YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 33.5 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 36 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 138 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 0 ms] (13) IntTRS (14) RankingReductionPairProof [EQUIVALENT, 0 ms] (15) IntTRS (16) RankingReductionPairProof [EQUIVALENT, 0 ms] (17) IntTRS (18) RankingReductionPairProof [EQUIVALENT, 0 ms] (19) YES (20) IRSwT (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IRSwT (23) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (24) IRSwT (25) TempFilterProof [SOUND, 11 ms] (26) IntTRS (27) RankingReductionPairProof [EQUIVALENT, 5 ms] (28) YES (29) IRSwT (30) IntTRSCompressionProof [EQUIVALENT, 0 ms] (31) IRSwT (32) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (33) IRSwT (34) TempFilterProof [SOUND, 12 ms] (35) IntTRS (36) PolynomialOrderProcessor [EQUIVALENT, 3 ms] (37) YES (38) IRSwT (39) IntTRSCompressionProof [EQUIVALENT, 0 ms] (40) IRSwT (41) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (42) IRSwT (43) TempFilterProof [SOUND, 16 ms] (44) IntTRS (45) RankingReductionPairProof [EQUIVALENT, 0 ms] (46) YES (47) IRSwT (48) IntTRSCompressionProof [EQUIVALENT, 0 ms] (49) IRSwT (50) TempFilterProof [SOUND, 11 ms] (51) IntTRS (52) RankingReductionPairProof [EQUIVALENT, 5 ms] (53) YES (54) IRSwT (55) IntTRSCompressionProof [EQUIVALENT, 0 ms] (56) IRSwT (57) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (58) IRSwT (59) TempFilterProof [SOUND, 37 ms] (60) IntTRS (61) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (62) YES ---------------------------------------- (0) Obligation: Rules: f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f165_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f165_0_main_GE(x, x1, x2, x3) -> f165_0_main_GE'(x4, x5, x6, x7) :|: x1 - 2 * x8 = 1 && x1 <= x2 - 1 && 0 <= x1 - 5 * x9 - 1 && 0 <= x1 - 3 * x10 - 1 && x11 <= x && 0 <= x - 1 && 0 <= x11 - 1 && x = x4 && x1 = x5 && x2 = x6 f165_0_main_GE'(x12, x13, x14, x15) -> f319_0_main_GE(x16, x17, x18, x19) :|: 0 <= x13 - 5 * x20 - 1 && 0 <= x13 - 3 * x21 - 1 && x13 - 2 * x22 = 1 && x13 <= x14 - 1 && x16 <= x12 && 0 <= x12 - 1 && 0 <= x16 - 1 && 0 <= x13 - 2 * x22 && x13 - 2 * x22 <= 1 && x13 - 3 * x21 <= 2 && x13 - 5 * x20 <= 4 && x13 = x17 && 0 = x18 && x14 = x19 f319_0_main_GE(x23, x24, x25, x26) -> f319_0_main_GE(x27, x28, x29, x30) :|: x26 = x30 && x25 + 1 = x29 && x24 = x28 && 0 <= x27 - 1 && 0 <= x23 - 1 && x25 <= 99 && x27 <= x23 f319_0_main_GE(x31, x32, x33, x34) -> f165_0_main_GE(x35, x36, x38, x39) :|: x34 = x38 && x32 + 1 = x36 && 0 <= x35 - 1 && 0 <= x31 - 1 && x35 <= x31 && 99 <= x33 - 1 && -1 <= x34 - 1 f165_0_main_GE(x40, x41, x42, x43) -> f165_0_main_GE'(x44, x45, x46, x47) :|: x41 <= x42 - 1 && 0 <= x42 - 1 && x41 - 2 * x48 = 1 && 0 <= x41 - 3 * x49 - 1 && x41 - 5 * x50 = 0 && x52 <= x40 && 0 <= x40 - 1 && 0 <= x52 - 1 && x40 = x44 && x41 = x45 && x42 = x46 f165_0_main_GE'(x53, x55, x56, x57) -> f165_0_main_GE(x58, x59, x60, x61) :|: 0 <= x55 - 3 * x62 - 1 && x55 <= x56 - 1 && 0 <= x56 - 1 && x55 - 2 * x63 = 1 && x55 - 5 * x65 = 0 && x58 <= x53 && 0 <= x53 - 1 && 0 <= x58 - 1 && 0 <= x55 - 2 * x63 && x55 - 2 * x63 <= 1 && x55 - 3 * x62 <= 2 && x55 - 5 * x65 <= 4 && 0 <= x55 - 5 * x65 && x55 + 1 = x59 && x56 = x60 f165_0_main_GE(x67, x68, x70, x71) -> f165_0_main_GE'(x72, x73, x74, x75) :|: x68 <= x70 - 1 && 0 <= x70 - 1 && x68 - 2 * x76 = 0 && x77 <= x67 && 0 <= x67 - 1 && 0 <= x77 - 1 && x67 = x72 && x68 = x73 && x70 = x74 f165_0_main_GE'(x78, x79, x80, x81) -> f165_0_main_GE(x82, x83, x84, x85) :|: x79 <= x80 - 1 && 0 <= x80 - 1 && x79 - 2 * x86 = 0 && x82 <= x78 && 0 <= x78 - 1 && 0 <= x82 - 1 && x79 - 2 * x86 <= 1 && 0 <= x79 - 2 * x86 && x79 + 1 = x83 && x80 = x84 f165_0_main_GE(x87, x88, x90, x91) -> f165_0_main_GE'(x92, x93, x94, x95) :|: x88 <= x90 - 1 && 0 <= x90 - 1 && x88 - 2 * x98 = 1 && x88 - 3 * x99 = 0 && x100 <= x87 && 0 <= x87 - 1 && 0 <= x100 - 1 && x87 = x92 && x88 = x93 && x90 = x94 f165_0_main_GE'(x105, x106, x107, x108) -> f165_0_main_GE(x112, x113, x114, x117) :|: x106 <= x107 - 1 && 0 <= x107 - 1 && x106 - 2 * x118 = 1 && x106 - 3 * x119 = 0 && x112 <= x105 && 0 <= x105 - 1 && 0 <= x112 - 1 && 0 <= x106 - 2 * x118 && x106 - 2 * x118 <= 1 && x106 - 3 * x119 <= 2 && 0 <= x106 - 3 * x119 && x106 + 1 = x113 && x107 = x114 f165_0_main_GE(x120, x122, x123, x124) -> f165_0_main_GE'(x128, x129, x130, x131) :|: x122 <= x123 - 1 && 0 <= x123 - 1 && x122 - 2 * x134 = 0 && 0 <= x120 - 1 && x120 = x128 && x122 = x129 && x123 = x130 f165_0_main_GE'(x135, x136, x138, x139) -> f861_0_sin_GT(x140, x142, x143, x149) :|: x136 <= x138 - 1 && 0 <= x138 - 1 && x136 - 2 * x150 = 0 && 0 <= x135 - 1 && x136 - 2 * x150 <= 1 && 0 <= x136 - 2 * x150 && 3 = x140 && x136 = x142 f1048_0_fact_Return(x151, x154, x155, x156) -> f861_0_sin_GT(x159, x160, x164, x165) :|: x151 = x160 && x154 + 2 = x159 f861_0_sin_GT(x167, x168, x173, x174) -> f861_0_sin_GT'(x175, x179, x180, x181) :|: 0 <= x185 - 1 && x167 <= x168 && x167 = x175 && x168 = x179 f861_0_sin_GT'(x186, x187, x191, x192) -> f861_0_sin_GT(x193, x194, x195, x197) :|: x186 <= x187 && 0 <= x198 - 1 && 0 <= x186 - 2 * x199 && x186 - 2 * x199 <= 1 && x200 * x201 - x198 * x202 <= x198 - 1 && 0 <= x200 * x201 - x198 * x202 && x186 + 2 = x193 && x187 = x194 f165_0_main_GE(x203, x204, x205, x206) -> f165_0_main_GE'(x207, x209, x210, x212) :|: x204 <= x205 - 1 && 0 <= x205 - 1 && x204 - 2 * x213 = 1 && x204 - 3 * x214 = 0 && 0 <= x203 - 1 && x203 = x207 && x204 = x209 && x205 = x210 f165_0_main_GE'(x215, x216, x218, x219) -> f862_0_cos_GT(x220, x221, x222, x223) :|: x216 <= x218 - 1 && 0 <= x218 - 1 && x216 - 2 * x224 = 1 && x216 - 3 * x225 = 0 && 0 <= x215 - 1 && 0 <= x216 - 2 * x224 && x216 - 2 * x224 <= 1 && x216 - 3 * x225 <= 2 && 0 <= x216 - 3 * x225 && 2 = x220 && x216 = x221 f1049_0_fact_Return(x226, x227, x228, x229) -> f1049_0_fact_Return'(x230, x231, x232, x233) :|: x227 = x231 && x226 = x230 f1049_0_fact_Return'(x234, x235, x236, x237) -> f862_0_cos_GT(x238, x239, x240, x241) :|: x242 - x243 * x244 <= x243 - 1 && 0 <= x242 - x243 * x244 && x235 + 2 = x238 && x234 = x239 f862_0_cos_GT(x245, x246, x247, x248) -> f862_0_cos_GT'(x249, x250, x251, x252) :|: 1 <= x245 - 1 && 0 <= x253 - 1 && 1 <= x246 - 1 && x245 <= x246 && x253 <= x245 - 1 && x245 = x249 && x246 = x250 f862_0_cos_GT'(x254, x255, x256, x257) -> f862_0_cos_GT(x258, x259, x260, x261) :|: 1 <= x254 - 1 && 0 <= x262 - 1 && 1 <= x255 - 1 && x262 <= x254 - 1 && x254 <= x255 && 0 <= x254 - 2 * x262 && x254 - 2 * x262 <= 1 && x263 - x264 * x265 <= x264 - 1 && 0 <= x263 - x264 * x265 && x254 + 2 = x258 && x255 = x259 f165_0_main_GE(x266, x267, x268, x269) -> f165_0_main_GE'(x270, x271, x272, x273) :|: x267 <= x268 - 1 && 0 <= x268 - 1 && x267 - 2 * x274 = 1 && 0 <= x267 - 3 * x275 - 1 && x267 - 5 * x276 = 0 && 0 <= x266 - 1 && x266 = x270 && x267 = x271 && x268 = x272 f165_0_main_GE'(x277, x278, x279, x280) -> f544_0_exp_GT(x281, x282, x283, x284) :|: 0 <= x278 - 3 * x285 - 1 && x278 <= x279 - 1 && 0 <= x279 - 1 && x278 - 2 * x286 = 1 && x278 - 5 * x287 = 0 && 0 <= x277 - 1 && 0 <= x278 - 2 * x286 && x278 - 2 * x286 <= 1 && x278 - 3 * x285 <= 2 && x278 - 5 * x287 <= 4 && 0 <= x278 - 5 * x287 && x279 = x281 && 0 = x282 && x278 = x283 f765_0_fact_Return(x288, x289, x290, x291) -> f544_0_exp_GT(x292, x293, x294, x295) :|: x289 = x294 && x290 + 1 = x293 && x288 = x292 f544_0_exp_GT(x296, x297, x298, x299) -> f544_0_exp_GT'(x300, x301, x302, x303) :|: 0 <= x296 - 1 && -1 <= x298 - 1 && x297 <= x298 && 0 <= x304 - 1 && x296 = x300 && x297 = x301 && x298 = x302 f544_0_exp_GT'(x305, x306, x307, x308) -> f544_0_exp_GT(x309, x310, x311, x312) :|: 0 <= x305 - 1 && -1 <= x307 - 1 && 0 <= x313 - 1 && x306 <= x307 && x314 - x313 * x315 <= x313 - 1 && 0 <= x314 - x313 * x315 && x305 = x309 && x306 + 1 = x310 && x307 = x311 f861_0_sin_GT(x316, x317, x318, x319) -> f861_0_sin_GT'(x320, x321, x322, x323) :|: x317 = x321 && x316 = x320 && x316 <= x317 f861_0_sin_GT'(x324, x325, x326, x327) -> f1011_0_power_GT(x328, x329, x330, x331) :|: 1 = x328 && 0 <= x324 - 2 * x329 && x324 - 2 * x329 <= 1 && x324 <= x325 f861_0_sin_GT'(x332, x333, x334, x335) -> f1011_0_power_GT(x336, x337, x338, x339) :|: x332 <= x333 && x332 - 2 * x340 <= 1 && 0 <= x332 - 2 * x340 && 1 = x336 && x332 = x337 f862_0_cos_GT'(x341, x342, x343, x344) -> f1011_0_power_GT(x345, x346, x347, x348) :|: 1 = x345 && 0 <= x341 - 2 * x346 && x341 - 2 * x346 <= 1 && x341 <= x342 && x346 <= x341 - 1 && 1 <= x342 - 1 && 0 <= x346 - 1 && 1 <= x341 - 1 f862_0_cos_GT'(x349, x350, x351, x352) -> f1011_0_power_GT(x353, x354, x355, x356) :|: 1 <= x349 - 1 && 0 <= x357 - 1 && 1 <= x350 - 1 && x357 <= x349 - 1 && x349 <= x350 && x349 - 2 * x357 <= 1 && 0 <= x349 - 2 * x357 && 1 = x353 && x349 = x354 f544_0_exp_GT(x358, x359, x360, x361) -> f1011_0_power_GT(x362, x363, x364, x365) :|: x359 = x363 && 1 = x362 && -1 <= x360 - 1 && x359 <= x360 && 0 <= x358 - 1 f1011_0_power_GT(x366, x367, x368, x369) -> f1011_0_power_GT(x370, x371, x372, x373) :|: x367 = x371 && x366 + 1 = x370 && x366 <= x367 f861_0_sin_GT'(x374, x375, x376, x377) -> f1113_0_fact_GT(x378, x379, x380, x381) :|: x374 <= x375 && x374 - 2 * x382 <= 1 && 0 <= x374 - 2 * x382 && 1 = x378 && 1 = x379 && 1 = x380 && x374 = x381 f862_0_cos_GT'(x383, x384, x385, x386) -> f1113_0_fact_GT(x387, x388, x389, x390) :|: 1 <= x383 - 1 && 0 <= x391 - 1 && 1 <= x384 - 1 && x391 <= x383 - 1 && x383 <= x384 && x383 - 2 * x391 <= 1 && 0 <= x383 - 2 * x391 && 1 = x387 && 1 = x388 && 1 = x389 && x383 = x390 f544_0_exp_GT(x392, x393, x394, x395) -> f1113_0_fact_GT(x396, x397, x398, x399) :|: x393 = x399 && 1 = x398 && 1 = x397 && 1 = x396 && -1 <= x394 - 1 && x393 <= x394 && 0 <= x392 - 1 f1113_0_fact_GT(x400, x401, x402, x403) -> f1113_0_fact_GT(x404, x405, x406, x407) :|: x403 = x407 && x401 + 1 = x406 && x401 + 1 = x405 && x400 * x401 = x404 && x401 = x402 && 0 <= x401 - 1 && 0 <= x400 - 1 && x401 <= x403 __init(x408, x409, x410, x411) -> f1_0_main_ConstantStackPush(x412, x413, x414, x415) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f165_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f165_0_main_GE(x, x1, x2, x3) -> f165_0_main_GE'(x4, x5, x6, x7) :|: x1 - 2 * x8 = 1 && x1 <= x2 - 1 && 0 <= x1 - 5 * x9 - 1 && 0 <= x1 - 3 * x10 - 1 && x11 <= x && 0 <= x - 1 && 0 <= x11 - 1 && x = x4 && x1 = x5 && x2 = x6 f165_0_main_GE'(x12, x13, x14, x15) -> f319_0_main_GE(x16, x17, x18, x19) :|: 0 <= x13 - 5 * x20 - 1 && 0 <= x13 - 3 * x21 - 1 && x13 - 2 * x22 = 1 && x13 <= x14 - 1 && x16 <= x12 && 0 <= x12 - 1 && 0 <= x16 - 1 && 0 <= x13 - 2 * x22 && x13 - 2 * x22 <= 1 && x13 - 3 * x21 <= 2 && x13 - 5 * x20 <= 4 && x13 = x17 && 0 = x18 && x14 = x19 f319_0_main_GE(x23, x24, x25, x26) -> f319_0_main_GE(x27, x28, x29, x30) :|: x26 = x30 && x25 + 1 = x29 && x24 = x28 && 0 <= x27 - 1 && 0 <= x23 - 1 && x25 <= 99 && x27 <= x23 f319_0_main_GE(x31, x32, x33, x34) -> f165_0_main_GE(x35, x36, x38, x39) :|: x34 = x38 && x32 + 1 = x36 && 0 <= x35 - 1 && 0 <= x31 - 1 && x35 <= x31 && 99 <= x33 - 1 && -1 <= x34 - 1 f165_0_main_GE(x40, x41, x42, x43) -> f165_0_main_GE'(x44, x45, x46, x47) :|: x41 <= x42 - 1 && 0 <= x42 - 1 && x41 - 2 * x48 = 1 && 0 <= x41 - 3 * x49 - 1 && x41 - 5 * x50 = 0 && x52 <= x40 && 0 <= x40 - 1 && 0 <= x52 - 1 && x40 = x44 && x41 = x45 && x42 = x46 f165_0_main_GE'(x53, x55, x56, x57) -> f165_0_main_GE(x58, x59, x60, x61) :|: 0 <= x55 - 3 * x62 - 1 && x55 <= x56 - 1 && 0 <= x56 - 1 && x55 - 2 * x63 = 1 && x55 - 5 * x65 = 0 && x58 <= x53 && 0 <= x53 - 1 && 0 <= x58 - 1 && 0 <= x55 - 2 * x63 && x55 - 2 * x63 <= 1 && x55 - 3 * x62 <= 2 && x55 - 5 * x65 <= 4 && 0 <= x55 - 5 * x65 && x55 + 1 = x59 && x56 = x60 f165_0_main_GE(x67, x68, x70, x71) -> f165_0_main_GE'(x72, x73, x74, x75) :|: x68 <= x70 - 1 && 0 <= x70 - 1 && x68 - 2 * x76 = 0 && x77 <= x67 && 0 <= x67 - 1 && 0 <= x77 - 1 && x67 = x72 && x68 = x73 && x70 = x74 f165_0_main_GE'(x78, x79, x80, x81) -> f165_0_main_GE(x82, x83, x84, x85) :|: x79 <= x80 - 1 && 0 <= x80 - 1 && x79 - 2 * x86 = 0 && x82 <= x78 && 0 <= x78 - 1 && 0 <= x82 - 1 && x79 - 2 * x86 <= 1 && 0 <= x79 - 2 * x86 && x79 + 1 = x83 && x80 = x84 f165_0_main_GE(x87, x88, x90, x91) -> f165_0_main_GE'(x92, x93, x94, x95) :|: x88 <= x90 - 1 && 0 <= x90 - 1 && x88 - 2 * x98 = 1 && x88 - 3 * x99 = 0 && x100 <= x87 && 0 <= x87 - 1 && 0 <= x100 - 1 && x87 = x92 && x88 = x93 && x90 = x94 f165_0_main_GE'(x105, x106, x107, x108) -> f165_0_main_GE(x112, x113, x114, x117) :|: x106 <= x107 - 1 && 0 <= x107 - 1 && x106 - 2 * x118 = 1 && x106 - 3 * x119 = 0 && x112 <= x105 && 0 <= x105 - 1 && 0 <= x112 - 1 && 0 <= x106 - 2 * x118 && x106 - 2 * x118 <= 1 && x106 - 3 * x119 <= 2 && 0 <= x106 - 3 * x119 && x106 + 1 = x113 && x107 = x114 f165_0_main_GE(x120, x122, x123, x124) -> f165_0_main_GE'(x128, x129, x130, x131) :|: x122 <= x123 - 1 && 0 <= x123 - 1 && x122 - 2 * x134 = 0 && 0 <= x120 - 1 && x120 = x128 && x122 = x129 && x123 = x130 f165_0_main_GE'(x135, x136, x138, x139) -> f861_0_sin_GT(x140, x142, x143, x149) :|: x136 <= x138 - 1 && 0 <= x138 - 1 && x136 - 2 * x150 = 0 && 0 <= x135 - 1 && x136 - 2 * x150 <= 1 && 0 <= x136 - 2 * x150 && 3 = x140 && x136 = x142 f1048_0_fact_Return(x151, x154, x155, x156) -> f861_0_sin_GT(x159, x160, x164, x165) :|: x151 = x160 && x154 + 2 = x159 f861_0_sin_GT(x167, x168, x173, x174) -> f861_0_sin_GT'(x175, x179, x180, x181) :|: 0 <= x185 - 1 && x167 <= x168 && x167 = x175 && x168 = x179 f861_0_sin_GT'(x186, x187, x191, x192) -> f861_0_sin_GT(x193, x194, x195, x197) :|: x186 <= x187 && 0 <= x198 - 1 && 0 <= x186 - 2 * x199 && x186 - 2 * x199 <= 1 && x200 * x201 - x198 * x202 <= x198 - 1 && 0 <= x200 * x201 - x198 * x202 && x186 + 2 = x193 && x187 = x194 f165_0_main_GE(x203, x204, x205, x206) -> f165_0_main_GE'(x207, x209, x210, x212) :|: x204 <= x205 - 1 && 0 <= x205 - 1 && x204 - 2 * x213 = 1 && x204 - 3 * x214 = 0 && 0 <= x203 - 1 && x203 = x207 && x204 = x209 && x205 = x210 f165_0_main_GE'(x215, x216, x218, x219) -> f862_0_cos_GT(x220, x221, x222, x223) :|: x216 <= x218 - 1 && 0 <= x218 - 1 && x216 - 2 * x224 = 1 && x216 - 3 * x225 = 0 && 0 <= x215 - 1 && 0 <= x216 - 2 * x224 && x216 - 2 * x224 <= 1 && x216 - 3 * x225 <= 2 && 0 <= x216 - 3 * x225 && 2 = x220 && x216 = x221 f1049_0_fact_Return(x226, x227, x228, x229) -> f1049_0_fact_Return'(x230, x231, x232, x233) :|: x227 = x231 && x226 = x230 f1049_0_fact_Return'(x234, x235, x236, x237) -> f862_0_cos_GT(x238, x239, x240, x241) :|: x242 - x243 * x244 <= x243 - 1 && 0 <= x242 - x243 * x244 && x235 + 2 = x238 && x234 = x239 f862_0_cos_GT(x245, x246, x247, x248) -> f862_0_cos_GT'(x249, x250, x251, x252) :|: 1 <= x245 - 1 && 0 <= x253 - 1 && 1 <= x246 - 1 && x245 <= x246 && x253 <= x245 - 1 && x245 = x249 && x246 = x250 f862_0_cos_GT'(x254, x255, x256, x257) -> f862_0_cos_GT(x258, x259, x260, x261) :|: 1 <= x254 - 1 && 0 <= x262 - 1 && 1 <= x255 - 1 && x262 <= x254 - 1 && x254 <= x255 && 0 <= x254 - 2 * x262 && x254 - 2 * x262 <= 1 && x263 - x264 * x265 <= x264 - 1 && 0 <= x263 - x264 * x265 && x254 + 2 = x258 && x255 = x259 f165_0_main_GE(x266, x267, x268, x269) -> f165_0_main_GE'(x270, x271, x272, x273) :|: x267 <= x268 - 1 && 0 <= x268 - 1 && x267 - 2 * x274 = 1 && 0 <= x267 - 3 * x275 - 1 && x267 - 5 * x276 = 0 && 0 <= x266 - 1 && x266 = x270 && x267 = x271 && x268 = x272 f165_0_main_GE'(x277, x278, x279, x280) -> f544_0_exp_GT(x281, x282, x283, x284) :|: 0 <= x278 - 3 * x285 - 1 && x278 <= x279 - 1 && 0 <= x279 - 1 && x278 - 2 * x286 = 1 && x278 - 5 * x287 = 0 && 0 <= x277 - 1 && 0 <= x278 - 2 * x286 && x278 - 2 * x286 <= 1 && x278 - 3 * x285 <= 2 && x278 - 5 * x287 <= 4 && 0 <= x278 - 5 * x287 && x279 = x281 && 0 = x282 && x278 = x283 f765_0_fact_Return(x288, x289, x290, x291) -> f544_0_exp_GT(x292, x293, x294, x295) :|: x289 = x294 && x290 + 1 = x293 && x288 = x292 f544_0_exp_GT(x296, x297, x298, x299) -> f544_0_exp_GT'(x300, x301, x302, x303) :|: 0 <= x296 - 1 && -1 <= x298 - 1 && x297 <= x298 && 0 <= x304 - 1 && x296 = x300 && x297 = x301 && x298 = x302 f544_0_exp_GT'(x305, x306, x307, x308) -> f544_0_exp_GT(x309, x310, x311, x312) :|: 0 <= x305 - 1 && -1 <= x307 - 1 && 0 <= x313 - 1 && x306 <= x307 && x314 - x313 * x315 <= x313 - 1 && 0 <= x314 - x313 * x315 && x305 = x309 && x306 + 1 = x310 && x307 = x311 f861_0_sin_GT(x316, x317, x318, x319) -> f861_0_sin_GT'(x320, x321, x322, x323) :|: x317 = x321 && x316 = x320 && x316 <= x317 f861_0_sin_GT'(x324, x325, x326, x327) -> f1011_0_power_GT(x328, x329, x330, x331) :|: 1 = x328 && 0 <= x324 - 2 * x329 && x324 - 2 * x329 <= 1 && x324 <= x325 f861_0_sin_GT'(x332, x333, x334, x335) -> f1011_0_power_GT(x336, x337, x338, x339) :|: x332 <= x333 && x332 - 2 * x340 <= 1 && 0 <= x332 - 2 * x340 && 1 = x336 && x332 = x337 f862_0_cos_GT'(x341, x342, x343, x344) -> f1011_0_power_GT(x345, x346, x347, x348) :|: 1 = x345 && 0 <= x341 - 2 * x346 && x341 - 2 * x346 <= 1 && x341 <= x342 && x346 <= x341 - 1 && 1 <= x342 - 1 && 0 <= x346 - 1 && 1 <= x341 - 1 f862_0_cos_GT'(x349, x350, x351, x352) -> f1011_0_power_GT(x353, x354, x355, x356) :|: 1 <= x349 - 1 && 0 <= x357 - 1 && 1 <= x350 - 1 && x357 <= x349 - 1 && x349 <= x350 && x349 - 2 * x357 <= 1 && 0 <= x349 - 2 * x357 && 1 = x353 && x349 = x354 f544_0_exp_GT(x358, x359, x360, x361) -> f1011_0_power_GT(x362, x363, x364, x365) :|: x359 = x363 && 1 = x362 && -1 <= x360 - 1 && x359 <= x360 && 0 <= x358 - 1 f1011_0_power_GT(x366, x367, x368, x369) -> f1011_0_power_GT(x370, x371, x372, x373) :|: x367 = x371 && x366 + 1 = x370 && x366 <= x367 f861_0_sin_GT'(x374, x375, x376, x377) -> f1113_0_fact_GT(x378, x379, x380, x381) :|: x374 <= x375 && x374 - 2 * x382 <= 1 && 0 <= x374 - 2 * x382 && 1 = x378 && 1 = x379 && 1 = x380 && x374 = x381 f862_0_cos_GT'(x383, x384, x385, x386) -> f1113_0_fact_GT(x387, x388, x389, x390) :|: 1 <= x383 - 1 && 0 <= x391 - 1 && 1 <= x384 - 1 && x391 <= x383 - 1 && x383 <= x384 && x383 - 2 * x391 <= 1 && 0 <= x383 - 2 * x391 && 1 = x387 && 1 = x388 && 1 = x389 && x383 = x390 f544_0_exp_GT(x392, x393, x394, x395) -> f1113_0_fact_GT(x396, x397, x398, x399) :|: x393 = x399 && 1 = x398 && 1 = x397 && 1 = x396 && -1 <= x394 - 1 && x393 <= x394 && 0 <= x392 - 1 f1113_0_fact_GT(x400, x401, x402, x403) -> f1113_0_fact_GT(x404, x405, x406, x407) :|: x403 = x407 && x401 + 1 = x406 && x401 + 1 = x405 && x400 * x401 = x404 && x401 = x402 && 0 <= x401 - 1 && 0 <= x400 - 1 && x401 <= x403 __init(x408, x409, x410, x411) -> f1_0_main_ConstantStackPush(x412, x413, x414, x415) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_ConstantStackPush(arg1, arg2, arg3, arg4) -> f165_0_main_GE(arg1P, arg2P, arg3P, arg4P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 (2) f165_0_main_GE(x, x1, x2, x3) -> f165_0_main_GE'(x4, x5, x6, x7) :|: x1 - 2 * x8 = 1 && x1 <= x2 - 1 && 0 <= x1 - 5 * x9 - 1 && 0 <= x1 - 3 * x10 - 1 && x11 <= x && 0 <= x - 1 && 0 <= x11 - 1 && x = x4 && x1 = x5 && x2 = x6 (3) f165_0_main_GE'(x12, x13, x14, x15) -> f319_0_main_GE(x16, x17, x18, x19) :|: 0 <= x13 - 5 * x20 - 1 && 0 <= x13 - 3 * x21 - 1 && x13 - 2 * x22 = 1 && x13 <= x14 - 1 && x16 <= x12 && 0 <= x12 - 1 && 0 <= x16 - 1 && 0 <= x13 - 2 * x22 && x13 - 2 * x22 <= 1 && x13 - 3 * x21 <= 2 && x13 - 5 * x20 <= 4 && x13 = x17 && 0 = x18 && x14 = x19 (4) f319_0_main_GE(x23, x24, x25, x26) -> f319_0_main_GE(x27, x28, x29, x30) :|: x26 = x30 && x25 + 1 = x29 && x24 = x28 && 0 <= x27 - 1 && 0 <= x23 - 1 && x25 <= 99 && x27 <= x23 (5) f319_0_main_GE(x31, x32, x33, x34) -> f165_0_main_GE(x35, x36, x38, x39) :|: x34 = x38 && x32 + 1 = x36 && 0 <= x35 - 1 && 0 <= x31 - 1 && x35 <= x31 && 99 <= x33 - 1 && -1 <= x34 - 1 (6) f165_0_main_GE(x40, x41, x42, x43) -> f165_0_main_GE'(x44, x45, x46, x47) :|: x41 <= x42 - 1 && 0 <= x42 - 1 && x41 - 2 * x48 = 1 && 0 <= x41 - 3 * x49 - 1 && x41 - 5 * x50 = 0 && x52 <= x40 && 0 <= x40 - 1 && 0 <= x52 - 1 && x40 = x44 && x41 = x45 && x42 = x46 (7) f165_0_main_GE'(x53, x55, x56, x57) -> f165_0_main_GE(x58, x59, x60, x61) :|: 0 <= x55 - 3 * x62 - 1 && x55 <= x56 - 1 && 0 <= x56 - 1 && x55 - 2 * x63 = 1 && x55 - 5 * x65 = 0 && x58 <= x53 && 0 <= x53 - 1 && 0 <= x58 - 1 && 0 <= x55 - 2 * x63 && x55 - 2 * x63 <= 1 && x55 - 3 * x62 <= 2 && x55 - 5 * x65 <= 4 && 0 <= x55 - 5 * x65 && x55 + 1 = x59 && x56 = x60 (8) f165_0_main_GE(x67, x68, x70, x71) -> f165_0_main_GE'(x72, x73, x74, x75) :|: x68 <= x70 - 1 && 0 <= x70 - 1 && x68 - 2 * x76 = 0 && x77 <= x67 && 0 <= x67 - 1 && 0 <= x77 - 1 && x67 = x72 && x68 = x73 && x70 = x74 (9) f165_0_main_GE'(x78, x79, x80, x81) -> f165_0_main_GE(x82, x83, x84, x85) :|: x79 <= x80 - 1 && 0 <= x80 - 1 && x79 - 2 * x86 = 0 && x82 <= x78 && 0 <= x78 - 1 && 0 <= x82 - 1 && x79 - 2 * x86 <= 1 && 0 <= x79 - 2 * x86 && x79 + 1 = x83 && x80 = x84 (10) f165_0_main_GE(x87, x88, x90, x91) -> f165_0_main_GE'(x92, x93, x94, x95) :|: x88 <= x90 - 1 && 0 <= x90 - 1 && x88 - 2 * x98 = 1 && x88 - 3 * x99 = 0 && x100 <= x87 && 0 <= x87 - 1 && 0 <= x100 - 1 && x87 = x92 && x88 = x93 && x90 = x94 (11) f165_0_main_GE'(x105, x106, x107, x108) -> f165_0_main_GE(x112, x113, x114, x117) :|: x106 <= x107 - 1 && 0 <= x107 - 1 && x106 - 2 * x118 = 1 && x106 - 3 * x119 = 0 && x112 <= x105 && 0 <= x105 - 1 && 0 <= x112 - 1 && 0 <= x106 - 2 * x118 && x106 - 2 * x118 <= 1 && x106 - 3 * x119 <= 2 && 0 <= x106 - 3 * x119 && x106 + 1 = x113 && x107 = x114 (12) f165_0_main_GE(x120, x122, x123, x124) -> f165_0_main_GE'(x128, x129, x130, x131) :|: x122 <= x123 - 1 && 0 <= x123 - 1 && x122 - 2 * x134 = 0 && 0 <= x120 - 1 && x120 = x128 && x122 = x129 && x123 = x130 (13) f165_0_main_GE'(x135, x136, x138, x139) -> f861_0_sin_GT(x140, x142, x143, x149) :|: x136 <= x138 - 1 && 0 <= x138 - 1 && x136 - 2 * x150 = 0 && 0 <= x135 - 1 && x136 - 2 * x150 <= 1 && 0 <= x136 - 2 * x150 && 3 = x140 && x136 = x142 (14) f1048_0_fact_Return(x151, x154, x155, x156) -> f861_0_sin_GT(x159, x160, x164, x165) :|: x151 = x160 && x154 + 2 = x159 (15) f861_0_sin_GT(x167, x168, x173, x174) -> f861_0_sin_GT'(x175, x179, x180, x181) :|: 0 <= x185 - 1 && x167 <= x168 && x167 = x175 && x168 = x179 (16) f861_0_sin_GT'(x186, x187, x191, x192) -> f861_0_sin_GT(x193, x194, x195, x197) :|: x186 <= x187 && 0 <= x198 - 1 && 0 <= x186 - 2 * x199 && x186 - 2 * x199 <= 1 && x200 * x201 - x198 * x202 <= x198 - 1 && 0 <= x200 * x201 - x198 * x202 && x186 + 2 = x193 && x187 = x194 (17) f165_0_main_GE(x203, x204, x205, x206) -> f165_0_main_GE'(x207, x209, x210, x212) :|: x204 <= x205 - 1 && 0 <= x205 - 1 && x204 - 2 * x213 = 1 && x204 - 3 * x214 = 0 && 0 <= x203 - 1 && x203 = x207 && x204 = x209 && x205 = x210 (18) f165_0_main_GE'(x215, x216, x218, x219) -> f862_0_cos_GT(x220, x221, x222, x223) :|: x216 <= x218 - 1 && 0 <= x218 - 1 && x216 - 2 * x224 = 1 && x216 - 3 * x225 = 0 && 0 <= x215 - 1 && 0 <= x216 - 2 * x224 && x216 - 2 * x224 <= 1 && x216 - 3 * x225 <= 2 && 0 <= x216 - 3 * x225 && 2 = x220 && x216 = x221 (19) f1049_0_fact_Return(x226, x227, x228, x229) -> f1049_0_fact_Return'(x230, x231, x232, x233) :|: x227 = x231 && x226 = x230 (20) f1049_0_fact_Return'(x234, x235, x236, x237) -> f862_0_cos_GT(x238, x239, x240, x241) :|: x242 - x243 * x244 <= x243 - 1 && 0 <= x242 - x243 * x244 && x235 + 2 = x238 && x234 = x239 (21) f862_0_cos_GT(x245, x246, x247, x248) -> f862_0_cos_GT'(x249, x250, x251, x252) :|: 1 <= x245 - 1 && 0 <= x253 - 1 && 1 <= x246 - 1 && x245 <= x246 && x253 <= x245 - 1 && x245 = x249 && x246 = x250 (22) f862_0_cos_GT'(x254, x255, x256, x257) -> f862_0_cos_GT(x258, x259, x260, x261) :|: 1 <= x254 - 1 && 0 <= x262 - 1 && 1 <= x255 - 1 && x262 <= x254 - 1 && x254 <= x255 && 0 <= x254 - 2 * x262 && x254 - 2 * x262 <= 1 && x263 - x264 * x265 <= x264 - 1 && 0 <= x263 - x264 * x265 && x254 + 2 = x258 && x255 = x259 (23) f165_0_main_GE(x266, x267, x268, x269) -> f165_0_main_GE'(x270, x271, x272, x273) :|: x267 <= x268 - 1 && 0 <= x268 - 1 && x267 - 2 * x274 = 1 && 0 <= x267 - 3 * x275 - 1 && x267 - 5 * x276 = 0 && 0 <= x266 - 1 && x266 = x270 && x267 = x271 && x268 = x272 (24) f165_0_main_GE'(x277, x278, x279, x280) -> f544_0_exp_GT(x281, x282, x283, x284) :|: 0 <= x278 - 3 * x285 - 1 && x278 <= x279 - 1 && 0 <= x279 - 1 && x278 - 2 * x286 = 1 && x278 - 5 * x287 = 0 && 0 <= x277 - 1 && 0 <= x278 - 2 * x286 && x278 - 2 * x286 <= 1 && x278 - 3 * x285 <= 2 && x278 - 5 * x287 <= 4 && 0 <= x278 - 5 * x287 && x279 = x281 && 0 = x282 && x278 = x283 (25) f765_0_fact_Return(x288, x289, x290, x291) -> f544_0_exp_GT(x292, x293, x294, x295) :|: x289 = x294 && x290 + 1 = x293 && x288 = x292 (26) f544_0_exp_GT(x296, x297, x298, x299) -> f544_0_exp_GT'(x300, x301, x302, x303) :|: 0 <= x296 - 1 && -1 <= x298 - 1 && x297 <= x298 && 0 <= x304 - 1 && x296 = x300 && x297 = x301 && x298 = x302 (27) f544_0_exp_GT'(x305, x306, x307, x308) -> f544_0_exp_GT(x309, x310, x311, x312) :|: 0 <= x305 - 1 && -1 <= x307 - 1 && 0 <= x313 - 1 && x306 <= x307 && x314 - x313 * x315 <= x313 - 1 && 0 <= x314 - x313 * x315 && x305 = x309 && x306 + 1 = x310 && x307 = x311 (28) f861_0_sin_GT(x316, x317, x318, x319) -> f861_0_sin_GT'(x320, x321, x322, x323) :|: x317 = x321 && x316 = x320 && x316 <= x317 (29) f861_0_sin_GT'(x324, x325, x326, x327) -> f1011_0_power_GT(x328, x329, x330, x331) :|: 1 = x328 && 0 <= x324 - 2 * x329 && x324 - 2 * x329 <= 1 && x324 <= x325 (30) f861_0_sin_GT'(x332, x333, x334, x335) -> f1011_0_power_GT(x336, x337, x338, x339) :|: x332 <= x333 && x332 - 2 * x340 <= 1 && 0 <= x332 - 2 * x340 && 1 = x336 && x332 = x337 (31) f862_0_cos_GT'(x341, x342, x343, x344) -> f1011_0_power_GT(x345, x346, x347, x348) :|: 1 = x345 && 0 <= x341 - 2 * x346 && x341 - 2 * x346 <= 1 && x341 <= x342 && x346 <= x341 - 1 && 1 <= x342 - 1 && 0 <= x346 - 1 && 1 <= x341 - 1 (32) f862_0_cos_GT'(x349, x350, x351, x352) -> f1011_0_power_GT(x353, x354, x355, x356) :|: 1 <= x349 - 1 && 0 <= x357 - 1 && 1 <= x350 - 1 && x357 <= x349 - 1 && x349 <= x350 && x349 - 2 * x357 <= 1 && 0 <= x349 - 2 * x357 && 1 = x353 && x349 = x354 (33) f544_0_exp_GT(x358, x359, x360, x361) -> f1011_0_power_GT(x362, x363, x364, x365) :|: x359 = x363 && 1 = x362 && -1 <= x360 - 1 && x359 <= x360 && 0 <= x358 - 1 (34) f1011_0_power_GT(x366, x367, x368, x369) -> f1011_0_power_GT(x370, x371, x372, x373) :|: x367 = x371 && x366 + 1 = x370 && x366 <= x367 (35) f861_0_sin_GT'(x374, x375, x376, x377) -> f1113_0_fact_GT(x378, x379, x380, x381) :|: x374 <= x375 && x374 - 2 * x382 <= 1 && 0 <= x374 - 2 * x382 && 1 = x378 && 1 = x379 && 1 = x380 && x374 = x381 (36) f862_0_cos_GT'(x383, x384, x385, x386) -> f1113_0_fact_GT(x387, x388, x389, x390) :|: 1 <= x383 - 1 && 0 <= x391 - 1 && 1 <= x384 - 1 && x391 <= x383 - 1 && x383 <= x384 && x383 - 2 * x391 <= 1 && 0 <= x383 - 2 * x391 && 1 = x387 && 1 = x388 && 1 = x389 && x383 = x390 (37) f544_0_exp_GT(x392, x393, x394, x395) -> f1113_0_fact_GT(x396, x397, x398, x399) :|: x393 = x399 && 1 = x398 && 1 = x397 && 1 = x396 && -1 <= x394 - 1 && x393 <= x394 && 0 <= x392 - 1 (38) f1113_0_fact_GT(x400, x401, x402, x403) -> f1113_0_fact_GT(x404, x405, x406, x407) :|: x403 = x407 && x401 + 1 = x406 && x401 + 1 = x405 && x400 * x401 = x404 && x401 = x402 && 0 <= x401 - 1 && 0 <= x400 - 1 && x401 <= x403 (39) __init(x408, x409, x410, x411) -> f1_0_main_ConstantStackPush(x412, x413, x414, x415) :|: 0 <= 0 Arcs: (1) -> (8), (12) (2) -> (3), (7), (11), (18), (24) (3) -> (4) (4) -> (4), (5) (5) -> (2), (6), (8), (10), (12), (17), (23) (6) -> (7), (11), (18), (24) (7) -> (8), (12) (8) -> (9), (13) (9) -> (2), (6), (10), (17), (23) (10) -> (11), (18) (11) -> (8), (12) (12) -> (9), (13) (13) -> (15), (28) (14) -> (15), (28) (15) -> (16), (29), (30), (35) (16) -> (15), (28) (17) -> (11), (18) (18) -> (21) (19) -> (20) (20) -> (21) (21) -> (22), (31), (32), (36) (22) -> (21) (23) -> (7), (11), (18), (24) (24) -> (26), (33), (37) (25) -> (26), (33), (37) (26) -> (27) (27) -> (26), (33), (37) (28) -> (16), (29), (30), (35) (29) -> (34) (30) -> (34) (31) -> (34) (32) -> (34) (33) -> (34) (34) -> (34) (35) -> (38) (36) -> (38) (37) -> (38) (38) -> (38) (39) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f165_0_main_GE(x67, x68, x70, x71) -> f165_0_main_GE'(x72, x73, x74, x75) :|: x68 <= x70 - 1 && 0 <= x70 - 1 && x68 - 2 * x76 = 0 && x77 <= x67 && 0 <= x67 - 1 && 0 <= x77 - 1 && x67 = x72 && x68 = x73 && x70 = x74 (2) f319_0_main_GE(x31, x32, x33, x34) -> f165_0_main_GE(x35, x36, x38, x39) :|: x34 = x38 && x32 + 1 = x36 && 0 <= x35 - 1 && 0 <= x31 - 1 && x35 <= x31 && 99 <= x33 - 1 && -1 <= x34 - 1 (3) f319_0_main_GE(x23, x24, x25, x26) -> f319_0_main_GE(x27, x28, x29, x30) :|: x26 = x30 && x25 + 1 = x29 && x24 = x28 && 0 <= x27 - 1 && 0 <= x23 - 1 && x25 <= 99 && x27 <= x23 (4) f165_0_main_GE'(x12, x13, x14, x15) -> f319_0_main_GE(x16, x17, x18, x19) :|: 0 <= x13 - 5 * x20 - 1 && 0 <= x13 - 3 * x21 - 1 && x13 - 2 * x22 = 1 && x13 <= x14 - 1 && x16 <= x12 && 0 <= x12 - 1 && 0 <= x16 - 1 && 0 <= x13 - 2 * x22 && x13 - 2 * x22 <= 1 && x13 - 3 * x21 <= 2 && x13 - 5 * x20 <= 4 && x13 = x17 && 0 = x18 && x14 = x19 (5) f165_0_main_GE(x, x1, x2, x3) -> f165_0_main_GE'(x4, x5, x6, x7) :|: x1 - 2 * x8 = 1 && x1 <= x2 - 1 && 0 <= x1 - 5 * x9 - 1 && 0 <= x1 - 3 * x10 - 1 && x11 <= x && 0 <= x - 1 && 0 <= x11 - 1 && x = x4 && x1 = x5 && x2 = x6 (6) f165_0_main_GE'(x78, x79, x80, x81) -> f165_0_main_GE(x82, x83, x84, x85) :|: x79 <= x80 - 1 && 0 <= x80 - 1 && x79 - 2 * x86 = 0 && x82 <= x78 && 0 <= x78 - 1 && 0 <= x82 - 1 && x79 - 2 * x86 <= 1 && 0 <= x79 - 2 * x86 && x79 + 1 = x83 && x80 = x84 (7) f165_0_main_GE(x120, x122, x123, x124) -> f165_0_main_GE'(x128, x129, x130, x131) :|: x122 <= x123 - 1 && 0 <= x123 - 1 && x122 - 2 * x134 = 0 && 0 <= x120 - 1 && x120 = x128 && x122 = x129 && x123 = x130 (8) f165_0_main_GE'(x105, x106, x107, x108) -> f165_0_main_GE(x112, x113, x114, x117) :|: x106 <= x107 - 1 && 0 <= x107 - 1 && x106 - 2 * x118 = 1 && x106 - 3 * x119 = 0 && x112 <= x105 && 0 <= x105 - 1 && 0 <= x112 - 1 && 0 <= x106 - 2 * x118 && x106 - 2 * x118 <= 1 && x106 - 3 * x119 <= 2 && 0 <= x106 - 3 * x119 && x106 + 1 = x113 && x107 = x114 (9) f165_0_main_GE(x203, x204, x205, x206) -> f165_0_main_GE'(x207, x209, x210, x212) :|: x204 <= x205 - 1 && 0 <= x205 - 1 && x204 - 2 * x213 = 1 && x204 - 3 * x214 = 0 && 0 <= x203 - 1 && x203 = x207 && x204 = x209 && x205 = x210 (10) f165_0_main_GE(x87, x88, x90, x91) -> f165_0_main_GE'(x92, x93, x94, x95) :|: x88 <= x90 - 1 && 0 <= x90 - 1 && x88 - 2 * x98 = 1 && x88 - 3 * x99 = 0 && x100 <= x87 && 0 <= x87 - 1 && 0 <= x100 - 1 && x87 = x92 && x88 = x93 && x90 = x94 (11) f165_0_main_GE'(x53, x55, x56, x57) -> f165_0_main_GE(x58, x59, x60, x61) :|: 0 <= x55 - 3 * x62 - 1 && x55 <= x56 - 1 && 0 <= x56 - 1 && x55 - 2 * x63 = 1 && x55 - 5 * x65 = 0 && x58 <= x53 && 0 <= x53 - 1 && 0 <= x58 - 1 && 0 <= x55 - 2 * x63 && x55 - 2 * x63 <= 1 && x55 - 3 * x62 <= 2 && x55 - 5 * x65 <= 4 && 0 <= x55 - 5 * x65 && x55 + 1 = x59 && x56 = x60 (12) f165_0_main_GE(x266, x267, x268, x269) -> f165_0_main_GE'(x270, x271, x272, x273) :|: x267 <= x268 - 1 && 0 <= x268 - 1 && x267 - 2 * x274 = 1 && 0 <= x267 - 3 * x275 - 1 && x267 - 5 * x276 = 0 && 0 <= x266 - 1 && x266 = x270 && x267 = x271 && x268 = x272 (13) f165_0_main_GE(x40, x41, x42, x43) -> f165_0_main_GE'(x44, x45, x46, x47) :|: x41 <= x42 - 1 && 0 <= x42 - 1 && x41 - 2 * x48 = 1 && 0 <= x41 - 3 * x49 - 1 && x41 - 5 * x50 = 0 && x52 <= x40 && 0 <= x40 - 1 && 0 <= x52 - 1 && x40 = x44 && x41 = x45 && x42 = x46 Arcs: (1) -> (6) (2) -> (1), (5), (7), (9), (10), (12), (13) (3) -> (2), (3) (4) -> (3) (5) -> (4), (8), (11) (6) -> (5), (9), (10), (12), (13) (7) -> (6) (8) -> (1), (7) (9) -> (8) (10) -> (8) (11) -> (1), (7) (12) -> (8), (11) (13) -> (8), (11) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f165_0_main_GE'(x12:0, x13:0, x14:0, x15:0) -> f319_0_main_GE(x16:0, x13:0, 0, x14:0) :|: x13:0 - 3 * x21:0 <= 2 && x13:0 - 5 * x20:0 <= 4 && x13:0 - 2 * x22:0 <= 1 && x13:0 - 2 * x22:0 >= 0 && x16:0 > 0 && x12:0 > 0 && x16:0 <= x12:0 && x14:0 - 1 >= x13:0 && x13:0 - 2 * x22:0 = 1 && x13:0 - 3 * x21:0 >= 1 && x13:0 - 5 * x20:0 >= 1 f165_0_main_GE'(x78:0, x79:0, x80:0, x81:0) -> f165_0_main_GE(x82:0, x79:0 + 1, x80:0, x85:0) :|: x79:0 - 2 * x86:0 <= 1 && x79:0 - 2 * x86:0 >= 0 && x82:0 > 0 && x78:0 > 0 && x82:0 <= x78:0 && x79:0 - 2 * x86:0 = 0 && x80:0 > 0 && x80:0 - 1 >= x79:0 f165_0_main_GE(x120:0, x122:0, x123:0, x124:0) -> f165_0_main_GE'(x120:0, x122:0, x123:0, x131:0) :|: x122:0 - 2 * x134:0 = 0 && x120:0 > 0 && x123:0 > 0 && x123:0 - 1 >= x122:0 f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, x32:0 + 1, x34:0, x39:0) :|: x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0 f165_0_main_GE(x4:0, x1:0, x2:0, x3:0) -> f165_0_main_GE'(x4:0, x1:0, x2:0, x7:0) :|: x4:0 > 0 && x11:0 > 0 && x4:0 >= x11:0 && x1:0 - 3 * x10:0 >= 1 && x1:0 - 5 * x9:0 >= 1 && x2:0 - 1 >= x1:0 && x1:0 - 2 * x8:0 = 1 f165_0_main_GE(x40:0, x41:0, x42:0, x43:0) -> f165_0_main_GE'(x40:0, x41:0, x42:0, x47:0) :|: x40:0 > 0 && x52:0 > 0 && x52:0 <= x40:0 && x41:0 - 5 * x50:0 = 0 && x41:0 - 3 * x49:0 >= 1 && x41:0 - 2 * x48:0 = 1 && x42:0 > 0 && x42:0 - 1 >= x41:0 f165_0_main_GE'(x53:0, x55:0, x56:0, x57:0) -> f165_0_main_GE(x58:0, x55:0 + 1, x56:0, x61:0) :|: x55:0 - 5 * x65:0 <= 4 && x55:0 - 5 * x65:0 >= 0 && x55:0 - 3 * x62:0 <= 2 && x55:0 - 2 * x63:0 <= 1 && x55:0 - 2 * x63:0 >= 0 && x58:0 > 0 && x53:0 > 0 && x58:0 <= x53:0 && x55:0 - 5 * x65:0 = 0 && x55:0 - 2 * x63:0 = 1 && x56:0 > 0 && x56:0 - 1 >= x55:0 && x55:0 - 3 * x62:0 >= 1 f165_0_main_GE(x203:0, x204:0, x205:0, x206:0) -> f165_0_main_GE'(x203:0, x204:0, x205:0, x212:0) :|: x204:0 - 3 * x214:0 = 0 && x203:0 > 0 && x204:0 - 2 * x213:0 = 1 && x205:0 > 0 && x205:0 - 1 >= x204:0 f165_0_main_GE(x266:0, x267:0, x268:0, x269:0) -> f165_0_main_GE'(x266:0, x267:0, x268:0, x273:0) :|: x267:0 - 5 * x276:0 = 0 && x266:0 > 0 && x267:0 - 3 * x275:0 >= 1 && x267:0 - 2 * x274:0 = 1 && x268:0 > 0 && x268:0 - 1 >= x267:0 f165_0_main_GE(x67:0, x68:0, x70:0, x71:0) -> f165_0_main_GE'(x67:0, x68:0, x70:0, x75:0) :|: x67:0 > 0 && x77:0 > 0 && x77:0 <= x67:0 && x68:0 - 2 * x76:0 = 0 && x70:0 > 0 && x70:0 - 1 >= x68:0 f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, x25:0 + 1, x26:0) :|: x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0 f165_0_main_GE'(x105:0, x106:0, x107:0, x108:0) -> f165_0_main_GE(x112:0, x106:0 + 1, x107:0, x117:0) :|: x106:0 - 3 * x119:0 <= 2 && x106:0 - 3 * x119:0 >= 0 && x106:0 - 2 * x118:0 <= 1 && x106:0 - 2 * x118:0 >= 0 && x112:0 > 0 && x105:0 > 0 && x112:0 <= x105:0 && x106:0 - 3 * x119:0 = 0 && x106:0 - 2 * x118:0 = 1 && x107:0 > 0 && x107:0 - 1 >= x106:0 f165_0_main_GE(x87:0, x88:0, x90:0, x91:0) -> f165_0_main_GE'(x87:0, x88:0, x90:0, x95:0) :|: x87:0 > 0 && x100:0 > 0 && x87:0 >= x100:0 && x88:0 - 3 * x99:0 = 0 && x88:0 - 2 * x98:0 = 1 && x90:0 > 0 && x90:0 - 1 >= x88:0 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f165_0_main_GE'(x1, x2, x3, x4) -> f165_0_main_GE'(x1, x2, x3) f165_0_main_GE(x1, x2, x3, x4) -> f165_0_main_GE(x1, x2, x3) ---------------------------------------- (9) Obligation: Rules: f165_0_main_GE'(x12:0, x13:0, x14:0) -> f319_0_main_GE(x16:0, x13:0, 0, x14:0) :|: x13:0 - 3 * x21:0 <= 2 && x13:0 - 5 * x20:0 <= 4 && x13:0 - 2 * x22:0 <= 1 && x13:0 - 2 * x22:0 >= 0 && x16:0 > 0 && x12:0 > 0 && x16:0 <= x12:0 && x14:0 - 1 >= x13:0 && x13:0 - 2 * x22:0 = 1 && x13:0 - 3 * x21:0 >= 1 && x13:0 - 5 * x20:0 >= 1 f165_0_main_GE'(x78:0, x79:0, x80:0) -> f165_0_main_GE(x82:0, x79:0 + 1, x80:0) :|: x79:0 - 2 * x86:0 <= 1 && x79:0 - 2 * x86:0 >= 0 && x82:0 > 0 && x78:0 > 0 && x82:0 <= x78:0 && x79:0 - 2 * x86:0 = 0 && x80:0 > 0 && x80:0 - 1 >= x79:0 f165_0_main_GE(x120:0, x122:0, x123:0) -> f165_0_main_GE'(x120:0, x122:0, x123:0) :|: x122:0 - 2 * x134:0 = 0 && x120:0 > 0 && x123:0 > 0 && x123:0 - 1 >= x122:0 f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, x32:0 + 1, x34:0) :|: x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0 f165_0_main_GE(x4:0, x1:0, x2:0) -> f165_0_main_GE'(x4:0, x1:0, x2:0) :|: x4:0 > 0 && x11:0 > 0 && x4:0 >= x11:0 && x1:0 - 3 * x10:0 >= 1 && x1:0 - 5 * x9:0 >= 1 && x2:0 - 1 >= x1:0 && x1:0 - 2 * x8:0 = 1 f165_0_main_GE(x40:0, x41:0, x42:0) -> f165_0_main_GE'(x40:0, x41:0, x42:0) :|: x40:0 > 0 && x52:0 > 0 && x52:0 <= x40:0 && x41:0 - 5 * x50:0 = 0 && x41:0 - 3 * x49:0 >= 1 && x41:0 - 2 * x48:0 = 1 && x42:0 > 0 && x42:0 - 1 >= x41:0 f165_0_main_GE'(x53:0, x55:0, x56:0) -> f165_0_main_GE(x58:0, x55:0 + 1, x56:0) :|: x55:0 - 5 * x65:0 <= 4 && x55:0 - 5 * x65:0 >= 0 && x55:0 - 3 * x62:0 <= 2 && x55:0 - 2 * x63:0 <= 1 && x55:0 - 2 * x63:0 >= 0 && x58:0 > 0 && x53:0 > 0 && x58:0 <= x53:0 && x55:0 - 5 * x65:0 = 0 && x55:0 - 2 * x63:0 = 1 && x56:0 > 0 && x56:0 - 1 >= x55:0 && x55:0 - 3 * x62:0 >= 1 f165_0_main_GE(x203:0, x204:0, x205:0) -> f165_0_main_GE'(x203:0, x204:0, x205:0) :|: x204:0 - 3 * x214:0 = 0 && x203:0 > 0 && x204:0 - 2 * x213:0 = 1 && x205:0 > 0 && x205:0 - 1 >= x204:0 f165_0_main_GE(x266:0, x267:0, x268:0) -> f165_0_main_GE'(x266:0, x267:0, x268:0) :|: x267:0 - 5 * x276:0 = 0 && x266:0 > 0 && x267:0 - 3 * x275:0 >= 1 && x267:0 - 2 * x274:0 = 1 && x268:0 > 0 && x268:0 - 1 >= x267:0 f165_0_main_GE(x67:0, x68:0, x70:0) -> f165_0_main_GE'(x67:0, x68:0, x70:0) :|: x67:0 > 0 && x77:0 > 0 && x77:0 <= x67:0 && x68:0 - 2 * x76:0 = 0 && x70:0 > 0 && x70:0 - 1 >= x68:0 f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, x25:0 + 1, x26:0) :|: x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0 f165_0_main_GE'(x105:0, x106:0, x107:0) -> f165_0_main_GE(x112:0, x106:0 + 1, x107:0) :|: x106:0 - 3 * x119:0 <= 2 && x106:0 - 3 * x119:0 >= 0 && x106:0 - 2 * x118:0 <= 1 && x106:0 - 2 * x118:0 >= 0 && x112:0 > 0 && x105:0 > 0 && x112:0 <= x105:0 && x106:0 - 3 * x119:0 = 0 && x106:0 - 2 * x118:0 = 1 && x107:0 > 0 && x107:0 - 1 >= x106:0 f165_0_main_GE(x87:0, x88:0, x90:0) -> f165_0_main_GE'(x87:0, x88:0, x90:0) :|: x87:0 > 0 && x100:0 > 0 && x87:0 >= x100:0 && x88:0 - 3 * x99:0 = 0 && x88:0 - 2 * x98:0 = 1 && x90:0 > 0 && x90:0 - 1 >= x88:0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f165_0_main_GE'(INTEGER, INTEGER, INTEGER) f319_0_main_GE(INTEGER, VARIABLE, VARIABLE, VARIABLE) f165_0_main_GE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: f165_0_main_GE'(x12:0, x13:0, x14:0) -> f319_0_main_GE(x16:0, x13:0, c, x14:0) :|: c = 0 && (x13:0 - 3 * x21:0 <= 2 && x13:0 - 5 * x20:0 <= 4 && x13:0 - 2 * x22:0 <= 1 && x13:0 - 2 * x22:0 >= 0 && x16:0 > 0 && x12:0 > 0 && x16:0 <= x12:0 && x14:0 - 1 >= x13:0 && x13:0 - 2 * x22:0 = 1 && x13:0 - 3 * x21:0 >= 1 && x13:0 - 5 * x20:0 >= 1) f165_0_main_GE'(x78:0, x79:0, x80:0) -> f165_0_main_GE(x82:0, c1, x80:0) :|: c1 = x79:0 + 1 && (x79:0 - 2 * x86:0 <= 1 && x79:0 - 2 * x86:0 >= 0 && x82:0 > 0 && x78:0 > 0 && x82:0 <= x78:0 && x79:0 - 2 * x86:0 = 0 && x80:0 > 0 && x80:0 - 1 >= x79:0) f165_0_main_GE(x120:0, x122:0, x123:0) -> f165_0_main_GE'(x120:0, x122:0, x123:0) :|: x122:0 - 2 * x134:0 = 0 && x120:0 > 0 && x123:0 > 0 && x123:0 - 1 >= x122:0 f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, c2, x34:0) :|: c2 = x32:0 + 1 && (x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0) f165_0_main_GE(x4:0, x1:0, x2:0) -> f165_0_main_GE'(x4:0, x1:0, x2:0) :|: x4:0 > 0 && x11:0 > 0 && x4:0 >= x11:0 && x1:0 - 3 * x10:0 >= 1 && x1:0 - 5 * x9:0 >= 1 && x2:0 - 1 >= x1:0 && x1:0 - 2 * x8:0 = 1 f165_0_main_GE(x40:0, x41:0, x42:0) -> f165_0_main_GE'(x40:0, x41:0, x42:0) :|: x40:0 > 0 && x52:0 > 0 && x52:0 <= x40:0 && x41:0 - 5 * x50:0 = 0 && x41:0 - 3 * x49:0 >= 1 && x41:0 - 2 * x48:0 = 1 && x42:0 > 0 && x42:0 - 1 >= x41:0 f165_0_main_GE'(x53:0, x55:0, x56:0) -> f165_0_main_GE(x58:0, c3, x56:0) :|: c3 = x55:0 + 1 && (x55:0 - 5 * x65:0 <= 4 && x55:0 - 5 * x65:0 >= 0 && x55:0 - 3 * x62:0 <= 2 && x55:0 - 2 * x63:0 <= 1 && x55:0 - 2 * x63:0 >= 0 && x58:0 > 0 && x53:0 > 0 && x58:0 <= x53:0 && x55:0 - 5 * x65:0 = 0 && x55:0 - 2 * x63:0 = 1 && x56:0 > 0 && x56:0 - 1 >= x55:0 && x55:0 - 3 * x62:0 >= 1) f165_0_main_GE(x203:0, x204:0, x205:0) -> f165_0_main_GE'(x203:0, x204:0, x205:0) :|: x204:0 - 3 * x214:0 = 0 && x203:0 > 0 && x204:0 - 2 * x213:0 = 1 && x205:0 > 0 && x205:0 - 1 >= x204:0 f165_0_main_GE(x266:0, x267:0, x268:0) -> f165_0_main_GE'(x266:0, x267:0, x268:0) :|: x267:0 - 5 * x276:0 = 0 && x266:0 > 0 && x267:0 - 3 * x275:0 >= 1 && x267:0 - 2 * x274:0 = 1 && x268:0 > 0 && x268:0 - 1 >= x267:0 f165_0_main_GE(x67:0, x68:0, x70:0) -> f165_0_main_GE'(x67:0, x68:0, x70:0) :|: x67:0 > 0 && x77:0 > 0 && x77:0 <= x67:0 && x68:0 - 2 * x76:0 = 0 && x70:0 > 0 && x70:0 - 1 >= x68:0 f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, c4, x26:0) :|: c4 = x25:0 + 1 && (x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0) f165_0_main_GE'(x105:0, x106:0, x107:0) -> f165_0_main_GE(x112:0, c5, x107:0) :|: c5 = x106:0 + 1 && (x106:0 - 3 * x119:0 <= 2 && x106:0 - 3 * x119:0 >= 0 && x106:0 - 2 * x118:0 <= 1 && x106:0 - 2 * x118:0 >= 0 && x112:0 > 0 && x105:0 > 0 && x112:0 <= x105:0 && x106:0 - 3 * x119:0 = 0 && x106:0 - 2 * x118:0 = 1 && x107:0 > 0 && x107:0 - 1 >= x106:0) f165_0_main_GE(x87:0, x88:0, x90:0) -> f165_0_main_GE'(x87:0, x88:0, x90:0) :|: x87:0 > 0 && x100:0 > 0 && x87:0 >= x100:0 && x88:0 - 3 * x99:0 = 0 && x88:0 - 2 * x98:0 = 1 && x90:0 > 0 && x90:0 - 1 >= x88:0 ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f165_0_main_GE' ] = 3*f165_0_main_GE'_3 + -3*f165_0_main_GE'_2 [ f319_0_main_GE ] = -3*f319_0_main_GE_2 + 3*f319_0_main_GE_4 + -1 [ f165_0_main_GE ] = 3*f165_0_main_GE_3 + -3*f165_0_main_GE_2 + 1 The following rules are decreasing: f165_0_main_GE'(x12:0, x13:0, x14:0) -> f319_0_main_GE(x16:0, x13:0, c, x14:0) :|: c = 0 && (x13:0 - 3 * x21:0 <= 2 && x13:0 - 5 * x20:0 <= 4 && x13:0 - 2 * x22:0 <= 1 && x13:0 - 2 * x22:0 >= 0 && x16:0 > 0 && x12:0 > 0 && x16:0 <= x12:0 && x14:0 - 1 >= x13:0 && x13:0 - 2 * x22:0 = 1 && x13:0 - 3 * x21:0 >= 1 && x13:0 - 5 * x20:0 >= 1) f165_0_main_GE'(x78:0, x79:0, x80:0) -> f165_0_main_GE(x82:0, c1, x80:0) :|: c1 = x79:0 + 1 && (x79:0 - 2 * x86:0 <= 1 && x79:0 - 2 * x86:0 >= 0 && x82:0 > 0 && x78:0 > 0 && x82:0 <= x78:0 && x79:0 - 2 * x86:0 = 0 && x80:0 > 0 && x80:0 - 1 >= x79:0) f165_0_main_GE(x120:0, x122:0, x123:0) -> f165_0_main_GE'(x120:0, x122:0, x123:0) :|: x122:0 - 2 * x134:0 = 0 && x120:0 > 0 && x123:0 > 0 && x123:0 - 1 >= x122:0 f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, c2, x34:0) :|: c2 = x32:0 + 1 && (x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0) f165_0_main_GE(x4:0, x1:0, x2:0) -> f165_0_main_GE'(x4:0, x1:0, x2:0) :|: x4:0 > 0 && x11:0 > 0 && x4:0 >= x11:0 && x1:0 - 3 * x10:0 >= 1 && x1:0 - 5 * x9:0 >= 1 && x2:0 - 1 >= x1:0 && x1:0 - 2 * x8:0 = 1 f165_0_main_GE(x40:0, x41:0, x42:0) -> f165_0_main_GE'(x40:0, x41:0, x42:0) :|: x40:0 > 0 && x52:0 > 0 && x52:0 <= x40:0 && x41:0 - 5 * x50:0 = 0 && x41:0 - 3 * x49:0 >= 1 && x41:0 - 2 * x48:0 = 1 && x42:0 > 0 && x42:0 - 1 >= x41:0 f165_0_main_GE'(x53:0, x55:0, x56:0) -> f165_0_main_GE(x58:0, c3, x56:0) :|: c3 = x55:0 + 1 && (x55:0 - 5 * x65:0 <= 4 && x55:0 - 5 * x65:0 >= 0 && x55:0 - 3 * x62:0 <= 2 && x55:0 - 2 * x63:0 <= 1 && x55:0 - 2 * x63:0 >= 0 && x58:0 > 0 && x53:0 > 0 && x58:0 <= x53:0 && x55:0 - 5 * x65:0 = 0 && x55:0 - 2 * x63:0 = 1 && x56:0 > 0 && x56:0 - 1 >= x55:0 && x55:0 - 3 * x62:0 >= 1) f165_0_main_GE(x203:0, x204:0, x205:0) -> f165_0_main_GE'(x203:0, x204:0, x205:0) :|: x204:0 - 3 * x214:0 = 0 && x203:0 > 0 && x204:0 - 2 * x213:0 = 1 && x205:0 > 0 && x205:0 - 1 >= x204:0 f165_0_main_GE(x266:0, x267:0, x268:0) -> f165_0_main_GE'(x266:0, x267:0, x268:0) :|: x267:0 - 5 * x276:0 = 0 && x266:0 > 0 && x267:0 - 3 * x275:0 >= 1 && x267:0 - 2 * x274:0 = 1 && x268:0 > 0 && x268:0 - 1 >= x267:0 f165_0_main_GE(x67:0, x68:0, x70:0) -> f165_0_main_GE'(x67:0, x68:0, x70:0) :|: x67:0 > 0 && x77:0 > 0 && x77:0 <= x67:0 && x68:0 - 2 * x76:0 = 0 && x70:0 > 0 && x70:0 - 1 >= x68:0 f165_0_main_GE'(x105:0, x106:0, x107:0) -> f165_0_main_GE(x112:0, c5, x107:0) :|: c5 = x106:0 + 1 && (x106:0 - 3 * x119:0 <= 2 && x106:0 - 3 * x119:0 >= 0 && x106:0 - 2 * x118:0 <= 1 && x106:0 - 2 * x118:0 >= 0 && x112:0 > 0 && x105:0 > 0 && x112:0 <= x105:0 && x106:0 - 3 * x119:0 = 0 && x106:0 - 2 * x118:0 = 1 && x107:0 > 0 && x107:0 - 1 >= x106:0) f165_0_main_GE(x87:0, x88:0, x90:0) -> f165_0_main_GE'(x87:0, x88:0, x90:0) :|: x87:0 > 0 && x100:0 > 0 && x87:0 >= x100:0 && x88:0 - 3 * x99:0 = 0 && x88:0 - 2 * x98:0 = 1 && x90:0 > 0 && x90:0 - 1 >= x88:0 The following rules are bounded: f165_0_main_GE'(x78:0, x79:0, x80:0) -> f165_0_main_GE(x82:0, c1, x80:0) :|: c1 = x79:0 + 1 && (x79:0 - 2 * x86:0 <= 1 && x79:0 - 2 * x86:0 >= 0 && x82:0 > 0 && x78:0 > 0 && x82:0 <= x78:0 && x79:0 - 2 * x86:0 = 0 && x80:0 > 0 && x80:0 - 1 >= x79:0) f165_0_main_GE(x120:0, x122:0, x123:0) -> f165_0_main_GE'(x120:0, x122:0, x123:0) :|: x122:0 - 2 * x134:0 = 0 && x120:0 > 0 && x123:0 > 0 && x123:0 - 1 >= x122:0 f165_0_main_GE(x4:0, x1:0, x2:0) -> f165_0_main_GE'(x4:0, x1:0, x2:0) :|: x4:0 > 0 && x11:0 > 0 && x4:0 >= x11:0 && x1:0 - 3 * x10:0 >= 1 && x1:0 - 5 * x9:0 >= 1 && x2:0 - 1 >= x1:0 && x1:0 - 2 * x8:0 = 1 f165_0_main_GE(x40:0, x41:0, x42:0) -> f165_0_main_GE'(x40:0, x41:0, x42:0) :|: x40:0 > 0 && x52:0 > 0 && x52:0 <= x40:0 && x41:0 - 5 * x50:0 = 0 && x41:0 - 3 * x49:0 >= 1 && x41:0 - 2 * x48:0 = 1 && x42:0 > 0 && x42:0 - 1 >= x41:0 f165_0_main_GE'(x53:0, x55:0, x56:0) -> f165_0_main_GE(x58:0, c3, x56:0) :|: c3 = x55:0 + 1 && (x55:0 - 5 * x65:0 <= 4 && x55:0 - 5 * x65:0 >= 0 && x55:0 - 3 * x62:0 <= 2 && x55:0 - 2 * x63:0 <= 1 && x55:0 - 2 * x63:0 >= 0 && x58:0 > 0 && x53:0 > 0 && x58:0 <= x53:0 && x55:0 - 5 * x65:0 = 0 && x55:0 - 2 * x63:0 = 1 && x56:0 > 0 && x56:0 - 1 >= x55:0 && x55:0 - 3 * x62:0 >= 1) f165_0_main_GE(x203:0, x204:0, x205:0) -> f165_0_main_GE'(x203:0, x204:0, x205:0) :|: x204:0 - 3 * x214:0 = 0 && x203:0 > 0 && x204:0 - 2 * x213:0 = 1 && x205:0 > 0 && x205:0 - 1 >= x204:0 f165_0_main_GE(x266:0, x267:0, x268:0) -> f165_0_main_GE'(x266:0, x267:0, x268:0) :|: x267:0 - 5 * x276:0 = 0 && x266:0 > 0 && x267:0 - 3 * x275:0 >= 1 && x267:0 - 2 * x274:0 = 1 && x268:0 > 0 && x268:0 - 1 >= x267:0 f165_0_main_GE(x67:0, x68:0, x70:0) -> f165_0_main_GE'(x67:0, x68:0, x70:0) :|: x67:0 > 0 && x77:0 > 0 && x77:0 <= x67:0 && x68:0 - 2 * x76:0 = 0 && x70:0 > 0 && x70:0 - 1 >= x68:0 f165_0_main_GE'(x105:0, x106:0, x107:0) -> f165_0_main_GE(x112:0, c5, x107:0) :|: c5 = x106:0 + 1 && (x106:0 - 3 * x119:0 <= 2 && x106:0 - 3 * x119:0 >= 0 && x106:0 - 2 * x118:0 <= 1 && x106:0 - 2 * x118:0 >= 0 && x112:0 > 0 && x105:0 > 0 && x112:0 <= x105:0 && x106:0 - 3 * x119:0 = 0 && x106:0 - 2 * x118:0 = 1 && x107:0 > 0 && x107:0 - 1 >= x106:0) ---------------------------------------- (13) Obligation: Rules: f165_0_main_GE'(x12:0, x13:0, x14:0) -> f319_0_main_GE(x16:0, x13:0, c, x14:0) :|: c = 0 && (x13:0 - 3 * x21:0 <= 2 && x13:0 - 5 * x20:0 <= 4 && x13:0 - 2 * x22:0 <= 1 && x13:0 - 2 * x22:0 >= 0 && x16:0 > 0 && x12:0 > 0 && x16:0 <= x12:0 && x14:0 - 1 >= x13:0 && x13:0 - 2 * x22:0 = 1 && x13:0 - 3 * x21:0 >= 1 && x13:0 - 5 * x20:0 >= 1) f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, c2, x34:0) :|: c2 = x32:0 + 1 && (x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0) f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, c4, x26:0) :|: c4 = x25:0 + 1 && (x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0) f165_0_main_GE(x87:0, x88:0, x90:0) -> f165_0_main_GE'(x87:0, x88:0, x90:0) :|: x87:0 > 0 && x100:0 > 0 && x87:0 >= x100:0 && x88:0 - 3 * x99:0 = 0 && x88:0 - 2 * x98:0 = 1 && x90:0 > 0 && x90:0 - 1 >= x88:0 ---------------------------------------- (14) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f165_0_main_GE' ] = 3*f165_0_main_GE'_3 + -3*f165_0_main_GE'_2 + -1 [ f319_0_main_GE ] = -3*f319_0_main_GE_2 + 3*f319_0_main_GE_4 + -2 [ f165_0_main_GE ] = 3*f165_0_main_GE_3 + -3*f165_0_main_GE_2 The following rules are decreasing: f165_0_main_GE'(x12:0, x13:0, x14:0) -> f319_0_main_GE(x16:0, x13:0, c, x14:0) :|: c = 0 && (x13:0 - 3 * x21:0 <= 2 && x13:0 - 5 * x20:0 <= 4 && x13:0 - 2 * x22:0 <= 1 && x13:0 - 2 * x22:0 >= 0 && x16:0 > 0 && x12:0 > 0 && x16:0 <= x12:0 && x14:0 - 1 >= x13:0 && x13:0 - 2 * x22:0 = 1 && x13:0 - 3 * x21:0 >= 1 && x13:0 - 5 * x20:0 >= 1) f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, c2, x34:0) :|: c2 = x32:0 + 1 && (x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0) f165_0_main_GE(x87:0, x88:0, x90:0) -> f165_0_main_GE'(x87:0, x88:0, x90:0) :|: x87:0 > 0 && x100:0 > 0 && x87:0 >= x100:0 && x88:0 - 3 * x99:0 = 0 && x88:0 - 2 * x98:0 = 1 && x90:0 > 0 && x90:0 - 1 >= x88:0 The following rules are bounded: f165_0_main_GE'(x12:0, x13:0, x14:0) -> f319_0_main_GE(x16:0, x13:0, c, x14:0) :|: c = 0 && (x13:0 - 3 * x21:0 <= 2 && x13:0 - 5 * x20:0 <= 4 && x13:0 - 2 * x22:0 <= 1 && x13:0 - 2 * x22:0 >= 0 && x16:0 > 0 && x12:0 > 0 && x16:0 <= x12:0 && x14:0 - 1 >= x13:0 && x13:0 - 2 * x22:0 = 1 && x13:0 - 3 * x21:0 >= 1 && x13:0 - 5 * x20:0 >= 1) f165_0_main_GE(x87:0, x88:0, x90:0) -> f165_0_main_GE'(x87:0, x88:0, x90:0) :|: x87:0 > 0 && x100:0 > 0 && x87:0 >= x100:0 && x88:0 - 3 * x99:0 = 0 && x88:0 - 2 * x98:0 = 1 && x90:0 > 0 && x90:0 - 1 >= x88:0 ---------------------------------------- (15) Obligation: Rules: f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, c2, x34:0) :|: c2 = x32:0 + 1 && (x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0) f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, c4, x26:0) :|: c4 = x25:0 + 1 && (x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0) ---------------------------------------- (16) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f319_0_main_GE ] = 0 [ f165_0_main_GE ] = -1*f165_0_main_GE_1 The following rules are decreasing: f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, c2, x34:0) :|: c2 = x32:0 + 1 && (x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0) The following rules are bounded: f319_0_main_GE(x31:0, x32:0, x33:0, x34:0) -> f165_0_main_GE(x35:0, c2, x34:0) :|: c2 = x32:0 + 1 && (x33:0 > 99 && x34:0 > -1 && x35:0 <= x31:0 && x35:0 > 0 && x31:0 > 0) f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, c4, x26:0) :|: c4 = x25:0 + 1 && (x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0) ---------------------------------------- (17) Obligation: Rules: f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, c4, x26:0) :|: c4 = x25:0 + 1 && (x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0) ---------------------------------------- (18) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f319_0_main_GE ] = -1*f319_0_main_GE_3 The following rules are decreasing: f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, c4, x26:0) :|: c4 = x25:0 + 1 && (x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0) The following rules are bounded: f319_0_main_GE(x23:0, x24:0, x25:0, x26:0) -> f319_0_main_GE(x27:0, x24:0, c4, x26:0) :|: c4 = x25:0 + 1 && (x25:0 < 100 && x27:0 <= x23:0 && x27:0 > 0 && x23:0 > 0) ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f544_0_exp_GT(x296, x297, x298, x299) -> f544_0_exp_GT'(x300, x301, x302, x303) :|: 0 <= x296 - 1 && -1 <= x298 - 1 && x297 <= x298 && 0 <= x304 - 1 && x296 = x300 && x297 = x301 && x298 = x302 (2) f544_0_exp_GT'(x305, x306, x307, x308) -> f544_0_exp_GT(x309, x310, x311, x312) :|: 0 <= x305 - 1 && -1 <= x307 - 1 && 0 <= x313 - 1 && x306 <= x307 && x314 - x313 * x315 <= x313 - 1 && 0 <= x314 - x313 * x315 && x305 = x309 && x306 + 1 = x310 && x307 = x311 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f544_0_exp_GT(x296:0, x297:0, x298:0, x299:0) -> f544_0_exp_GT(x296:0, x297:0 + 1, x298:0, x312:0) :|: x314:0 - x313:0 * x315:0 >= 0 && x304:0 > 0 && x314:0 - x313:0 * x315:0 <= x313:0 - 1 && x298:0 >= x297:0 && x313:0 > 0 && x298:0 > -1 && x296:0 > 0 ---------------------------------------- (23) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f544_0_exp_GT(x1, x2, x3, x4) -> f544_0_exp_GT(x1, x2, x3) ---------------------------------------- (24) Obligation: Rules: f544_0_exp_GT(x296:0, x297:0, x298:0) -> f544_0_exp_GT(x296:0, x297:0 + 1, x298:0) :|: x314:0 - x313:0 * x315:0 >= 0 && x304:0 > 0 && x314:0 - x313:0 * x315:0 <= x313:0 - 1 && x298:0 >= x297:0 && x313:0 > 0 && x298:0 > -1 && x296:0 > 0 ---------------------------------------- (25) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f544_0_exp_GT(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (26) Obligation: Rules: f544_0_exp_GT(x296:0, x297:0, x298:0) -> f544_0_exp_GT(x296:0, c, x298:0) :|: c = x297:0 + 1 && (x314:0 - x313:0 * x315:0 >= 0 && x304:0 > 0 && x314:0 - x313:0 * x315:0 <= x313:0 - 1 && x298:0 >= x297:0 && x313:0 > 0 && x298:0 > -1 && x296:0 > 0) ---------------------------------------- (27) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f544_0_exp_GT ] = -1*f544_0_exp_GT_2 + f544_0_exp_GT_3 The following rules are decreasing: f544_0_exp_GT(x296:0, x297:0, x298:0) -> f544_0_exp_GT(x296:0, c, x298:0) :|: c = x297:0 + 1 && (x314:0 - x313:0 * x315:0 >= 0 && x304:0 > 0 && x314:0 - x313:0 * x315:0 <= x313:0 - 1 && x298:0 >= x297:0 && x313:0 > 0 && x298:0 > -1 && x296:0 > 0) The following rules are bounded: f544_0_exp_GT(x296:0, x297:0, x298:0) -> f544_0_exp_GT(x296:0, c, x298:0) :|: c = x297:0 + 1 && (x314:0 - x313:0 * x315:0 >= 0 && x304:0 > 0 && x314:0 - x313:0 * x315:0 <= x313:0 - 1 && x298:0 >= x297:0 && x313:0 > 0 && x298:0 > -1 && x296:0 > 0) ---------------------------------------- (28) YES ---------------------------------------- (29) Obligation: Termination digraph: Nodes: (1) f862_0_cos_GT(x245, x246, x247, x248) -> f862_0_cos_GT'(x249, x250, x251, x252) :|: 1 <= x245 - 1 && 0 <= x253 - 1 && 1 <= x246 - 1 && x245 <= x246 && x253 <= x245 - 1 && x245 = x249 && x246 = x250 (2) f862_0_cos_GT'(x254, x255, x256, x257) -> f862_0_cos_GT(x258, x259, x260, x261) :|: 1 <= x254 - 1 && 0 <= x262 - 1 && 1 <= x255 - 1 && x262 <= x254 - 1 && x254 <= x255 && 0 <= x254 - 2 * x262 && x254 - 2 * x262 <= 1 && x263 - x264 * x265 <= x264 - 1 && 0 <= x263 - x264 * x265 && x254 + 2 = x258 && x255 = x259 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (30) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (31) Obligation: Rules: f862_0_cos_GT(x245:0, x246:0, x247:0, x248:0) -> f862_0_cos_GT(x245:0 + 2, x246:0, x260:0, x261:0) :|: x263:0 - x264:0 * x265:0 >= 0 && x253:0 <= x245:0 - 1 && x264:0 - 1 >= x263:0 - x264:0 * x265:0 && x245:0 - 2 * x262:0 <= 1 && x253:0 > 0 && x245:0 - 2 * x262:0 >= 0 && x246:0 >= x245:0 && x262:0 <= x245:0 - 1 && x246:0 > 1 && x262:0 > 0 && x245:0 > 1 ---------------------------------------- (32) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f862_0_cos_GT(x1, x2, x3, x4) -> f862_0_cos_GT(x1, x2) ---------------------------------------- (33) Obligation: Rules: f862_0_cos_GT(x245:0, x246:0) -> f862_0_cos_GT(x245:0 + 2, x246:0) :|: x263:0 - x264:0 * x265:0 >= 0 && x253:0 <= x245:0 - 1 && x264:0 - 1 >= x263:0 - x264:0 * x265:0 && x245:0 - 2 * x262:0 <= 1 && x253:0 > 0 && x245:0 - 2 * x262:0 >= 0 && x246:0 >= x245:0 && x262:0 <= x245:0 - 1 && x246:0 > 1 && x262:0 > 0 && x245:0 > 1 ---------------------------------------- (34) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f862_0_cos_GT(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (35) Obligation: Rules: f862_0_cos_GT(x245:0, x246:0) -> f862_0_cos_GT(c, x246:0) :|: c = x245:0 + 2 && (x263:0 - x264:0 * x265:0 >= 0 && x253:0 <= x245:0 - 1 && x264:0 - 1 >= x263:0 - x264:0 * x265:0 && x245:0 - 2 * x262:0 <= 1 && x253:0 > 0 && x245:0 - 2 * x262:0 >= 0 && x246:0 >= x245:0 && x262:0 <= x245:0 - 1 && x246:0 > 1 && x262:0 > 0 && x245:0 > 1) ---------------------------------------- (36) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f862_0_cos_GT(x, x1)] = -x + x1 The following rules are decreasing: f862_0_cos_GT(x245:0, x246:0) -> f862_0_cos_GT(c, x246:0) :|: c = x245:0 + 2 && (x263:0 - x264:0 * x265:0 >= 0 && x253:0 <= x245:0 - 1 && x264:0 - 1 >= x263:0 - x264:0 * x265:0 && x245:0 - 2 * x262:0 <= 1 && x253:0 > 0 && x245:0 - 2 * x262:0 >= 0 && x246:0 >= x245:0 && x262:0 <= x245:0 - 1 && x246:0 > 1 && x262:0 > 0 && x245:0 > 1) The following rules are bounded: f862_0_cos_GT(x245:0, x246:0) -> f862_0_cos_GT(c, x246:0) :|: c = x245:0 + 2 && (x263:0 - x264:0 * x265:0 >= 0 && x253:0 <= x245:0 - 1 && x264:0 - 1 >= x263:0 - x264:0 * x265:0 && x245:0 - 2 * x262:0 <= 1 && x253:0 > 0 && x245:0 - 2 * x262:0 >= 0 && x246:0 >= x245:0 && x262:0 <= x245:0 - 1 && x246:0 > 1 && x262:0 > 0 && x245:0 > 1) ---------------------------------------- (37) YES ---------------------------------------- (38) Obligation: Termination digraph: Nodes: (1) f861_0_sin_GT(x167, x168, x173, x174) -> f861_0_sin_GT'(x175, x179, x180, x181) :|: 0 <= x185 - 1 && x167 <= x168 && x167 = x175 && x168 = x179 (2) f861_0_sin_GT'(x186, x187, x191, x192) -> f861_0_sin_GT(x193, x194, x195, x197) :|: x186 <= x187 && 0 <= x198 - 1 && 0 <= x186 - 2 * x199 && x186 - 2 * x199 <= 1 && x200 * x201 - x198 * x202 <= x198 - 1 && 0 <= x200 * x201 - x198 * x202 && x186 + 2 = x193 && x187 = x194 (3) f861_0_sin_GT(x316, x317, x318, x319) -> f861_0_sin_GT'(x320, x321, x322, x323) :|: x317 = x321 && x316 = x320 && x316 <= x317 Arcs: (1) -> (2) (2) -> (1), (3) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (39) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (40) Obligation: Rules: f861_0_sin_GT(x167:0, x168:0, x173:0, x174:0) -> f861_0_sin_GT(x167:0 + 2, x168:0, x195:0, x197:0) :|: x185:0 > 0 && x200:0 * x201:0 - x198:0 * x202:0 >= 0 && x200:0 * x201:0 - x198:0 * x202:0 <= x198:0 - 1 && x167:0 - 2 * x199:0 <= 1 && x167:0 - 2 * x199:0 >= 0 && x198:0 > 0 && x168:0 >= x167:0 f861_0_sin_GT(x, x1, x2, x3) -> f861_0_sin_GT(x + 2, x1, x4, x5) :|: x6 * x7 - x8 * x9 >= 0 && x6 * x7 - x8 * x9 <= x8 - 1 && x - 2 * x10 <= 1 && x - 2 * x10 >= 0 && x8 > 0 && x <= x1 ---------------------------------------- (41) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f861_0_sin_GT(x1, x2, x3, x4) -> f861_0_sin_GT(x1, x2) ---------------------------------------- (42) Obligation: Rules: f861_0_sin_GT(x167:0, x168:0) -> f861_0_sin_GT(x167:0 + 2, x168:0) :|: x185:0 > 0 && x200:0 * x201:0 - x198:0 * x202:0 >= 0 && x200:0 * x201:0 - x198:0 * x202:0 <= x198:0 - 1 && x167:0 - 2 * x199:0 <= 1 && x167:0 - 2 * x199:0 >= 0 && x198:0 > 0 && x168:0 >= x167:0 f861_0_sin_GT(x, x1) -> f861_0_sin_GT(x + 2, x1) :|: x6 * x7 - x8 * x9 >= 0 && x6 * x7 - x8 * x9 <= x8 - 1 && x - 2 * x10 <= 1 && x - 2 * x10 >= 0 && x8 > 0 && x <= x1 ---------------------------------------- (43) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f861_0_sin_GT(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (44) Obligation: Rules: f861_0_sin_GT(x167:0, x168:0) -> f861_0_sin_GT(c, x168:0) :|: c = x167:0 + 2 && (x185:0 > 0 && x200:0 * x201:0 - x198:0 * x202:0 >= 0 && x200:0 * x201:0 - x198:0 * x202:0 <= x198:0 - 1 && x167:0 - 2 * x199:0 <= 1 && x167:0 - 2 * x199:0 >= 0 && x198:0 > 0 && x168:0 >= x167:0) f861_0_sin_GT(x, x1) -> f861_0_sin_GT(c1, x1) :|: c1 = x + 2 && (x6 * x7 - x8 * x9 >= 0 && x6 * x7 - x8 * x9 <= x8 - 1 && x - 2 * x10 <= 1 && x - 2 * x10 >= 0 && x8 > 0 && x <= x1) ---------------------------------------- (45) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f861_0_sin_GT ] = -1/2*f861_0_sin_GT_1 + 1/2*f861_0_sin_GT_2 The following rules are decreasing: f861_0_sin_GT(x167:0, x168:0) -> f861_0_sin_GT(c, x168:0) :|: c = x167:0 + 2 && (x185:0 > 0 && x200:0 * x201:0 - x198:0 * x202:0 >= 0 && x200:0 * x201:0 - x198:0 * x202:0 <= x198:0 - 1 && x167:0 - 2 * x199:0 <= 1 && x167:0 - 2 * x199:0 >= 0 && x198:0 > 0 && x168:0 >= x167:0) f861_0_sin_GT(x, x1) -> f861_0_sin_GT(c1, x1) :|: c1 = x + 2 && (x6 * x7 - x8 * x9 >= 0 && x6 * x7 - x8 * x9 <= x8 - 1 && x - 2 * x10 <= 1 && x - 2 * x10 >= 0 && x8 > 0 && x <= x1) The following rules are bounded: f861_0_sin_GT(x167:0, x168:0) -> f861_0_sin_GT(c, x168:0) :|: c = x167:0 + 2 && (x185:0 > 0 && x200:0 * x201:0 - x198:0 * x202:0 >= 0 && x200:0 * x201:0 - x198:0 * x202:0 <= x198:0 - 1 && x167:0 - 2 * x199:0 <= 1 && x167:0 - 2 * x199:0 >= 0 && x198:0 > 0 && x168:0 >= x167:0) f861_0_sin_GT(x, x1) -> f861_0_sin_GT(c1, x1) :|: c1 = x + 2 && (x6 * x7 - x8 * x9 >= 0 && x6 * x7 - x8 * x9 <= x8 - 1 && x - 2 * x10 <= 1 && x - 2 * x10 >= 0 && x8 > 0 && x <= x1) ---------------------------------------- (46) YES ---------------------------------------- (47) Obligation: Termination digraph: Nodes: (1) f1113_0_fact_GT(x400, x401, x402, x403) -> f1113_0_fact_GT(x404, x405, x406, x407) :|: x403 = x407 && x401 + 1 = x406 && x401 + 1 = x405 && x400 * x401 = x404 && x401 = x402 && 0 <= x401 - 1 && 0 <= x400 - 1 && x401 <= x403 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (48) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (49) Obligation: Rules: f1113_0_fact_GT(x400:0, x401:0, x401:0, x403:0) -> f1113_0_fact_GT(x400:0 * x401:0, x401:0 + 1, x401:0 + 1, x403:0) :|: x400:0 > 0 && x401:0 > 0 && x403:0 >= x401:0 ---------------------------------------- (50) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1113_0_fact_GT(INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (51) Obligation: Rules: f1113_0_fact_GT(x400:0, x401:0, x401:0, x403:0) -> f1113_0_fact_GT(c, c1, c2, x403:0) :|: c2 = x401:0 + 1 && (c1 = x401:0 + 1 && c = x400:0 * x401:0) && (x400:0 > 0 && x401:0 > 0 && x403:0 >= x401:0) ---------------------------------------- (52) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1113_0_fact_GT ] = -1*f1113_0_fact_GT_3 + f1113_0_fact_GT_4 The following rules are decreasing: f1113_0_fact_GT(x400:0, x401:0, x401:0, x403:0) -> f1113_0_fact_GT(c, c1, c2, x403:0) :|: c2 = x401:0 + 1 && (c1 = x401:0 + 1 && c = x400:0 * x401:0) && (x400:0 > 0 && x401:0 > 0 && x403:0 >= x401:0) The following rules are bounded: f1113_0_fact_GT(x400:0, x401:0, x401:0, x403:0) -> f1113_0_fact_GT(c, c1, c2, x403:0) :|: c2 = x401:0 + 1 && (c1 = x401:0 + 1 && c = x400:0 * x401:0) && (x400:0 > 0 && x401:0 > 0 && x403:0 >= x401:0) ---------------------------------------- (53) YES ---------------------------------------- (54) Obligation: Termination digraph: Nodes: (1) f1011_0_power_GT(x366, x367, x368, x369) -> f1011_0_power_GT(x370, x371, x372, x373) :|: x367 = x371 && x366 + 1 = x370 && x366 <= x367 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (55) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (56) Obligation: Rules: f1011_0_power_GT(x366:0, x367:0, x368:0, x369:0) -> f1011_0_power_GT(x366:0 + 1, x367:0, x372:0, x373:0) :|: x367:0 >= x366:0 ---------------------------------------- (57) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f1011_0_power_GT(x1, x2, x3, x4) -> f1011_0_power_GT(x1, x2) ---------------------------------------- (58) Obligation: Rules: f1011_0_power_GT(x366:0, x367:0) -> f1011_0_power_GT(x366:0 + 1, x367:0) :|: x367:0 >= x366:0 ---------------------------------------- (59) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1011_0_power_GT(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (60) Obligation: Rules: f1011_0_power_GT(x366:0, x367:0) -> f1011_0_power_GT(c, x367:0) :|: c = x366:0 + 1 && x367:0 >= x366:0 ---------------------------------------- (61) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1011_0_power_GT(x, x1)] = -x + x1 The following rules are decreasing: f1011_0_power_GT(x366:0, x367:0) -> f1011_0_power_GT(c, x367:0) :|: c = x366:0 + 1 && x367:0 >= x366:0 The following rules are bounded: f1011_0_power_GT(x366:0, x367:0) -> f1011_0_power_GT(c, x367:0) :|: c = x366:0 + 1 && x367:0 >= x366:0 ---------------------------------------- (62) YES