) :|: TRUE f2216_in(x1) -> f2086_in(x1 - 1 - 2) :|: TRUE f2717_in(T118) -> f2718_in :|: TRUE f2717_in(x2) -> f2731_in(x2) :|: x2 - 1 - 2 - 2 - 2 - 2 - 2 - 2 < 2 f2730_out(x3) -> f2717_out(x3) :|: x3 - 1 - 2 - 2 - 2 - 2 - 2 - 2 >= 2 f2731_out(x4) -> f2717_out(x4) :|: x4 - 1 - 2 - 2 - 2 - 2 - 2 - 2 < 2 f2718_out -> f2717_out(x5) :|: TRUE f2717_in(x6) -> f2730_in(x6) :|: x6 - 1 - 2 - 2 - 2 - 2 - 2 - 2 >= 2 f2227_in(T50, T53) -> f2795_in(T53, T50, T141) :|: T141 = T50 + T53 f2794_out -> f2227_out(x7, x8) :|: TRUE f2795_out(x9, x10, x11) -> f2227_out(x10, x9) :|: TRUE f2227_in(x12, x13) -> f2794_in :|: TRUE f2551_out(T92, T95) -> f2549_out(T90, T92) :|: TRUE f2549_in(x14, x15) -> f2550_in(x14) :|: TRUE f2550_out(x16) -> f2551_in(x17, x18) :|: TRUE f2244_in(x19) -> f2257_in(x19) :|: x19 - 1 - 2 - 2 < 2 f2257_out(x20) -> f2244_out(x20) :|: x20 - 1 - 2 - 2 < 2 f2256_out(x21) -> f2244_out(x21) :|: x21 - 1 - 2 - 2 >= 2 f2244_in(x22) -> f2256_in(x22) :|: x22 - 1 - 2 - 2 >= 2 f2245_out -> f2244_out(x23) :|: TRUE f2244_in(x24) -> f2245_in :|: TRUE f2088_out(T23) -> f2086_out(T23) :|: TRUE f2086_in(x25) -> f2088_in(x25) :|: TRUE f2256_in(x26) -> f2258_in(x26) :|: TRUE f2259_out(x27, x28) -> f2256_out(x27) :|: TRUE f2258_out(x29) -> f2259_in(x29, x30) :|: TRUE f2798_in(T36, T142, T39) -> f2798_out(T36, T142, T39) :|: TRUE f2750_out(T120) -> f2751_in(T122, T125) :|: TRUE f2751_out(x31, x32) -> f2741_out(x33, x31) :|: TRUE f2741_in(x34, x35) -> f2750_in(x34) :|: TRUE f2226_out(x36) -> f2227_in(x37, x38) :|: TRUE f2217_in(x39, x40) -> f2226_in(x39) :|: TRUE f2227_out(x41, x42) -> f2217_out(x43, x41) :|: TRUE f2780_in(x44, x45, x46) -> f2780_out(x44, x45, x46) :|: TRUE f2259_in(x47, x48) -> f2264_in(x47) :|: TRUE f2264_out(x49) -> f2265_in(x50, x51) :|: TRUE f2265_out(x52, x53) -> f2259_out(x54, x52) :|: TRUE f2610_in(T104) -> f2612_in(T104) :|: TRUE f2613_out(x55, x56) -> f2610_out(x55) :|: TRUE f2612_out(x57) -> f2613_in(x57, x58) :|: TRUE f2086_out(T76 - 1 - 2 - 2 - 2) -> f2407_out(T76) :|: TRUE f2407_in(x59) -> f2086_in(x59 - 1 - 2 - 2 - 2) :|: TRUE f2777_in(T134) -> f2739_in(T134 - 2) :|: TRUE f2739_out(x60 - 2) -> f2777_out(x60) :|: TRUE f2442_in(T78, T81) -> f2789_in(T81, T78, T139) :|: T139 = T78 + T81 f2442_in(x61, x62) -> f2788_in :|: TRUE f2789_out(x63, x64, x65) -> f2442_out(x64, x63) :|: TRUE f2788_out -> f2442_out(x66, x67) :|: TRUE f2564_in(x68) -> f2565_in :|: TRUE f2565_out -> f2564_out(x69) :|: TRUE f2564_in(x70) -> f2611_in(x70) :|: x70 - 1 - 2 - 2 - 2 - 2 - 2 < 2 f2610_out(x71) -> f2564_out(x71) :|: x71 - 1 - 2 - 2 - 2 - 2 - 2 >= 2 f2611_out(x72) -> f2564_out(x72) :|: x72 - 1 - 2 - 2 - 2 - 2 - 2 < 2 f2564_in(x73) -> f2610_in(x73) :|: x73 - 1 - 2 - 2 - 2 - 2 - 2 >= 2 f2783_in(T137, T109, T106) -> f2783_out(T137, T109, T106) :|: TRUE f2292_in(x74) -> f2406_in(x74) :|: x74 - 1 - 2 - 2 - 2 < 2 f2293_out -> f2292_out(x75) :|: TRUE f2405_out(x76) -> f2292_out(x76) :|: x76 - 1 - 2 - 2 - 2 >= 2 f2292_in(x77) -> f2405_in(x77) :|: x77 - 1 - 2 - 2 - 2 >= 2 f2292_in(x78) -> f2293_in :|: TRUE f2406_out(x79) -> f2292_out(x79) :|: x79 - 1 - 2 - 2 - 2 < 2 f2612_in(x80) -> f2086_in(x80 - 1 - 2 - 2 - 2 - 2 - 2) :|: TRUE f2086_out(x81 - 1 - 2 - 2 - 2 - 2 - 2) -> f2612_out(x81) :|: TRUE f2687_in(x82) -> f2689_in(x82) :|: TRUE f2689_out(x83) -> f2687_out(x83) :|: TRUE f2214_in(x84) -> f2216_in(x84) :|: TRUE f2217_out(x85, x86) -> f2214_out(x85) :|: TRUE f2216_out(x87) -> f2217_in(x87, x88) :|: TRUE f2443_in(x89) -> f2490_in(x89) :|: TRUE f2490_out(x90) -> f2443_out(x90) :|: TRUE f2443_in(x91) -> f2491_in(x91) :|: TRUE f2491_out(x92) -> f2443_out(x92) :|: TRUE f2740_in(x93) -> f2086_in(x93) :|: TRUE f2086_out(x94) -> f2740_out(x94) :|: TRUE f2530_in(x95) -> f2544_in(x95) :|: x95 - 1 - 2 - 2 - 2 - 2 >= 2 f2531_out -> f2530_out(x96) :|: TRUE f2545_out(x97) -> f2530_out(x97) :|: x97 - 1 - 2 - 2 - 2 - 2 < 2 f2544_out(x98) -> f2530_out(x98) :|: x98 - 1 - 2 - 2 - 2 - 2 >= 2 f2530_in(x99) -> f2531_in :|: TRUE f2530_in(x100) -> f2545_in(x100) :|: x100 - 1 - 2 - 2 - 2 - 2 < 2 f2183_in(T34) -> f2184_in(T34) :|: TRUE f2184_out(x101) -> f2183_out(x101) :|: TRUE f2185_out(x102) -> f2183_out(x102) :|: TRUE f2183_in(x103) -> f2185_in(x103) :|: TRUE f2752_in(x104) -> f2753_in(x104) :|: TRUE f2754_out(x105) -> f2752_out(x105) :|: TRUE f2753_out(x106) -> f2752_out(x106) :|: TRUE f2752_in(x107) -> f2754_in(x107) :|: TRUE f2228_in(x108) -> f2229_in(x108) :|: TRUE f2229_out(x109) -> f2228_out(x109) :|: TRUE f2228_in(x110) -> f2230_in(x110) :|: TRUE f2230_out(x111) -> f2228_out(x111) :|: TRUE f2086_out(x112 - 1) -> f2169_out(x112) :|: TRUE f2169_in(x113) -> f2086_in(x113 - 1) :|: TRUE f2752_out(x114) -> f2750_out(x114) :|: TRUE f2750_in(x115) -> f2752_in(x115) :|: TRUE f2789_in(x116, x117, x118) -> f2789_out(x116, x117, x118) :|: TRUE f2754_in(x119) -> f2767_in(x119) :|: TRUE f2767_out(x120) -> f2754_out(x120) :|: TRUE f2689_in(x121) -> f2690_in(x121) :|: TRUE f2691_out(x122) -> f2689_out(x122) :|: TRUE f2689_in(x123) -> f2691_in(x123) :|: TRUE f2690_out(x124) -> f2689_out(x124) :|: TRUE f2551_in(x125, x126) -> f2786_in(x125, x127, x126) :|: x127 = x125 + x126 f2551_in(x128, x129) -> f2785_in :|: TRUE f2786_out(x130, x131, x132) -> f2551_out(x130, x132) :|: TRUE f2785_out -> f2551_out(x133, x134) :|: TRUE f2268_in(x135) -> f2292_in(x135) :|: TRUE f2292_out(x136) -> f2268_out(x136) :|: TRUE f2405_in(x137) -> f2407_in(x137) :|: TRUE f2408_out(x138, x139) -> f2405_out(x138) :|: TRUE f2407_out(x140) -> f2408_in(x140, x141) :|: TRUE f2150_in(x142) -> f2167_in(x142) :|: x142 - 1 >= 2 f2150_in(x143) -> f2168_in(x143) :|: x143 - 1 < 2 f2168_out(x144) -> f2150_out(x144) :|: x144 - 1 < 2 f2167_out(x145) -> f2150_out(x145) :|: x145 - 1 >= 2 f2170_out(x146, x147) -> f2167_out(x146) :|: TRUE f2167_in(x148) -> f2169_in(x148) :|: TRUE f2169_out(x149) -> f2170_in(x149, x150) :|: TRUE f2228_out(x151) -> f2226_out(x151) :|: TRUE f2226_in(x152) -> f2228_in(x152) :|: TRUE f2564_out(x153) -> f2554_out(x153) :|: TRUE f2554_in(x154) -> f2564_in(x154) :|: TRUE f2181_in(x155) -> f2183_in(x155) :|: TRUE f2183_out(x156) -> f2181_out(x156) :|: TRUE f2195_in(x157) -> f2214_in(x157) :|: x157 - 1 - 2 >= 2 f2215_out(x158) -> f2195_out(x158) :|: x158 - 1 - 2 < 2 f2195_in(x159) -> f2196_in :|: TRUE f2196_out -> f2195_out(x160) :|: TRUE f2195_in(x161) -> f2215_in(x161) :|: x161 - 1 - 2 < 2 f2214_out(x162) -> f2195_out(x162) :|: x162 - 1 - 2 >= 2 f2266_in(x163) -> f2268_in(x163) :|: TRUE f2266_in(x164) -> f2267_in(x164) :|: TRUE f2268_out(x165) -> f2266_out(x165) :|: TRUE f2267_out(x166) -> f2266_out(x166) :|: TRUE f2730_in(x167) -> f2739_in(x167 - 1 - 2 - 2 - 2 - 2 - 2 - 2) :|: TRUE f2739_out(x168 - 1 - 2 - 2 - 2 - 2 - 2 - 2) -> f2730_out(x168) :|: TRUE f2783_out(x169, x170, x171) -> f2688_out(x171, x170) :|: TRUE f2782_out -> f2688_out(x172, x173) :|: TRUE f2688_in(x174, x175) -> f2783_in(x176, x175, x174) :|: x176 = x174 + x175 f2688_in(x177, x178) -> f2782_in :|: TRUE f2443_out(x179) -> f2441_out(x179) :|: TRUE f2441_in(x180) -> f2443_in(x180) :|: TRUE f2441_out(x181) -> f2442_in(x182, x183) :|: TRUE f2408_in(x184, x185) -> f2441_in(x184) :|: TRUE f2442_out(x186, x187) -> f2408_out(x188, x186) :|: TRUE f2548_in(x189) -> f2086_in(x189 - 1 - 2 - 2 - 2 - 2) :|: TRUE f2086_out(x190 - 1 - 2 - 2 - 2 - 2) -> f2548_out(x190) :|: TRUE f2552_in(x191) -> f2553_in(x191) :|: TRUE f2553_out(x192) -> f2552_out(x192) :|: TRUE f2552_in(x193) -> f2554_in(x193) :|: TRUE f2554_out(x194) -> f2552_out(x194) :|: TRUE f2185_in(x195) -> f2195_in(x195) :|: TRUE f2195_out(x196) -> f2185_out(x196) :|: TRUE f2786_in(x197, x198, x199) -> f2786_out(x197, x198, x199) :|: TRUE f2230_in(x200) -> f2244_in(x200) :|: TRUE f2244_out(x201) -> f2230_out(x201) :|: TRUE f2777_out(x202) -> f2767_out(x202) :|: x202 - 2 >= 2 f2778_out(x203) -> f2767_out(x203) :|: x203 - 2 < 2 f2767_in(x204) -> f2777_in(x204) :|: x204 - 2 >= 2 f2767_in(x205) -> f2768_in :|: TRUE f2767_in(x206) -> f2778_in(x206) :|: x206 - 2 < 2 f2768_out -> f2767_out(x207) :|: TRUE f2550_in(x208) -> f2552_in(x208) :|: TRUE f2552_out(x209) -> f2550_out(x209) :|: TRUE f2264_in(x210) -> f2266_in(x210) :|: TRUE f2266_out(x211) -> f2264_out(x211) :|: TRUE f2544_in(x212) -> f2548_in(x212) :|: TRUE f2548_out(x213) -> f2549_in(x213, x214) :|: TRUE f2549_out(x215, x216) -> f2544_out(x215) :|: TRUE f2795_in(x217, x218, x219) -> f2795_out(x217, x218, x219) :|: TRUE f2751_in(x220, x221) -> f2779_in :|: TRUE f2780_out(x222, x223, x224) -> f2751_out(x224, x222) :|: TRUE f2779_out -> f2751_out(x225, x226) :|: TRUE f2751_in(x227, x228) -> f2780_in(x228, x229, x227) :|: x229 = x227 + x228 f2691_in(x230) -> f2717_in(x230) :|: TRUE f2717_out(x231) -> f2691_out(x231) :|: TRUE f2791_out -> f2265_out(x232, x233) :|: TRUE f2265_in(x234, x235) -> f2791_in :|: TRUE f2265_in(x236, x237) -> f2792_in(x236, x237, x238) :|: x238 = x236 + x237 f2792_out(x239, x240, x241) -> f2265_out(x239, x240) :|: TRUE f2491_in(x242) -> f2530_in(x242) :|: TRUE f2530_out(x243) -> f2491_out(x243) :|: TRUE f2613_in(x244, x245) -> f2687_in(x244) :|: TRUE f2687_out(x246) -> f2688_in(x247, x248) :|: TRUE f2688_out(x249, x250) -> f2613_out(x251, x249) :|: TRUE f2182_out(x252, x253) -> f2170_out(x254, x252) :|: TRUE f2181_out(x255) -> f2182_in(x256, x257) :|: TRUE f2170_in(x258, x259) -> f2181_in(x258) :|: TRUE f2093_in(x260) -> f2150_in(x260) :|: TRUE f2150_out(x261) -> f2093_out(x261) :|: TRUE f2182_in(x262, x263) -> f2797_in :|: TRUE f2182_in(x264, x265) -> f2798_in(x264, x266, x265) :|: x266 = x264 + x265 f2798_out(x267, x268, x269) -> f2182_out(x267, x269) :|: TRUE f2797_out -> f2182_out(x270, x271) :|: TRUE f2739_in(x272) -> f2740_in(x272) :|: TRUE f2740_out(x273) -> f2741_in(x273, x274) :|: TRUE f2741_out(x275, x276) -> f2739_out(x275) :|: TRUE f2088_in(x277) -> f2092_in(x277) :|: TRUE f2093_out(x278) -> f2088_out(x278) :|: TRUE f2088_in(x279) -> f2093_in(x279) :|: TRUE f2092_out(x280) -> f2088_out(x280) :|: TRUE f6_out(T2) -> f3_out(T2) :|: TRUE f3_in(x281) -> f6_in(x281) :|: TRUE f6_in(x282) -> f8_in(x282) :|: TRUE f6_in(x283) -> f9_in(x283) :|: TRUE f8_out(x284) -> f6_out(x284) :|: TRUE f9_out(x285) -> f6_out(x285) :|: TRUE f2075_out(T22) -> f9_out(T22) :|: TRUE f9_in(x286) -> f2075_in(x286) :|: TRUE f2076_out -> f2075_out(x287) :|: TRUE f2075_in(x288) -> f2084_in(x289, x288) :|: x289 >= 2 f2084_out(x290, x291) -> f2075_out(x291) :|: x290 >= 2 f2085_out(x292, x293) -> f2075_out(x293) :|: x292 < 2 f2075_in(x294) -> f2076_in :|: TRUE f2075_in(x295) -> f2085_in(x296, x295) :|: x296 < 2 f2084_in(x297, x298) -> f2086_in(x297) :|: TRUE f2086_out(x299) -> f2087_in(x299, x300, x301) :|: TRUE f2087_out(x302, x303, x304) -> f2084_out(x302, x303) :|: TRUE f2801_out(x305) -> f2802_in(x306, x307, x308) :|: TRUE f2802_out(x309, x310, x311) -> f2087_out(x312, x309, x310) :|: TRUE f2087_in(x313, x314, x315) -> f2801_in(x313) :|: TRUE f2750_out(x316) -> f2801_out(x316) :|: TRUE f2801_in(x317) -> f2750_in(x317) :|: TRUE Start term: f3_in(T2) ---------------------------------------- (3) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f2086_in(x25) -> f2088_in(x25) :|: TRUE f2169_in(x113) -> f2086_in(x113 - 1) :|: TRUE f2150_in(x142) -> f2167_in(x142) :|: x142 - 1 >= 2 f2167_in(x148) -> f2169_in(x148) :|: TRUE f2093_in(x260) -> f2150_in(x260) :|: TRUE f2088_in(x279) -> f2093_in(x279) :|: TRUE ---------------------------------------- (4) Obligation: Rules: f2086_in(x25) -> f2088_in(x25) :|: TRUE f2169_in(x113) -> f2086_in(x113 - 1) :|: TRUE f2150_in(x142) -> f2167_in(x142) :|: x142 - 1 >= 2 f2167_in(x148) -> f2169_in(x148) :|: TRUE f2093_in(x260) -> f2150_in(x260) :|: TRUE f2088_in(x279) -> f2093_in(x279) :|: TRUE ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f2093_in(x260:0) -> f2093_in(x260:0 - 1) :|: x260:0 > 2 ---------------------------------------- (7) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (8) Obligation: Rules: f2093_in(x260:0) -> f2093_in(arith) :|: x260:0 > 2 && arith = x260:0 - 1 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f2093_in(x260:0) -> f2093_in(arith) :|: x260:0 > 2 && arith = x260:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) f2093_in(x260:0) -> f2093_in(arith) :|: x260:0 > 2 && arith = x260:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f2093_in(x260:0:0) -> f2093_in(x260:0:0 - 1) :|: x260:0:0 > 2 ---------------------------------------- (13) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f2093_in(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (14) Obligation: Rules: f2093_in(x260:0:0) -> f2093_in(c) :|: c = x260:0:0 - 1 && x260:0:0 > 2 ---------------------------------------- (15) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f2093_in(x)] = x The following rules are decreasing: f2093_in(x260:0:0) -> f2093_in(c) :|: c = x260:0:0 - 1 && x260:0:0 > 2 The following rules are bounded: f2093_in(x260:0:0) -> f2093_in(c) :|: c = x260:0:0 - 1 && x260:0:0 > 2 ---------------------------------------- (16) YES