/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern test_fun(g,g,g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 77 ms] (2) IRSwT (3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 35 ms] (6) IRSwT (7) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 56 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IRSwTToIntTRSProof [SOUND, 6 ms] (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TerminationGraphProcessor [EQUIVALENT, 13 ms] (20) IntTRS (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IntTRS (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Clauses: test_fun(I, J, K, Tmp) :- loop(I, J, K, Tmp, 0). loop(I, J, K, Tmp, C) :- ','(=<(I, 100), ','(=<(J, K), ','(is(Tmp1, I), ','(is(I1, J), ','(is(J1, +(Tmp, 1)), ','(is(K1, -(K, 1)), ','(is(C1, +(C, 1)), loop(I1, J1, K1, Tmp1, C1)))))))). loop(I, J, K, Tmp, C) :- >(I, 100). loop(I, J, K, Tmp, C) :- >(J, K). Query: test_fun(g,g,g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 1, "program": { "directives": [], "clauses": [ [ "(test_fun I J K Tmp)", "(loop I J K Tmp (0))" ], [ "(loop I J K Tmp C)", "(',' (=< I (100)) (',' (=< J K) (',' (is Tmp1 I) (',' (is I1 J) (',' (is J1 (+ Tmp (1))) (',' (is K1 (- K (1))) (',' (is C1 (+ C (1))) (loop I1 J1 K1 Tmp1 C1))))))))" ], [ "(loop I J K Tmp C)", "(> I (100))" ], [ "(loop I J K Tmp C)", "(> J K)" ] ] }, "graph": { "nodes": { "4210": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X69 T42) (',' (is X70 (+ T44 (1))) (',' (is X71 (- T43 (1))) (',' (is X72 (+ (0) (1))) (loop X69 X70 X71 T45 X72)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "=" }, { "lhs": { "name": "T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "100" }, "operation": "<=" }, { "lhs": { "name": "T42", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T43", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T42", "T41", "T45", "T44", "T43" ], "free": [ "X68", "X69", "X70", "X71", "X72" ], "exprvars": [ "T42", "T41", "T45", "T43" ] } }, "4211": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X70 (+ T44 (1))) (',' (is X71 (- T43 (1))) (',' (is X72 (+ (0) (1))) (loop T46 X70 X71 T45 X72))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "=" }, { "lhs": { "name": "T46", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "=" 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"lhs": { "name": "T48", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T43", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "name": "T49", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": "=" }, { "lhs": { "name": "T42", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T44", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T44", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T43", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T43", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "-" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "100" }, "type": "PlainIntegerRelation", "rhs": { "name": "T110", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T41", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "100" }, "operation": "<=" }, { "lhs": { "name": "T42", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T43", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "100" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "100" }, "operation": "<=" }, { "lhs": { "name": "T43", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T43", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": ["T110"], "free": [], "exprvars": [ "T42", "T47", "T114", "T111", "T44", "T49", "T113", "T41", "T46", "T110", "T45", "T112", "T43", "T48" ] } } }, "edges": [ { "from": 1, "to": 4, "label": "CASE" }, { "from": 4, "to": 9, "label": "ONLY EVAL with clause\ntest_fun(X19, X20, X21, X22) :- loop(X19, X20, X21, X22, 0).\nand substitutionT1 -> T17,\nX19 -> T17,\nT2 -> T18,\nX20 -> T18,\nT3 -> T19,\nX21 -> T19,\nT4 -> T20,\nX22 -> T20" }, { "from": 9, "to": 12, "label": "CASE" }, { "from": 12, "to": 21, "label": "PARALLEL" }, { "from": 12, "to": 22, "label": "PARALLEL" }, { "from": 21, "to": 23, "label": "ONLY EVAL with clause\nloop(X63, X64, X65, X66, X67) :- ','(=<(X63, 100), ','(=<(X64, X65), ','(is(X68, X63), ','(is(X69, X64), ','(is(X70, +(X66, 1)), ','(is(X71, -(X65, 1)), ','(is(X72, +(X67, 1)), loop(X69, X70, X71, X68, X72)))))))).\nand substitutionT17 -> T41,\nX63 -> T41,\nT18 -> T42,\nX64 -> T42,\nT19 -> T43,\nX65 -> T43,\nT20 -> T44,\nX66 -> T44,\nX67 -> 0" }, { "from": 22, "to": 4534, "label": "PARALLEL" }, { "from": 22, "to": 4535, "label": "PARALLEL" }, { "from": 23, "to": 24, "label": "IS ERROR" }, { "from": 23, "to": 3833, "label": "ARITHCOMP SUCCESS" }, { "from": 23, "to": 3834, "label": "ARITHCOMP FAIL" }, { "from": 3833, "to": 3835, "label": "IS ERROR" }, { "from": 3833, "to": 4066, "label": "ARITHCOMP SUCCESS" }, { "from": 3833, "to": 4067, "label": "ARITHCOMP FAIL" }, { "from": 4066, "to": 4210, "label": "\nX68 -> T45" }, { "from": 4210, "to": 4211, "label": "\nX69 -> T46" }, { "from": 4211, "to": 4212, "label": "IS ERROR" }, { "from": 4211, "to": 4215, "label": "\nX70 -> T47" }, { "from": 4215, "to": 4216, "label": "\nX71 -> T48" }, { "from": 4216, "to": 4217, "label": "\nX72 -> T49" }, { "from": 4217, "to": 4218, "label": "CASE" }, { "from": 4218, "to": 4219, "label": "PARALLEL" }, { "from": 4218, "to": 4220, "label": "PARALLEL" }, { "from": 4219, "to": 4382, "label": "ONLY EVAL with clause\nloop(X113, X114, X115, X116, X117) :- ','(=<(X113, 100), ','(=<(X114, X115), ','(is(X118, X113), ','(is(X119, X114), ','(is(X120, +(X116, 1)), ','(is(X121, -(X115, 1)), ','(is(X122, +(X117, 1)), loop(X119, X120, X121, X118, X122)))))))).\nand substitutionT46 -> T75,\nX113 -> T75,\nT47 -> T76,\nX114 -> T76,\nT48 -> T77,\nX115 -> T77,\nT45 -> T78,\nX116 -> T78,\nT49 -> T79,\nX117 -> T79" }, { "from": 4220, "to": 4497, "label": "PARALLEL" }, { "from": 4220, "to": 4498, "label": "PARALLEL" }, { "from": 4382, "to": 4385, "label": "ARITHCOMP SUCCESS" }, { "from": 4382, "to": 4386, "label": "ARITHCOMP FAIL" }, { "from": 4385, "to": 4425, "label": "ARITHCOMP SUCCESS" }, { "from": 4385, "to": 4426, "label": "ARITHCOMP FAIL" }, { "from": 4425, "to": 4443, "label": "\nX118 -> T80" }, { "from": 4443, "to": 4444, "label": "\nX119 -> T81" }, { "from": 4444, "to": 4445, "label": "\nX120 -> T82" }, { "from": 4445, "to": 4446, "label": "\nX121 -> T83" }, { "from": 4446, "to": 4447, "label": "\nX122 -> T84" }, { "from": 4447, "to": 4217, "label": "INSTANCE with matching:\nT46 -> T81\nT47 -> T82\nT48 -> T83\nT45 -> T80\nT49 -> T84\nX68 -> X118\nX69 -> X119\nX70 -> X120\nX71 -> X121\nX72 -> X122" }, { "from": 4497, "to": 4502, "label": "ONLY EVAL with clause\nloop(X153, X154, X155, X156, X157) :- >(X153, 100).\nand substitutionT46 -> T110,\nX153 -> T110,\nT47 -> T111,\nX154 -> T111,\nT48 -> T112,\nX155 -> T112,\nT45 -> T113,\nX156 -> T113,\nT49 -> T114,\nX157 -> T114" }, { "from": 4498, "to": 4522, "label": "ONLY EVAL with clause\nloop(X168, X169, X170, X171, X172) :- >(X169, X170).\nand substitutionT46 -> T125,\nX168 -> T125,\nT47 -> T126,\nX169 -> T126,\nT48 -> T127,\nX170 -> T127,\nT45 -> T128,\nX171 -> T128,\nT49 -> T129,\nX172 -> T129" }, { "from": 4502, "to": 4519, "label": "ARITHCOMP SUCCESS" }, { "from": 4502, "to": 4520, "label": "ARITHCOMP FAIL" }, { "from": 4519, "to": 4521, "label": "SUCCESS" }, { "from": 4522, "to": 4531, "label": "ARITHCOMP SUCCESS" }, { "from": 4522, "to": 4532, "label": "ARITHCOMP FAIL" }, { "from": 4531, "to": 4533, "label": "SUCCESS" }, { "from": 4534, "to": 4536, "label": "ONLY EVAL with clause\nloop(X193, X194, X195, X196, X197) :- >(X193, 100).\nand substitutionT17 -> T146,\nX193 -> T146,\nT18 -> T147,\nX194 -> T147,\nT19 -> T148,\nX195 -> T148,\nT20 -> T149,\nX196 -> T149,\nX197 -> 0" }, { "from": 4535, "to": 4544, "label": "ONLY EVAL with clause\nloop(X208, X209, X210, X211, X212) :- >(X209, X210).\nand substitutionT17 -> T158,\nX208 -> T158,\nT18 -> T159,\nX209 -> T159,\nT19 -> T160,\nX210 -> T160,\nT20 -> T161,\nX211 -> T161,\nX212 -> 0" }, { "from": 4536, "to": 4537, "label": "IS ERROR" }, { "from": 4536, "to": 4541, "label": "ARITHCOMP SUCCESS" }, { "from": 4536, "to": 4542, "label": "ARITHCOMP FAIL" }, { "from": 4541, "to": 4543, "label": "SUCCESS" }, { "from": 4544, "to": 4545, "label": "IS ERROR" }, { "from": 4544, "to": 4549, "label": "ARITHCOMP SUCCESS" }, { "from": 4544, "to": 4550, "label": "ARITHCOMP FAIL" }, { "from": 4549, "to": 4551, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Rules: f4443_out(T76, T78, T77, T79, T80, T75) -> f4425_out(T75, T76, T78, T77, T79) :|: TRUE f4425_in(x, x1, x2, x3, x4) -> f4443_in(x1, x2, x3, x4, x5, x) :|: x5 = x f4385_in(x6, x7, x8, x9, x10) -> f4426_in(x8, x10, x9, x7, x6) :|: x6 > x7 f4425_out(x11, x12, x13, x14, x15) -> f4385_out(x12, x14, x11, x13, x15) :|: x12 <= x14 f4426_out(x16, x17, x18, x19, x20) -> f4385_out(x20, x19, x16, x18, x17) :|: x20 > x19 f4385_in(x21, x22, x23, x24, x25) -> f4425_in(x23, x21, x24, x22, x25) :|: x21 <= x22 f4447_out(x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> f4446_out(x32, x26, x27, x28, x29, x31, x33, x34, x35) :|: TRUE f4446_in(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> f4447_in(x37, x38, x39, x40, x45, x41, x36, x42, x43, x44) :|: x45 = x36 + 1 f4217_out(x46, x47, x48, x49, x50, x51, x52, x53, x54) -> f4447_out(x46, x47, x48, x49, x50, x55, x56, x57, x58, x59) :|: TRUE f4447_in(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> f4217_in(x60, x61, x62, x63, x64, x70, x71, x72, x73) :|: TRUE f4219_out(T46, T47, T48, T45, T49) -> f4218_out(T46, T47, T48, T45, T49) :|: TRUE f4218_in(x74, x75, x76, x77, x78) -> f4220_in(x74, x75, x76, x77, x78) :|: TRUE f4220_out(x79, x80, x81, x82, x83) -> f4218_out(x79, x80, x81, x82, x83) :|: TRUE f4218_in(x84, x85, x86, x87, x88) -> f4219_in(x84, x85, x86, x87, x88) :|: TRUE f4385_out(x89, x90, x91, x92, x93) -> f4382_out(x91, x89, x90, x92, x93) :|: x91 <= 100 f4382_in(x94, x95, x96, x97, x98) -> f4386_in(x94, x98, x97, x96, x95) :|: x94 > 100 f4386_out(x99, x100, x101, x102, x103) -> f4382_out(x99, x103, x102, x101, x100) :|: x99 > 100 f4382_in(x104, x105, x106, x107, x108) -> f4385_in(x105, x106, x104, x107, x108) :|: x104 <= 100 f4444_in(x109, x110, x111, x112, x113, x114, x115) -> f4445_in(x110, x111, x112, x116, x113, x114, x109, x115) :|: x116 = x109 + 1 f4445_out(x117, x118, x119, x120, x121, x122, x123, x124) -> f4444_out(x123, x117, x118, x119, x121, x122, x124) :|: TRUE f4445_in(x125, x126, x127, x128, x129, x130, x131, x132) -> f4446_in(x126, x127, x128, x133, x129, x130, x131, x125, x132) :|: x133 = x125 - 1 f4446_out(x134, x135, x136, x137, x138, x139, x140, x141, x142) -> f4445_out(x141, x134, x135, x136, x138, x139, x140, x142) :|: TRUE f4217_in(x143, x144, x145, x146, x147, x148, x149, x150, x151) -> f4218_in(x143, x144, x145, x146, x147) :|: TRUE f4218_out(x152, x153, x154, x155, x156) -> f4217_out(x152, x153, x154, x155, x156, x157, x158, x159, x160) :|: TRUE f4219_in(x161, x162, x163, x164, x165) -> f4382_in(x161, x162, x163, x164, x165) :|: TRUE f4382_out(x166, x167, x168, x169, x170) -> f4219_out(x166, x167, x168, x169, x170) :|: TRUE f4443_in(x171, x172, x173, x174, x175, x176) -> f4444_in(x172, x173, x174, x177, x175, x176, x171) :|: x177 = x171 f4444_out(x178, x179, x180, x181, x182, x183, x184) -> f4443_out(x184, x178, x179, x180, x182, x183) :|: TRUE f1_in(T1, T2, T3, T4) -> f4_in(T1, T2, T3, T4) :|: TRUE f4_out(x185, x186, x187, x188) -> f1_out(x185, x186, x187, x188) :|: TRUE f9_out(T17, T18, T19, T20) -> f4_out(T17, T18, T19, T20) :|: TRUE f4_in(x189, x190, x191, x192) -> f9_in(x189, x190, x191, x192) :|: TRUE f9_in(x193, x194, x195, x196) -> f12_in(x193, x194, x195, x196) :|: TRUE f12_out(x197, x198, x199, x200) -> f9_out(x197, x198, x199, x200) :|: TRUE f22_out(x201, x202, x203, x204) -> f12_out(x201, x202, x203, x204) :|: TRUE f21_out(x205, x206, x207, x208) -> f12_out(x205, x206, x207, x208) :|: TRUE f12_in(x209, x210, x211, x212) -> f22_in(x209, x210, x211, x212) :|: TRUE f12_in(x213, x214, x215, x216) -> f21_in(x213, x214, x215, x216) :|: TRUE f23_out(T41, T42, T43, T44) -> f21_out(T41, T42, T43, T44) :|: TRUE f21_in(x217, x218, x219, x220) -> f23_in(x217, x218, x219, x220) :|: TRUE f23_in(x221, x222, x223, x224) -> f3833_in(x222, x223, x221, x224) :|: x221 <= 100 f23_in(x225, x226, x227, x228) -> f24_in :|: TRUE f3833_out(x229, x230, x231, x232) -> f23_out(x231, x229, x230, x232) :|: x231 <= 100 f23_in(x233, x234, x235, x236) -> f3834_in(x234, x233, x236, x235) :|: x233 > 100 f3834_out(x237, x238, x239, x240) -> f23_out(x238, x237, x240, x239) :|: x238 > 100 f24_out -> f23_out(x241, x242, x243, x244) :|: TRUE f4066_out(x245, x246, x247, x248) -> f3833_out(x246, x248, x245, x247) :|: x246 <= x248 f3833_in(x249, x250, x251, x252) -> f3835_in :|: TRUE f3835_out -> f3833_out(x253, x254, x255, x256) :|: TRUE f3833_in(x257, x258, x259, x260) -> f4066_in(x259, x257, x260, x258) :|: x257 <= x258 f4067_out(x261, x262, x263, x264) -> f3833_out(x261, x264, x262, x263) :|: x261 > x264 f3833_in(x265, x266, x267, x268) -> f4067_in(x265, x267, x268, x266) :|: x265 > x266 f4210_out(x269, x270, x271, x272, x273) -> f4066_out(x273, x269, x270, x271) :|: TRUE f4066_in(x274, x275, x276, x277) -> f4210_in(x275, x276, x277, x278, x274) :|: x278 = x274 f4210_in(x279, x280, x281, x282, x283) -> f4211_in(x280, x281, x284, x282, x279, x283) :|: x284 = x279 f4211_out(x285, x286, x287, x288, x289, x290) -> f4210_out(x289, x285, x286, x288, x290) :|: TRUE f4211_in(x291, x292, x293, x294, x295, x296) -> f4215_in(x292, x293, x297, x294, x295, x296, x291) :|: x297 = x291 + 1 f4215_out(x298, x299, x300, x301, x302, x303, x304) -> f4211_out(x304, x298, x299, x301, x302, x303) :|: TRUE f4211_in(x305, x306, x307, x308, x309, x310) -> f4212_in :|: TRUE f4212_out -> f4211_out(x311, x312, x313, x314, x315, x316) :|: TRUE f4216_out(x317, x318, x319, x320, x321, x322, x323, x324) -> f4215_out(x324, x317, x318, x320, x321, x322, x323) :|: TRUE f4215_in(x325, x326, x327, x328, x329, x330, x331) -> f4216_in(x326, x327, x332, x328, x329, x330, x331, x325) :|: x332 = x325 - 1 f4216_in(x333, x334, x335, x336, x337, x338, x339, x340) -> f4217_in(x333, x334, x335, x336, x341, x337, x338, x339, x340) :|: x341 = 0 + 1 f4217_out(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> f4216_out(x342, x343, x344, x345, x347, x348, x349, x350) :|: TRUE Start term: f1_in(T1, T2, T3, T4) ---------------------------------------- (3) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f4425_in(x, x1, x2, x3, x4) -> f4443_in(x1, x2, x3, x4, x5, x) :|: x5 = x f4385_in(x21, x22, x23, x24, x25) -> f4425_in(x23, x21, x24, x22, x25) :|: x21 <= x22 f4446_in(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> f4447_in(x37, x38, x39, x40, x45, x41, x36, x42, x43, x44) :|: x45 = x36 + 1 f4447_in(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> f4217_in(x60, x61, x62, x63, x64, x70, x71, x72, x73) :|: TRUE f4218_in(x84, x85, x86, x87, x88) -> f4219_in(x84, x85, x86, x87, x88) :|: TRUE f4382_in(x104, x105, x106, x107, x108) -> f4385_in(x105, x106, x104, x107, x108) :|: x104 <= 100 f4444_in(x109, x110, x111, x112, x113, x114, x115) -> f4445_in(x110, x111, x112, x116, x113, x114, x109, x115) :|: x116 = x109 + 1 f4445_in(x125, x126, x127, x128, x129, x130, x131, x132) -> f4446_in(x126, x127, x128, x133, x129, x130, x131, x125, x132) :|: x133 = x125 - 1 f4217_in(x143, x144, x145, x146, x147, x148, x149, x150, x151) -> f4218_in(x143, x144, x145, x146, x147) :|: TRUE f4219_in(x161, x162, x163, x164, x165) -> f4382_in(x161, x162, x163, x164, x165) :|: TRUE f4443_in(x171, x172, x173, x174, x175, x176) -> f4444_in(x172, x173, x174, x177, x175, x176, x171) :|: x177 = x171 ---------------------------------------- (4) Obligation: Rules: f4425_in(x, x1, x2, x3, x4) -> f4443_in(x1, x2, x3, x4, x5, x) :|: x5 = x f4385_in(x21, x22, x23, x24, x25) -> f4425_in(x23, x21, x24, x22, x25) :|: x21 <= x22 f4446_in(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> f4447_in(x37, x38, x39, x40, x45, x41, x36, x42, x43, x44) :|: x45 = x36 + 1 f4447_in(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> f4217_in(x60, x61, x62, x63, x64, x70, x71, x72, x73) :|: TRUE f4218_in(x84, x85, x86, x87, x88) -> f4219_in(x84, x85, x86, x87, x88) :|: TRUE f4382_in(x104, x105, x106, x107, x108) -> f4385_in(x105, x106, x104, x107, x108) :|: x104 <= 100 f4444_in(x109, x110, x111, x112, x113, x114, x115) -> f4445_in(x110, x111, x112, x116, x113, x114, x109, x115) :|: x116 = x109 + 1 f4445_in(x125, x126, x127, x128, x129, x130, x131, x132) -> f4446_in(x126, x127, x128, x133, x129, x130, x131, x125, x132) :|: x133 = x125 - 1 f4217_in(x143, x144, x145, x146, x147, x148, x149, x150, x151) -> f4218_in(x143, x144, x145, x146, x147) :|: TRUE f4219_in(x161, x162, x163, x164, x165) -> f4382_in(x161, x162, x163, x164, x165) :|: TRUE f4443_in(x171, x172, x173, x174, x175, x176) -> f4444_in(x172, x173, x174, x177, x175, x176, x171) :|: x177 = x171 ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f4444_in(x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f4444_in(x113:0, x110:0 - 1, x111:0 + 1, x109:0 + 1, x112:0, x112:0, x109:0 + 1) :|: x112:0 < 101 && x110:0 - 1 >= x109:0 + 1 ---------------------------------------- (7) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (8) Obligation: Rules: f4444_in(x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f4444_in(x113:0, arith, arith1, arith2, x112:0, x112:0, arith2) :|: x112:0 < 101 && x110:0 - 1 >= x109:0 + 1 && arith = x110:0 - 1 && arith1 = x111:0 + 1 && arith2 = x109:0 + 1 && arith2 = x109:0 + 1 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f4444_in(x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f4444_in(x113:0, arith, arith1, arith2, x112:0, x112:0, arith2) :|: x112:0 < 101 && x110:0 - 1 >= x109:0 + 1 && arith = x110:0 - 1 && arith1 = x111:0 + 1 && arith2 = x109:0 + 1 && arith2 = x109:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) f4444_in(x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0) -> f4444_in(x113:0, arith, arith1, arith2, x112:0, x112:0, arith2) :|: x112:0 < 101 && x110:0 - 1 >= x109:0 + 1 && arith = x110:0 - 1 && arith1 = x111:0 + 1 && arith2 = x109:0 + 1 && arith2 = x109:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f4444_in(x109:0:0, x110:0:0, x111:0:0, x112:0:0, x113:0:0, x114:0:0, x115:0:0) -> f4444_in(x113:0:0, x110:0:0 - 1, x111:0:0 + 1, x109:0:0 + 1, x112:0:0, x112:0:0, x109:0:0 + 1) :|: x112:0:0 < 101 && x110:0:0 - 1 >= x109:0:0 + 1 ---------------------------------------- (13) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f4444_in(x1, x2, x3, x4, x5, x6, x7) -> f4444_in(x1, x2, x4, x5) ---------------------------------------- (14) Obligation: Rules: f4444_in(x109:0:0, x110:0:0, x112:0:0, x113:0:0) -> f4444_in(x113:0:0, x110:0:0 - 1, x109:0:0 + 1, x112:0:0) :|: x112:0:0 < 101 && x110:0:0 - 1 >= x109:0:0 + 1 ---------------------------------------- (15) IRSwTToIntTRSProof (SOUND) Applied path-length measure to transform intTRS with terms to intTRS. ---------------------------------------- (16) Obligation: Rules: f4444_in(x, x1, x2, x3) -> f4444_in(x3, x1 - 1, x + 1, x2) :|: x2 < 101 && x1 - 1 >= x + 1 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f4444_in(x:0, x1:0, x2:0, x3:0) -> f4444_in(x3:0, x1:0 - 1, x:0 + 1, x2:0) :|: x2:0 < 101 && x:0 + 1 <= x1:0 - 1 ---------------------------------------- (19) TerminationGraphProcessor (EQUIVALENT) Constructed the termination graph and obtained one non-trivial SCC. f4444_in(x:0, x1:0, x2:0, x3:0) -> f4444_in(x3:0, x1:0 - 1, x:0 + 1, x2:0) :|: x2:0 < 101 && x:0 + 1 <= x1:0 - 1 has been transformed into f4444_in(x:0, x1:0, x2:0, x3:0) -> f4444_in(x3:0, x1:0 - 1, x:0 + 1, x2:0) :|: x3:0 = x10 && (x2:0 = x8 + 1 && (x1:0 = x9 - 1 && (x2:0 < 101 && x:0 + 1 <= x1:0 - 1))) && x10 < 101 && x8 + 1 <= x9 - 1. f4444_in(x:0, x1:0, x2:0, x3:0) -> f4444_in(x3:0, x1:0 - 1, x:0 + 1, x2:0) :|: x3:0 = x10 && (x2:0 = x8 + 1 && (x1:0 = x9 - 1 && (x2:0 < 101 && x:0 + 1 <= x1:0 - 1))) && x10 < 101 && x8 + 1 <= x9 - 1 and f4444_in(x:0, x1:0, x2:0, x3:0) -> f4444_in(x3:0, x1:0 - 1, x:0 + 1, x2:0) :|: x3:0 = x10 && (x2:0 = x8 + 1 && (x1:0 = x9 - 1 && (x2:0 < 101 && x:0 + 1 <= x1:0 - 1))) && x10 < 101 && x8 + 1 <= x9 - 1 have been merged into the new rule f4444_in(x26, x27, x28, x29) -> f4444_in(x28, x27 - 1 - 1, x29 + 1, x26 + 1) :|: x29 = x30 && (x28 = x31 + 1 && (x27 = x32 - 1 && (x28 < 101 && x26 + 1 <= x27 - 1))) && x30 < 101 && x31 + 1 <= x32 - 1 && (x28 = x33 && (x26 + 1 = x34 + 1 && (x27 - 1 = x35 - 1 && (x26 + 1 < 101 && x29 + 1 <= x27 - 1 - 1))) && x33 < 101 && x34 + 1 <= x35 - 1) ---------------------------------------- (20) Obligation: Rules: f4444_in(x36, x37, x38, x39) -> f4444_in(x38, x37 + -2, x39 + 1, x36 + 1) :|: TRUE && x39 + -1 * x40 = 0 && x38 + -1 * x41 = 1 && x37 + -1 * x42 = -1 && x38 <= 100 && x36 + -1 * x37 <= -2 && x40 <= 100 && x41 + -1 * x42 <= -2 && x38 + -1 * x43 = 0 && x36 + -1 * x44 = 0 && x37 + -1 * x45 = 0 && x36 <= 99 && x39 + -1 * x37 <= -3 && x43 <= 100 && x44 + -1 * x45 <= -2 ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f4444_in(x36:0, x37:0, x38:0, x39:0) -> f4444_in(x38:0, x37:0 - 2, x39:0 + 1, x36:0 + 1) :|: x43:0 < 101 && x44:0 + -1 * x45:0 <= -2 && x39:0 + -1 * x37:0 <= -3 && x36:0 < 100 && x37:0 + -1 * x45:0 = 0 && x36:0 + -1 * x44:0 = 0 && x38:0 + -1 * x43:0 = 0 && x41:0 + -1 * x42:0 <= -2 && x40:0 < 101 && x36:0 + -1 * x37:0 <= -2 && x38:0 < 101 && x37:0 + -1 * x42:0 = -1 && x39:0 + -1 * x40:0 = 0 && x38:0 + -1 * x41:0 = 1 ---------------------------------------- (23) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f4444_in(x, x1, x2, x3)] = 95 - x + 2*x1 - x2 - x3 The following rules are decreasing: f4444_in(x36:0, x37:0, x38:0, x39:0) -> f4444_in(x38:0, x37:0 - 2, x39:0 + 1, x36:0 + 1) :|: x43:0 < 101 && x44:0 + -1 * x45:0 <= -2 && x39:0 + -1 * x37:0 <= -3 && x36:0 < 100 && x37:0 + -1 * x45:0 = 0 && x36:0 + -1 * x44:0 = 0 && x38:0 + -1 * x43:0 = 0 && x41:0 + -1 * x42:0 <= -2 && x40:0 < 101 && x36:0 + -1 * x37:0 <= -2 && x38:0 < 101 && x37:0 + -1 * x42:0 = -1 && x39:0 + -1 * x40:0 = 0 && x38:0 + -1 * x41:0 = 1 The following rules are bounded: f4444_in(x36:0, x37:0, x38:0, x39:0) -> f4444_in(x38:0, x37:0 - 2, x39:0 + 1, x36:0 + 1) :|: x43:0 < 101 && x44:0 + -1 * x45:0 <= -2 && x39:0 + -1 * x37:0 <= -3 && x36:0 < 100 && x37:0 + -1 * x45:0 = 0 && x36:0 + -1 * x44:0 = 0 && x38:0 + -1 * x43:0 = 0 && x41:0 + -1 * x42:0 <= -2 && x40:0 < 101 && x36:0 + -1 * x37:0 <= -2 && x38:0 < 101 && x37:0 + -1 * x42:0 = -1 && x39:0 + -1 * x40:0 = 0 && x38:0 + -1 * x41:0 = 1 ---------------------------------------- (24) YES