YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 16.7 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 7 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 4 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 6 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 91 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 0 ms] (22) YES (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 2 ms] (25) IRSwT (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (27) IRSwT (28) TempFilterProof [SOUND, 18 ms] (29) IntTRS (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (31) YES (32) IRSwT (33) IntTRSCompressionProof [EQUIVALENT, 15 ms] (34) IRSwT (35) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (36) IRSwT (37) TempFilterProof [SOUND, 33 ms] (38) IntTRS (39) RankingReductionPairProof [EQUIVALENT, 0 ms] (40) YES (41) IRSwT (42) IntTRSCompressionProof [EQUIVALENT, 4 ms] (43) IRSwT (44) TempFilterProof [SOUND, 33 ms] (45) IntTRS (46) RankingReductionPairProof [EQUIVALENT, 0 ms] (47) YES ---------------------------------------- (0) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f229_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f229_0_main_GE(x, x1, x2, x3, x4, x5, x6) -> f229_0_main_GE(x7, x8, x9, x10, x11, x12, x13) :|: x2 = x9 && x1 + 1 = x8 && 0 <= x7 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x7 <= x f229_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f507_0_sort_GE(x21, x22, x23, x24, x25, x26, x27) :|: x16 = x25 && x16 - 1 = x24 && 0 = x23 && 0 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x14 - 1 && x22 <= x14 && x21 <= x14 && x16 <= x15 && -1 <= x16 - 1 && x16 - 1 <= x16 - 1 f507_0_sort_GE(x28, x29, x30, x31, x32, x33, x34) -> f507_0_sort_GE'(x35, x36, x37, x38, x39, x40, x41) :|: x30 <= x31 - 1 && x42 - x30 <= x31 - x30 - 1 && x43 <= x28 && x43 <= x29 && x44 <= x28 && x44 <= x29 && 0 <= x28 - 1 && 0 <= x29 - 1 && 0 <= x43 - 1 && 0 <= x44 - 1 && x28 = x35 && x29 = x36 && x30 = x37 && x31 = x38 && x32 = x39 f507_0_sort_GE'(x45, x46, x47, x48, x49, x50, x51) -> f507_0_sort_GE(x52, x53, x54, x55, x57, x58, x59) :|: x49 = x57 && x47 = x54 && 0 <= x47 + x48 - 2 * x55 && x47 + x48 - 2 * x55 <= 1 && 0 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x46 - 1 && 0 <= x45 - 1 && x53 <= x46 && x53 <= x45 && x52 <= x46 && x52 <= x45 && x55 - x47 <= x48 - x47 - 1 && x47 <= x48 - 1 f507_0_sort_GE(x60, x61, x62, x64, x65, x66, x67) -> f507_0_sort_GE'(x68, x69, x70, x71, x72, x73, x74) :|: x62 <= x64 - 1 && x64 - x62 <= x75 - x62 && x64 - (x75 + 1) <= x64 - x62 - 1 && x75 <= x75 + 1 - 1 && x76 <= x60 && x76 <= x61 && x77 <= x60 && x77 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x76 - 1 && 0 <= x77 - 1 && x60 = x68 && x61 = x69 && x62 = x70 && x64 = x71 && x65 = x72 f507_0_sort_GE'(x78, x79, x80, x81, x82, x83, x84) -> f507_0_sort_GE(x85, x86, x87, x88, x89, x90, x91) :|: x80 <= x81 - 1 && x81 - x80 <= x92 - x80 && x81 - (x92 + 1) <= x81 - x80 - 1 && x92 <= x92 + 1 - 1 && x85 <= x78 && x85 <= x79 && x86 <= x78 && x86 <= x79 && 0 <= x78 - 1 && 0 <= x79 - 1 && 0 <= x85 - 1 && 0 <= x86 - 1 && x80 + x81 - 2 * x92 <= 1 && 0 <= x80 + x81 - 2 * x92 && x92 + 1 = x87 && x81 = x88 && x82 = x89 f507_0_sort_GE(x93, x94, x95, x96, x97, x98, x99) -> f507_0_sort_GE'(x100, x101, x102, x103, x104, x107, x108) :|: x95 <= x96 - 1 && x109 - x95 <= x96 - x95 - 1 && x109 <= x109 + 1 - 1 && x96 - (x109 + 1) <= x96 - x95 - 1 && x110 <= x93 && x110 <= x94 && x111 <= x93 && x111 <= x94 && 0 <= x93 - 1 && 0 <= x94 - 1 && 0 <= x110 - 1 && 0 <= x111 - 1 && x93 = x100 && x94 = x101 && x95 = x102 && x96 = x103 && x97 = x104 f507_0_sort_GE'(x112, x113, x117, x118, x119, x120, x121) -> f507_0_sort_GE(x122, x123, x124, x125, x126, x127, x128) :|: x117 <= x118 - 1 && x129 - x117 <= x118 - x117 - 1 && x129 <= x129 + 1 - 1 && x118 - (x129 + 1) <= x118 - x117 - 1 && x122 <= x112 && x122 <= x113 && x123 <= x112 && x123 <= x113 && 0 <= x112 - 1 && 0 <= x113 - 1 && 0 <= x122 - 1 && 0 <= x123 - 1 && x117 + x118 - 2 * x129 <= 1 && 0 <= x117 + x118 - 2 * x129 && x129 + 1 = x124 && x118 = x125 && x119 = x126 f507_0_sort_GE(x133, x134, x135, x136, x137, x138, x139) -> f507_0_sort_GE'(x141, x142, x143, x144, x145, x149, x150) :|: x135 <= x136 - 1 && x151 - x135 <= x136 - x135 - 1 && x136 - x135 <= x136 - (x151 + 1) && x152 <= x133 && x152 <= x134 && 0 <= x133 - 1 && 0 <= x134 - 1 && 0 <= x152 - 1 && x133 = x141 && x134 = x142 && x135 = x143 && x136 = x144 && x137 = x145 f507_0_sort_GE'(x153, x154, x155, x157, x158, x159, x160) -> f1503_0_sort_InvokeMethod(x161, x164, x165, x166, x167, x168, x169) :|: x158 = x167 && x157 = x164 && x155 = x161 && 0 <= x155 + x157 - 2 * x165 && x155 + x157 - 2 * x165 <= 1 && 0 <= x166 - 1 && 0 <= x154 - 1 && 0 <= x153 - 1 && x166 <= x154 && x166 <= x153 && x157 - x155 <= x157 - (x165 + 1) && x165 - x155 <= x157 - x155 - 1 && x155 <= x157 - 1 f507_0_sort_GE(x170, x171, x172, x173, x174, x175, x178) -> f507_0_sort_GE'(x179, x180, x181, x182, x183, x184, x185) :|: x172 <= x173 - 1 && x186 - x172 <= x173 - x172 - 1 && x186 <= x186 + 1 - 1 && x173 - (x186 + 1) <= x173 - x172 - 1 && x187 <= x170 && x187 <= x171 && 0 <= x170 - 1 && 0 <= x171 - 1 && 0 <= x187 - 1 && x170 = x179 && x171 = x180 && x172 = x181 && x173 = x182 && x174 = x183 f507_0_sort_GE'(x188, x189, x192, x193, x194, x195, x196) -> f1503_0_sort_InvokeMethod(x197, x198, x199, x200, x201, x202, x203) :|: x194 = x201 && x193 = x198 && x192 = x197 && 0 <= x192 + x193 - 2 * x199 && x192 + x193 - 2 * x199 <= 1 && 0 <= x200 - 1 && 0 <= x189 - 1 && 0 <= x188 - 1 && x200 <= x189 && x200 <= x188 && x193 - (x199 + 1) <= x193 - x192 - 1 && x199 <= x199 + 1 - 1 && x199 - x192 <= x193 - x192 - 1 && x192 <= x193 - 1 f507_0_sort_GE(x206, x207, x208, x209, x210, x211, x212) -> f507_0_sort_GE'(x213, x214, x215, x216, x217, x218, x219) :|: x208 <= x209 - 1 && x209 - x208 <= x220 - x208 && x209 - x208 <= x209 - (x220 + 1) && -1 <= x210 - 1 && x221 <= x206 && x221 <= x207 && 0 <= x206 - 1 && 0 <= x207 - 1 && 0 <= x221 - 1 && x206 = x213 && x207 = x214 && x208 = x215 && x209 = x216 && x210 = x217 f507_0_sort_GE'(x222, x223, x224, x225, x226, x227, x228) -> f757_0_merge_GT(x229, x230, x231, x232, x233, x234, x235) :|: x226 = x235 && x224 = x233 && x224 = x232 && x225 = x230 && x224 = x229 && 0 <= x224 + x225 - 2 * x234 && x224 + x225 - 2 * x234 <= 1 && 0 <= x231 - 1 && 0 <= x223 - 1 && 0 <= x222 - 1 && x231 <= x223 && x231 <= x222 && -1 <= x226 - 1 && x225 - x224 <= x225 - (x234 + 1) && x225 - x224 <= x234 - x224 && x224 <= x225 - 1 f507_0_sort_GE(x236, x237, x238, x239, x240, x241, x242) -> f507_0_sort_GE'(x243, x244, x245, x246, x247, x248, x249) :|: x238 <= x239 - 1 && x239 - x238 <= x250 - x238 && x239 - (x250 + 1) <= x239 - x238 - 1 && x250 <= x250 + 1 - 1 && -1 <= x240 - 1 && x251 <= x236 && x251 <= x237 && 0 <= x236 - 1 && 0 <= x237 - 1 && 0 <= x251 - 1 && x236 = x243 && x237 = x244 && x238 = x245 && x239 = x246 && x240 = x247 f507_0_sort_GE'(x252, x253, x254, x255, x256, x257, x258) -> f757_0_merge_GT(x259, x260, x261, x262, x263, x264, x265) :|: x256 = x265 && x254 = x263 && x254 = x262 && x255 = x260 && x254 = x259 && 0 <= x254 + x255 - 2 * x264 && x254 + x255 - 2 * x264 <= 1 && 0 <= x261 - 1 && 0 <= x253 - 1 && 0 <= x252 - 1 && x261 <= x253 && x261 <= x252 && -1 <= x256 - 1 && x264 <= x264 + 1 - 1 && x255 - (x264 + 1) <= x255 - x254 - 1 && x255 - x254 <= x264 - x254 && x254 <= x255 - 1 f1503_0_sort_InvokeMethod(x266, x267, x268, x269, x270, x271, x272) -> f757_0_merge_GT(x273, x274, x275, x276, x277, x278, x279) :|: x270 = x279 && x268 = x278 && x266 = x277 && x266 = x276 && x267 = x274 && x266 = x273 && 0 <= x275 - 1 && 0 <= x269 - 1 && -1 <= x270 - 1 && x275 <= x269 f757_0_merge_GT(x280, x281, x282, x283, x284, x285, x286) -> f774_0_merge_GT(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x292 && x281 = x291 && x285 + 1 = x290 && x285 = x288 && x280 = x287 && x283 = x284 && 0 <= x289 - 1 && 0 <= x282 - 1 && x285 <= x283 - 1 && x289 <= x282 f757_0_merge_GT(x294, x295, x296, x297, x298, x299, x300) -> f757_0_merge_GT(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x297 + 1 = x305 && x297 + 1 = x304 && x295 = x302 && x294 = x301 && x297 = x298 && 0 <= x303 - 1 && 0 <= x296 - 1 && x303 <= x296 && x297 <= x300 - 1 && x297 <= x299 f774_0_merge_GT(x308, x309, x310, x311, x312, x313, x314) -> f774_0_merge_GT(x315, x316, x317, x318, x319, x320, x321) :|: x313 = x320 && x312 = x319 && x311 + 1 = x318 && x309 = x316 && x308 = x315 && 0 <= x317 - 1 && 0 <= x310 - 1 && x317 <= x310 && x311 <= x313 - 1 && x311 <= x312 && x312 + x309 + 1 - x311 <= x313 - 1 f774_0_merge_GT(x322, x323, x324, x325, x326, x327, x328) -> f1440_0_merge_GT(x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x322 = x333 && x322 = x332 && x326 = x331 && x322 = x330 && 0 <= x329 - 1 && 0 <= x324 - 1 && x326 <= x325 - 1 && x329 <= x324 f1440_0_merge_GT(x336, x337, x338, x339, x340, x341, x342) -> f1440_0_merge_GT(x343, x344, x345, x346, x347, x348, x349) :|: x339 <= x341 && x337 <= x342 - 1 && x338 <= x342 - 1 && x350 <= x351 && x339 <= x342 - 1 && x343 <= x336 && 0 <= x336 - 1 && 0 <= x343 - 1 && x339 = x340 && x337 = x344 && x338 - 1 = x345 && x339 + 1 = x346 && x339 + 1 = x347 && x341 = x348 && x342 = x349 f1440_0_merge_GT(x352, x353, x354, x355, x356, x357, x358) -> f1440_0_merge_GT(x359, x360, x361, x362, x363, x364, x365) :|: x355 <= x357 && x353 <= x358 - 1 && x354 <= x358 - 1 && x366 <= x367 - 1 && x355 <= x358 - 1 && x359 <= x352 && 0 <= x352 - 1 && 0 <= x359 - 1 && x355 = x356 && x353 + 1 = x360 && x354 = x361 && x355 + 1 = x362 && x355 + 1 = x363 && x357 = x364 && x358 = x365 __init(x368, x369, x370, x371, x372, x373, x374) -> f1_0_main_Load(x375, x376, x377, x378, x379, x380, x381) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f229_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 f229_0_main_GE(x, x1, x2, x3, x4, x5, x6) -> f229_0_main_GE(x7, x8, x9, x10, x11, x12, x13) :|: x2 = x9 && x1 + 1 = x8 && 0 <= x7 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x7 <= x f229_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f507_0_sort_GE(x21, x22, x23, x24, x25, x26, x27) :|: x16 = x25 && x16 - 1 = x24 && 0 = x23 && 0 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x14 - 1 && x22 <= x14 && x21 <= x14 && x16 <= x15 && -1 <= x16 - 1 && x16 - 1 <= x16 - 1 f507_0_sort_GE(x28, x29, x30, x31, x32, x33, x34) -> f507_0_sort_GE'(x35, x36, x37, x38, x39, x40, x41) :|: x30 <= x31 - 1 && x42 - x30 <= x31 - x30 - 1 && x43 <= x28 && x43 <= x29 && x44 <= x28 && x44 <= x29 && 0 <= x28 - 1 && 0 <= x29 - 1 && 0 <= x43 - 1 && 0 <= x44 - 1 && x28 = x35 && x29 = x36 && x30 = x37 && x31 = x38 && x32 = x39 f507_0_sort_GE'(x45, x46, x47, x48, x49, x50, x51) -> f507_0_sort_GE(x52, x53, x54, x55, x57, x58, x59) :|: x49 = x57 && x47 = x54 && 0 <= x47 + x48 - 2 * x55 && x47 + x48 - 2 * x55 <= 1 && 0 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x46 - 1 && 0 <= x45 - 1 && x53 <= x46 && x53 <= x45 && x52 <= x46 && x52 <= x45 && x55 - x47 <= x48 - x47 - 1 && x47 <= x48 - 1 f507_0_sort_GE(x60, x61, x62, x64, x65, x66, x67) -> f507_0_sort_GE'(x68, x69, x70, x71, x72, x73, x74) :|: x62 <= x64 - 1 && x64 - x62 <= x75 - x62 && x64 - (x75 + 1) <= x64 - x62 - 1 && x75 <= x75 + 1 - 1 && x76 <= x60 && x76 <= x61 && x77 <= x60 && x77 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x76 - 1 && 0 <= x77 - 1 && x60 = x68 && x61 = x69 && x62 = x70 && x64 = x71 && x65 = x72 f507_0_sort_GE'(x78, x79, x80, x81, x82, x83, x84) -> f507_0_sort_GE(x85, x86, x87, x88, x89, x90, x91) :|: x80 <= x81 - 1 && x81 - x80 <= x92 - x80 && x81 - (x92 + 1) <= x81 - x80 - 1 && x92 <= x92 + 1 - 1 && x85 <= x78 && x85 <= x79 && x86 <= x78 && x86 <= x79 && 0 <= x78 - 1 && 0 <= x79 - 1 && 0 <= x85 - 1 && 0 <= x86 - 1 && x80 + x81 - 2 * x92 <= 1 && 0 <= x80 + x81 - 2 * x92 && x92 + 1 = x87 && x81 = x88 && x82 = x89 f507_0_sort_GE(x93, x94, x95, x96, x97, x98, x99) -> f507_0_sort_GE'(x100, x101, x102, x103, x104, x107, x108) :|: x95 <= x96 - 1 && x109 - x95 <= x96 - x95 - 1 && x109 <= x109 + 1 - 1 && x96 - (x109 + 1) <= x96 - x95 - 1 && x110 <= x93 && x110 <= x94 && x111 <= x93 && x111 <= x94 && 0 <= x93 - 1 && 0 <= x94 - 1 && 0 <= x110 - 1 && 0 <= x111 - 1 && x93 = x100 && x94 = x101 && x95 = x102 && x96 = x103 && x97 = x104 f507_0_sort_GE'(x112, x113, x117, x118, x119, x120, x121) -> f507_0_sort_GE(x122, x123, x124, x125, x126, x127, x128) :|: x117 <= x118 - 1 && x129 - x117 <= x118 - x117 - 1 && x129 <= x129 + 1 - 1 && x118 - (x129 + 1) <= x118 - x117 - 1 && x122 <= x112 && x122 <= x113 && x123 <= x112 && x123 <= x113 && 0 <= x112 - 1 && 0 <= x113 - 1 && 0 <= x122 - 1 && 0 <= x123 - 1 && x117 + x118 - 2 * x129 <= 1 && 0 <= x117 + x118 - 2 * x129 && x129 + 1 = x124 && x118 = x125 && x119 = x126 f507_0_sort_GE(x133, x134, x135, x136, x137, x138, x139) -> f507_0_sort_GE'(x141, x142, x143, x144, x145, x149, x150) :|: x135 <= x136 - 1 && x151 - x135 <= x136 - x135 - 1 && x136 - x135 <= x136 - (x151 + 1) && x152 <= x133 && x152 <= x134 && 0 <= x133 - 1 && 0 <= x134 - 1 && 0 <= x152 - 1 && x133 = x141 && x134 = x142 && x135 = x143 && x136 = x144 && x137 = x145 f507_0_sort_GE'(x153, x154, x155, x157, x158, x159, x160) -> f1503_0_sort_InvokeMethod(x161, x164, x165, x166, x167, x168, x169) :|: x158 = x167 && x157 = x164 && x155 = x161 && 0 <= x155 + x157 - 2 * x165 && x155 + x157 - 2 * x165 <= 1 && 0 <= x166 - 1 && 0 <= x154 - 1 && 0 <= x153 - 1 && x166 <= x154 && x166 <= x153 && x157 - x155 <= x157 - (x165 + 1) && x165 - x155 <= x157 - x155 - 1 && x155 <= x157 - 1 f507_0_sort_GE(x170, x171, x172, x173, x174, x175, x178) -> f507_0_sort_GE'(x179, x180, x181, x182, x183, x184, x185) :|: x172 <= x173 - 1 && x186 - x172 <= x173 - x172 - 1 && x186 <= x186 + 1 - 1 && x173 - (x186 + 1) <= x173 - x172 - 1 && x187 <= x170 && x187 <= x171 && 0 <= x170 - 1 && 0 <= x171 - 1 && 0 <= x187 - 1 && x170 = x179 && x171 = x180 && x172 = x181 && x173 = x182 && x174 = x183 f507_0_sort_GE'(x188, x189, x192, x193, x194, x195, x196) -> f1503_0_sort_InvokeMethod(x197, x198, x199, x200, x201, x202, x203) :|: x194 = x201 && x193 = x198 && x192 = x197 && 0 <= x192 + x193 - 2 * x199 && x192 + x193 - 2 * x199 <= 1 && 0 <= x200 - 1 && 0 <= x189 - 1 && 0 <= x188 - 1 && x200 <= x189 && x200 <= x188 && x193 - (x199 + 1) <= x193 - x192 - 1 && x199 <= x199 + 1 - 1 && x199 - x192 <= x193 - x192 - 1 && x192 <= x193 - 1 f507_0_sort_GE(x206, x207, x208, x209, x210, x211, x212) -> f507_0_sort_GE'(x213, x214, x215, x216, x217, x218, x219) :|: x208 <= x209 - 1 && x209 - x208 <= x220 - x208 && x209 - x208 <= x209 - (x220 + 1) && -1 <= x210 - 1 && x221 <= x206 && x221 <= x207 && 0 <= x206 - 1 && 0 <= x207 - 1 && 0 <= x221 - 1 && x206 = x213 && x207 = x214 && x208 = x215 && x209 = x216 && x210 = x217 f507_0_sort_GE'(x222, x223, x224, x225, x226, x227, x228) -> f757_0_merge_GT(x229, x230, x231, x232, x233, x234, x235) :|: x226 = x235 && x224 = x233 && x224 = x232 && x225 = x230 && x224 = x229 && 0 <= x224 + x225 - 2 * x234 && x224 + x225 - 2 * x234 <= 1 && 0 <= x231 - 1 && 0 <= x223 - 1 && 0 <= x222 - 1 && x231 <= x223 && x231 <= x222 && -1 <= x226 - 1 && x225 - x224 <= x225 - (x234 + 1) && x225 - x224 <= x234 - x224 && x224 <= x225 - 1 f507_0_sort_GE(x236, x237, x238, x239, x240, x241, x242) -> f507_0_sort_GE'(x243, x244, x245, x246, x247, x248, x249) :|: x238 <= x239 - 1 && x239 - x238 <= x250 - x238 && x239 - (x250 + 1) <= x239 - x238 - 1 && x250 <= x250 + 1 - 1 && -1 <= x240 - 1 && x251 <= x236 && x251 <= x237 && 0 <= x236 - 1 && 0 <= x237 - 1 && 0 <= x251 - 1 && x236 = x243 && x237 = x244 && x238 = x245 && x239 = x246 && x240 = x247 f507_0_sort_GE'(x252, x253, x254, x255, x256, x257, x258) -> f757_0_merge_GT(x259, x260, x261, x262, x263, x264, x265) :|: x256 = x265 && x254 = x263 && x254 = x262 && x255 = x260 && x254 = x259 && 0 <= x254 + x255 - 2 * x264 && x254 + x255 - 2 * x264 <= 1 && 0 <= x261 - 1 && 0 <= x253 - 1 && 0 <= x252 - 1 && x261 <= x253 && x261 <= x252 && -1 <= x256 - 1 && x264 <= x264 + 1 - 1 && x255 - (x264 + 1) <= x255 - x254 - 1 && x255 - x254 <= x264 - x254 && x254 <= x255 - 1 f1503_0_sort_InvokeMethod(x266, x267, x268, x269, x270, x271, x272) -> f757_0_merge_GT(x273, x274, x275, x276, x277, x278, x279) :|: x270 = x279 && x268 = x278 && x266 = x277 && x266 = x276 && x267 = x274 && x266 = x273 && 0 <= x275 - 1 && 0 <= x269 - 1 && -1 <= x270 - 1 && x275 <= x269 f757_0_merge_GT(x280, x281, x282, x283, x284, x285, x286) -> f774_0_merge_GT(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x292 && x281 = x291 && x285 + 1 = x290 && x285 = x288 && x280 = x287 && x283 = x284 && 0 <= x289 - 1 && 0 <= x282 - 1 && x285 <= x283 - 1 && x289 <= x282 f757_0_merge_GT(x294, x295, x296, x297, x298, x299, x300) -> f757_0_merge_GT(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x297 + 1 = x305 && x297 + 1 = x304 && x295 = x302 && x294 = x301 && x297 = x298 && 0 <= x303 - 1 && 0 <= x296 - 1 && x303 <= x296 && x297 <= x300 - 1 && x297 <= x299 f774_0_merge_GT(x308, x309, x310, x311, x312, x313, x314) -> f774_0_merge_GT(x315, x316, x317, x318, x319, x320, x321) :|: x313 = x320 && x312 = x319 && x311 + 1 = x318 && x309 = x316 && x308 = x315 && 0 <= x317 - 1 && 0 <= x310 - 1 && x317 <= x310 && x311 <= x313 - 1 && x311 <= x312 && x312 + x309 + 1 - x311 <= x313 - 1 f774_0_merge_GT(x322, x323, x324, x325, x326, x327, x328) -> f1440_0_merge_GT(x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x322 = x333 && x322 = x332 && x326 = x331 && x322 = x330 && 0 <= x329 - 1 && 0 <= x324 - 1 && x326 <= x325 - 1 && x329 <= x324 f1440_0_merge_GT(x336, x337, x338, x339, x340, x341, x342) -> f1440_0_merge_GT(x343, x344, x345, x346, x347, x348, x349) :|: x339 <= x341 && x337 <= x342 - 1 && x338 <= x342 - 1 && x350 <= x351 && x339 <= x342 - 1 && x343 <= x336 && 0 <= x336 - 1 && 0 <= x343 - 1 && x339 = x340 && x337 = x344 && x338 - 1 = x345 && x339 + 1 = x346 && x339 + 1 = x347 && x341 = x348 && x342 = x349 f1440_0_merge_GT(x352, x353, x354, x355, x356, x357, x358) -> f1440_0_merge_GT(x359, x360, x361, x362, x363, x364, x365) :|: x355 <= x357 && x353 <= x358 - 1 && x354 <= x358 - 1 && x366 <= x367 - 1 && x355 <= x358 - 1 && x359 <= x352 && 0 <= x352 - 1 && 0 <= x359 - 1 && x355 = x356 && x353 + 1 = x360 && x354 = x361 && x355 + 1 = x362 && x355 + 1 = x363 && x357 = x364 && x358 = x365 __init(x368, x369, x370, x371, x372, x373, x374) -> f1_0_main_Load(x375, x376, x377, x378, x379, x380, x381) :|: 0 <= 0 Start term: __init(arg1, arg2, arg3, arg4, arg5, arg6, arg7) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1_0_main_Load(arg1, arg2, arg3, arg4, arg5, arg6, arg7) -> f229_0_main_GE(arg1P, arg2P, arg3P, arg4P, arg5P, arg6P, arg7P) :|: arg2 = arg3P && 0 = arg2P && 0 <= arg1P - 1 && 0 <= arg1 - 1 && -1 <= arg2 - 1 && arg1P <= arg1 (2) f229_0_main_GE(x, x1, x2, x3, x4, x5, x6) -> f229_0_main_GE(x7, x8, x9, x10, x11, x12, x13) :|: x2 = x9 && x1 + 1 = x8 && 0 <= x7 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x7 <= x (3) f229_0_main_GE(x14, x15, x16, x17, x18, x19, x20) -> f507_0_sort_GE(x21, x22, x23, x24, x25, x26, x27) :|: x16 = x25 && x16 - 1 = x24 && 0 = x23 && 0 <= x22 - 1 && 0 <= x21 - 1 && 0 <= x14 - 1 && x22 <= x14 && x21 <= x14 && x16 <= x15 && -1 <= x16 - 1 && x16 - 1 <= x16 - 1 (4) f507_0_sort_GE(x28, x29, x30, x31, x32, x33, x34) -> f507_0_sort_GE'(x35, x36, x37, x38, x39, x40, x41) :|: x30 <= x31 - 1 && x42 - x30 <= x31 - x30 - 1 && x43 <= x28 && x43 <= x29 && x44 <= x28 && x44 <= x29 && 0 <= x28 - 1 && 0 <= x29 - 1 && 0 <= x43 - 1 && 0 <= x44 - 1 && x28 = x35 && x29 = x36 && x30 = x37 && x31 = x38 && x32 = x39 (5) f507_0_sort_GE'(x45, x46, x47, x48, x49, x50, x51) -> f507_0_sort_GE(x52, x53, x54, x55, x57, x58, x59) :|: x49 = x57 && x47 = x54 && 0 <= x47 + x48 - 2 * x55 && x47 + x48 - 2 * x55 <= 1 && 0 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x46 - 1 && 0 <= x45 - 1 && x53 <= x46 && x53 <= x45 && x52 <= x46 && x52 <= x45 && x55 - x47 <= x48 - x47 - 1 && x47 <= x48 - 1 (6) f507_0_sort_GE(x60, x61, x62, x64, x65, x66, x67) -> f507_0_sort_GE'(x68, x69, x70, x71, x72, x73, x74) :|: x62 <= x64 - 1 && x64 - x62 <= x75 - x62 && x64 - (x75 + 1) <= x64 - x62 - 1 && x75 <= x75 + 1 - 1 && x76 <= x60 && x76 <= x61 && x77 <= x60 && x77 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x76 - 1 && 0 <= x77 - 1 && x60 = x68 && x61 = x69 && x62 = x70 && x64 = x71 && x65 = x72 (7) f507_0_sort_GE'(x78, x79, x80, x81, x82, x83, x84) -> f507_0_sort_GE(x85, x86, x87, x88, x89, x90, x91) :|: x80 <= x81 - 1 && x81 - x80 <= x92 - x80 && x81 - (x92 + 1) <= x81 - x80 - 1 && x92 <= x92 + 1 - 1 && x85 <= x78 && x85 <= x79 && x86 <= x78 && x86 <= x79 && 0 <= x78 - 1 && 0 <= x79 - 1 && 0 <= x85 - 1 && 0 <= x86 - 1 && x80 + x81 - 2 * x92 <= 1 && 0 <= x80 + x81 - 2 * x92 && x92 + 1 = x87 && x81 = x88 && x82 = x89 (8) f507_0_sort_GE(x93, x94, x95, x96, x97, x98, x99) -> f507_0_sort_GE'(x100, x101, x102, x103, x104, x107, x108) :|: x95 <= x96 - 1 && x109 - x95 <= x96 - x95 - 1 && x109 <= x109 + 1 - 1 && x96 - (x109 + 1) <= x96 - x95 - 1 && x110 <= x93 && x110 <= x94 && x111 <= x93 && x111 <= x94 && 0 <= x93 - 1 && 0 <= x94 - 1 && 0 <= x110 - 1 && 0 <= x111 - 1 && x93 = x100 && x94 = x101 && x95 = x102 && x96 = x103 && x97 = x104 (9) f507_0_sort_GE'(x112, x113, x117, x118, x119, x120, x121) -> f507_0_sort_GE(x122, x123, x124, x125, x126, x127, x128) :|: x117 <= x118 - 1 && x129 - x117 <= x118 - x117 - 1 && x129 <= x129 + 1 - 1 && x118 - (x129 + 1) <= x118 - x117 - 1 && x122 <= x112 && x122 <= x113 && x123 <= x112 && x123 <= x113 && 0 <= x112 - 1 && 0 <= x113 - 1 && 0 <= x122 - 1 && 0 <= x123 - 1 && x117 + x118 - 2 * x129 <= 1 && 0 <= x117 + x118 - 2 * x129 && x129 + 1 = x124 && x118 = x125 && x119 = x126 (10) f507_0_sort_GE(x133, x134, x135, x136, x137, x138, x139) -> f507_0_sort_GE'(x141, x142, x143, x144, x145, x149, x150) :|: x135 <= x136 - 1 && x151 - x135 <= x136 - x135 - 1 && x136 - x135 <= x136 - (x151 + 1) && x152 <= x133 && x152 <= x134 && 0 <= x133 - 1 && 0 <= x134 - 1 && 0 <= x152 - 1 && x133 = x141 && x134 = x142 && x135 = x143 && x136 = x144 && x137 = x145 (11) f507_0_sort_GE'(x153, x154, x155, x157, x158, x159, x160) -> f1503_0_sort_InvokeMethod(x161, x164, x165, x166, x167, x168, x169) :|: x158 = x167 && x157 = x164 && x155 = x161 && 0 <= x155 + x157 - 2 * x165 && x155 + x157 - 2 * x165 <= 1 && 0 <= x166 - 1 && 0 <= x154 - 1 && 0 <= x153 - 1 && x166 <= x154 && x166 <= x153 && x157 - x155 <= x157 - (x165 + 1) && x165 - x155 <= x157 - x155 - 1 && x155 <= x157 - 1 (12) f507_0_sort_GE(x170, x171, x172, x173, x174, x175, x178) -> f507_0_sort_GE'(x179, x180, x181, x182, x183, x184, x185) :|: x172 <= x173 - 1 && x186 - x172 <= x173 - x172 - 1 && x186 <= x186 + 1 - 1 && x173 - (x186 + 1) <= x173 - x172 - 1 && x187 <= x170 && x187 <= x171 && 0 <= x170 - 1 && 0 <= x171 - 1 && 0 <= x187 - 1 && x170 = x179 && x171 = x180 && x172 = x181 && x173 = x182 && x174 = x183 (13) f507_0_sort_GE'(x188, x189, x192, x193, x194, x195, x196) -> f1503_0_sort_InvokeMethod(x197, x198, x199, x200, x201, x202, x203) :|: x194 = x201 && x193 = x198 && x192 = x197 && 0 <= x192 + x193 - 2 * x199 && x192 + x193 - 2 * x199 <= 1 && 0 <= x200 - 1 && 0 <= x189 - 1 && 0 <= x188 - 1 && x200 <= x189 && x200 <= x188 && x193 - (x199 + 1) <= x193 - x192 - 1 && x199 <= x199 + 1 - 1 && x199 - x192 <= x193 - x192 - 1 && x192 <= x193 - 1 (14) f507_0_sort_GE(x206, x207, x208, x209, x210, x211, x212) -> f507_0_sort_GE'(x213, x214, x215, x216, x217, x218, x219) :|: x208 <= x209 - 1 && x209 - x208 <= x220 - x208 && x209 - x208 <= x209 - (x220 + 1) && -1 <= x210 - 1 && x221 <= x206 && x221 <= x207 && 0 <= x206 - 1 && 0 <= x207 - 1 && 0 <= x221 - 1 && x206 = x213 && x207 = x214 && x208 = x215 && x209 = x216 && x210 = x217 (15) f507_0_sort_GE'(x222, x223, x224, x225, x226, x227, x228) -> f757_0_merge_GT(x229, x230, x231, x232, x233, x234, x235) :|: x226 = x235 && x224 = x233 && x224 = x232 && x225 = x230 && x224 = x229 && 0 <= x224 + x225 - 2 * x234 && x224 + x225 - 2 * x234 <= 1 && 0 <= x231 - 1 && 0 <= x223 - 1 && 0 <= x222 - 1 && x231 <= x223 && x231 <= x222 && -1 <= x226 - 1 && x225 - x224 <= x225 - (x234 + 1) && x225 - x224 <= x234 - x224 && x224 <= x225 - 1 (16) f507_0_sort_GE(x236, x237, x238, x239, x240, x241, x242) -> f507_0_sort_GE'(x243, x244, x245, x246, x247, x248, x249) :|: x238 <= x239 - 1 && x239 - x238 <= x250 - x238 && x239 - (x250 + 1) <= x239 - x238 - 1 && x250 <= x250 + 1 - 1 && -1 <= x240 - 1 && x251 <= x236 && x251 <= x237 && 0 <= x236 - 1 && 0 <= x237 - 1 && 0 <= x251 - 1 && x236 = x243 && x237 = x244 && x238 = x245 && x239 = x246 && x240 = x247 (17) f507_0_sort_GE'(x252, x253, x254, x255, x256, x257, x258) -> f757_0_merge_GT(x259, x260, x261, x262, x263, x264, x265) :|: x256 = x265 && x254 = x263 && x254 = x262 && x255 = x260 && x254 = x259 && 0 <= x254 + x255 - 2 * x264 && x254 + x255 - 2 * x264 <= 1 && 0 <= x261 - 1 && 0 <= x253 - 1 && 0 <= x252 - 1 && x261 <= x253 && x261 <= x252 && -1 <= x256 - 1 && x264 <= x264 + 1 - 1 && x255 - (x264 + 1) <= x255 - x254 - 1 && x255 - x254 <= x264 - x254 && x254 <= x255 - 1 (18) f1503_0_sort_InvokeMethod(x266, x267, x268, x269, x270, x271, x272) -> f757_0_merge_GT(x273, x274, x275, x276, x277, x278, x279) :|: x270 = x279 && x268 = x278 && x266 = x277 && x266 = x276 && x267 = x274 && x266 = x273 && 0 <= x275 - 1 && 0 <= x269 - 1 && -1 <= x270 - 1 && x275 <= x269 (19) f757_0_merge_GT(x280, x281, x282, x283, x284, x285, x286) -> f774_0_merge_GT(x287, x288, x289, x290, x291, x292, x293) :|: x286 = x292 && x281 = x291 && x285 + 1 = x290 && x285 = x288 && x280 = x287 && x283 = x284 && 0 <= x289 - 1 && 0 <= x282 - 1 && x285 <= x283 - 1 && x289 <= x282 (20) f757_0_merge_GT(x294, x295, x296, x297, x298, x299, x300) -> f757_0_merge_GT(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x297 + 1 = x305 && x297 + 1 = x304 && x295 = x302 && x294 = x301 && x297 = x298 && 0 <= x303 - 1 && 0 <= x296 - 1 && x303 <= x296 && x297 <= x300 - 1 && x297 <= x299 (21) f774_0_merge_GT(x308, x309, x310, x311, x312, x313, x314) -> f774_0_merge_GT(x315, x316, x317, x318, x319, x320, x321) :|: x313 = x320 && x312 = x319 && x311 + 1 = x318 && x309 = x316 && x308 = x315 && 0 <= x317 - 1 && 0 <= x310 - 1 && x317 <= x310 && x311 <= x313 - 1 && x311 <= x312 && x312 + x309 + 1 - x311 <= x313 - 1 (22) f774_0_merge_GT(x322, x323, x324, x325, x326, x327, x328) -> f1440_0_merge_GT(x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x322 = x333 && x322 = x332 && x326 = x331 && x322 = x330 && 0 <= x329 - 1 && 0 <= x324 - 1 && x326 <= x325 - 1 && x329 <= x324 (23) f1440_0_merge_GT(x336, x337, x338, x339, x340, x341, x342) -> f1440_0_merge_GT(x343, x344, x345, x346, x347, x348, x349) :|: x339 <= x341 && x337 <= x342 - 1 && x338 <= x342 - 1 && x350 <= x351 && x339 <= x342 - 1 && x343 <= x336 && 0 <= x336 - 1 && 0 <= x343 - 1 && x339 = x340 && x337 = x344 && x338 - 1 = x345 && x339 + 1 = x346 && x339 + 1 = x347 && x341 = x348 && x342 = x349 (24) f1440_0_merge_GT(x352, x353, x354, x355, x356, x357, x358) -> f1440_0_merge_GT(x359, x360, x361, x362, x363, x364, x365) :|: x355 <= x357 && x353 <= x358 - 1 && x354 <= x358 - 1 && x366 <= x367 - 1 && x355 <= x358 - 1 && x359 <= x352 && 0 <= x352 - 1 && 0 <= x359 - 1 && x355 = x356 && x353 + 1 = x360 && x354 = x361 && x355 + 1 = x362 && x355 + 1 = x363 && x357 = x364 && x358 = x365 (25) __init(x368, x369, x370, x371, x372, x373, x374) -> f1_0_main_Load(x375, x376, x377, x378, x379, x380, x381) :|: 0 <= 0 Arcs: (1) -> (2), (3) (2) -> (2), (3) (3) -> (4), (6), (8), (10), (12), (16) (4) -> (5), (9), (13) (5) -> (4), (6), (8), (10), (12), (16) (6) -> (5), (9), (13) (8) -> (5), (9), (13) (9) -> (4), (6), (8), (10), (12), (16) (10) -> (5), (9), (13) (12) -> (5), (9), (13) (13) -> (18) (16) -> (5), (9), (13) (18) -> (19), (20) (19) -> (21), (22) (20) -> (19), (20) (21) -> (21), (22) (22) -> (23), (24) (23) -> (23), (24) (24) -> (23), (24) (25) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) f229_0_main_GE(x, x1, x2, x3, x4, x5, x6) -> f229_0_main_GE(x7, x8, x9, x10, x11, x12, x13) :|: x2 = x9 && x1 + 1 = x8 && 0 <= x7 - 1 && 0 <= x - 1 && x1 <= x2 - 1 && x7 <= x Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: f229_0_main_GE(x:0, x1:0, x2:0, x3:0, x4:0, x5:0, x6:0) -> f229_0_main_GE(x7:0, x1:0 + 1, x2:0, x10:0, x11:0, x12:0, x13:0) :|: x2:0 - 1 >= x1:0 && x:0 >= x7:0 && x7:0 > 0 && x:0 > 0 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f229_0_main_GE(x1, x2, x3, x4, x5, x6, x7) -> f229_0_main_GE(x1, x2, x3) ---------------------------------------- (9) Obligation: Rules: f229_0_main_GE(x:0, x1:0, x2:0) -> f229_0_main_GE(x7:0, x1:0 + 1, x2:0) :|: x2:0 - 1 >= x1:0 && x:0 >= x7:0 && x7:0 > 0 && x:0 > 0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f229_0_main_GE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: f229_0_main_GE(x:0, x1:0, x2:0) -> f229_0_main_GE(x7:0, c, x2:0) :|: c = x1:0 + 1 && (x2:0 - 1 >= x1:0 && x:0 >= x7:0 && x7:0 > 0 && x:0 > 0) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f229_0_main_GE(x, x1, x2)] = -x1 + x2 The following rules are decreasing: f229_0_main_GE(x:0, x1:0, x2:0) -> f229_0_main_GE(x7:0, c, x2:0) :|: c = x1:0 + 1 && (x2:0 - 1 >= x1:0 && x:0 >= x7:0 && x7:0 > 0 && x:0 > 0) The following rules are bounded: f229_0_main_GE(x:0, x1:0, x2:0) -> f229_0_main_GE(x7:0, c, x2:0) :|: c = x1:0 + 1 && (x2:0 - 1 >= x1:0 && x:0 >= x7:0 && x7:0 > 0 && x:0 > 0) ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) f507_0_sort_GE(x28, x29, x30, x31, x32, x33, x34) -> f507_0_sort_GE'(x35, x36, x37, x38, x39, x40, x41) :|: x30 <= x31 - 1 && x42 - x30 <= x31 - x30 - 1 && x43 <= x28 && x43 <= x29 && x44 <= x28 && x44 <= x29 && 0 <= x28 - 1 && 0 <= x29 - 1 && 0 <= x43 - 1 && 0 <= x44 - 1 && x28 = x35 && x29 = x36 && x30 = x37 && x31 = x38 && x32 = x39 (2) f507_0_sort_GE'(x45, x46, x47, x48, x49, x50, x51) -> f507_0_sort_GE(x52, x53, x54, x55, x57, x58, x59) :|: x49 = x57 && x47 = x54 && 0 <= x47 + x48 - 2 * x55 && x47 + x48 - 2 * x55 <= 1 && 0 <= x53 - 1 && 0 <= x52 - 1 && 0 <= x46 - 1 && 0 <= x45 - 1 && x53 <= x46 && x53 <= x45 && x52 <= x46 && x52 <= x45 && x55 - x47 <= x48 - x47 - 1 && x47 <= x48 - 1 (3) f507_0_sort_GE(x60, x61, x62, x64, x65, x66, x67) -> f507_0_sort_GE'(x68, x69, x70, x71, x72, x73, x74) :|: x62 <= x64 - 1 && x64 - x62 <= x75 - x62 && x64 - (x75 + 1) <= x64 - x62 - 1 && x75 <= x75 + 1 - 1 && x76 <= x60 && x76 <= x61 && x77 <= x60 && x77 <= x61 && 0 <= x60 - 1 && 0 <= x61 - 1 && 0 <= x76 - 1 && 0 <= x77 - 1 && x60 = x68 && x61 = x69 && x62 = x70 && x64 = x71 && x65 = x72 (4) f507_0_sort_GE'(x112, x113, x117, x118, x119, x120, x121) -> f507_0_sort_GE(x122, x123, x124, x125, x126, x127, x128) :|: x117 <= x118 - 1 && x129 - x117 <= x118 - x117 - 1 && x129 <= x129 + 1 - 1 && x118 - (x129 + 1) <= x118 - x117 - 1 && x122 <= x112 && x122 <= x113 && x123 <= x112 && x123 <= x113 && 0 <= x112 - 1 && 0 <= x113 - 1 && 0 <= x122 - 1 && 0 <= x123 - 1 && x117 + x118 - 2 * x129 <= 1 && 0 <= x117 + x118 - 2 * x129 && x129 + 1 = x124 && x118 = x125 && x119 = x126 (5) f507_0_sort_GE(x236, x237, x238, x239, x240, x241, x242) -> f507_0_sort_GE'(x243, x244, x245, x246, x247, x248, x249) :|: x238 <= x239 - 1 && x239 - x238 <= x250 - x238 && x239 - (x250 + 1) <= x239 - x238 - 1 && x250 <= x250 + 1 - 1 && -1 <= x240 - 1 && x251 <= x236 && x251 <= x237 && 0 <= x236 - 1 && 0 <= x237 - 1 && 0 <= x251 - 1 && x236 = x243 && x237 = x244 && x238 = x245 && x239 = x246 && x240 = x247 (6) f507_0_sort_GE(x170, x171, x172, x173, x174, x175, x178) -> f507_0_sort_GE'(x179, x180, x181, x182, x183, x184, x185) :|: x172 <= x173 - 1 && x186 - x172 <= x173 - x172 - 1 && x186 <= x186 + 1 - 1 && x173 - (x186 + 1) <= x173 - x172 - 1 && x187 <= x170 && x187 <= x171 && 0 <= x170 - 1 && 0 <= x171 - 1 && 0 <= x187 - 1 && x170 = x179 && x171 = x180 && x172 = x181 && x173 = x182 && x174 = x183 (7) f507_0_sort_GE(x133, x134, x135, x136, x137, x138, x139) -> f507_0_sort_GE'(x141, x142, x143, x144, x145, x149, x150) :|: x135 <= x136 - 1 && x151 - x135 <= x136 - x135 - 1 && x136 - x135 <= x136 - (x151 + 1) && x152 <= x133 && x152 <= x134 && 0 <= x133 - 1 && 0 <= x134 - 1 && 0 <= x152 - 1 && x133 = x141 && x134 = x142 && x135 = x143 && x136 = x144 && x137 = x145 (8) f507_0_sort_GE(x93, x94, x95, x96, x97, x98, x99) -> f507_0_sort_GE'(x100, x101, x102, x103, x104, x107, x108) :|: x95 <= x96 - 1 && x109 - x95 <= x96 - x95 - 1 && x109 <= x109 + 1 - 1 && x96 - (x109 + 1) <= x96 - x95 - 1 && x110 <= x93 && x110 <= x94 && x111 <= x93 && x111 <= x94 && 0 <= x93 - 1 && 0 <= x94 - 1 && 0 <= x110 - 1 && 0 <= x111 - 1 && x93 = x100 && x94 = x101 && x95 = x102 && x96 = x103 && x97 = x104 Arcs: (1) -> (2), (4) (2) -> (1), (3), (5), (6), (7), (8) (3) -> (2), (4) (4) -> (1), (3), (5), (6), (7), (8) (5) -> (2), (4) (6) -> (2), (4) (7) -> (2), (4) (8) -> (2), (4) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: f507_0_sort_GE'(x112:0, x113:0, x117:0, x118:0, x119:0, x120:0, x121:0) -> f507_0_sort_GE(x122:0, x123:0, x129:0 + 1, x118:0, x119:0, x127:0, x128:0) :|: x117:0 + x118:0 - 2 * x129:0 <= 1 && x117:0 + x118:0 - 2 * x129:0 >= 0 && x123:0 > 0 && x122:0 > 0 && x113:0 > 0 && x112:0 > 0 && x123:0 <= x113:0 && x123:0 <= x112:0 && x122:0 <= x113:0 && x122:0 <= x112:0 && x118:0 - (x129:0 + 1) <= x118:0 - x117:0 - 1 && x129:0 - x117:0 <= x118:0 - x117:0 - 1 && x118:0 - 1 >= x117:0 f507_0_sort_GE(x170:0, x171:0, x172:0, x173:0, x174:0, x175:0, x178:0) -> f507_0_sort_GE'(x170:0, x171:0, x172:0, x173:0, x174:0, x184:0, x185:0) :|: x171:0 > 0 && x187:0 > 0 && x170:0 > 0 && x187:0 <= x171:0 && x187:0 <= x170:0 && x173:0 - (x186:0 + 1) <= x173:0 - x172:0 - 1 && x186:0 - x172:0 <= x173:0 - x172:0 - 1 && x173:0 - 1 >= x172:0 f507_0_sort_GE(x28:0, x29:0, x30:0, x31:0, x32:0, x33:0, x34:0) -> f507_0_sort_GE'(x28:0, x29:0, x30:0, x31:0, x32:0, x40:0, x41:0) :|: x43:0 > 0 && x44:0 > 0 && x29:0 > 0 && x28:0 > 0 && x44:0 <= x29:0 && x44:0 <= x28:0 && x43:0 <= x29:0 && x43:0 <= x28:0 && x42:0 - x30:0 <= x31:0 - x30:0 - 1 && x31:0 - 1 >= x30:0 f507_0_sort_GE(x100:0, x101:0, x102:0, x103:0, x104:0, x98:0, x99:0) -> f507_0_sort_GE'(x100:0, x101:0, x102:0, x103:0, x104:0, x107:0, x108:0) :|: x110:0 > 0 && x111:0 > 0 && x101:0 > 0 && x100:0 > 0 && x111:0 <= x101:0 && x111:0 <= x100:0 && x110:0 <= x101:0 && x110:0 <= x100:0 && x103:0 - (x109:0 + 1) <= x103:0 - x102:0 - 1 && x109:0 - x102:0 <= x103:0 - x102:0 - 1 && x103:0 - 1 >= x102:0 f507_0_sort_GE(x60:0, x61:0, x62:0, x64:0, x65:0, x66:0, x67:0) -> f507_0_sort_GE'(x60:0, x61:0, x62:0, x64:0, x65:0, x73:0, x74:0) :|: x76:0 > 0 && x77:0 > 0 && x61:0 > 0 && x60:0 > 0 && x77:0 <= x61:0 && x77:0 <= x60:0 && x76:0 <= x61:0 && x76:0 <= x60:0 && x64:0 - (x75:0 + 1) <= x64:0 - x62:0 - 1 && x75:0 - x62:0 >= x64:0 - x62:0 && x64:0 - 1 >= x62:0 f507_0_sort_GE'(x45:0, x46:0, x47:0, x48:0, x49:0, x50:0, x51:0) -> f507_0_sort_GE(x52:0, x53:0, x47:0, x55:0, x49:0, x58:0, x59:0) :|: x55:0 - x47:0 <= x48:0 - x47:0 - 1 && x48:0 - 1 >= x47:0 && x52:0 <= x45:0 && x52:0 <= x46:0 && x53:0 <= x45:0 && x53:0 <= x46:0 && x45:0 > 0 && x46:0 > 0 && x52:0 > 0 && x53:0 > 0 && x47:0 + x48:0 - 2 * x55:0 >= 0 && x47:0 + x48:0 - 2 * x55:0 <= 1 f507_0_sort_GE(x236:0, x237:0, x238:0, x239:0, x240:0, x241:0, x242:0) -> f507_0_sort_GE'(x236:0, x237:0, x238:0, x239:0, x240:0, x248:0, x249:0) :|: x237:0 > 0 && x251:0 > 0 && x236:0 > 0 && x251:0 <= x237:0 && x251:0 <= x236:0 && x240:0 > -1 && x239:0 - (x250:0 + 1) <= x239:0 - x238:0 - 1 && x250:0 - x238:0 >= x239:0 - x238:0 && x239:0 - 1 >= x238:0 f507_0_sort_GE(x133:0, x134:0, x135:0, x136:0, x137:0, x138:0, x139:0) -> f507_0_sort_GE'(x133:0, x134:0, x135:0, x136:0, x137:0, x149:0, x150:0) :|: x134:0 > 0 && x152:0 > 0 && x133:0 > 0 && x152:0 <= x134:0 && x152:0 <= x133:0 && x136:0 - (x151:0 + 1) >= x136:0 - x135:0 && x151:0 - x135:0 <= x136:0 - x135:0 - 1 && x136:0 - 1 >= x135:0 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f507_0_sort_GE'(x1, x2, x3, x4, x5, x6, x7) -> f507_0_sort_GE'(x1, x2, x3, x4, x5) f507_0_sort_GE(x1, x2, x3, x4, x5, x6, x7) -> f507_0_sort_GE(x1, x2, x3, x4, x5) ---------------------------------------- (18) Obligation: Rules: f507_0_sort_GE'(x112:0, x113:0, x117:0, x118:0, x119:0) -> f507_0_sort_GE(x122:0, x123:0, x129:0 + 1, x118:0, x119:0) :|: x117:0 + x118:0 - 2 * x129:0 <= 1 && x117:0 + x118:0 - 2 * x129:0 >= 0 && x123:0 > 0 && x122:0 > 0 && x113:0 > 0 && x112:0 > 0 && x123:0 <= x113:0 && x123:0 <= x112:0 && x122:0 <= x113:0 && x122:0 <= x112:0 && x118:0 - (x129:0 + 1) <= x118:0 - x117:0 - 1 && x129:0 - x117:0 <= x118:0 - x117:0 - 1 && x118:0 - 1 >= x117:0 f507_0_sort_GE(x170:0, x171:0, x172:0, x173:0, x174:0) -> f507_0_sort_GE'(x170:0, x171:0, x172:0, x173:0, x174:0) :|: x171:0 > 0 && x187:0 > 0 && x170:0 > 0 && x187:0 <= x171:0 && x187:0 <= x170:0 && x173:0 - (x186:0 + 1) <= x173:0 - x172:0 - 1 && x186:0 - x172:0 <= x173:0 - x172:0 - 1 && x173:0 - 1 >= x172:0 f507_0_sort_GE(x28:0, x29:0, x30:0, x31:0, x32:0) -> f507_0_sort_GE'(x28:0, x29:0, x30:0, x31:0, x32:0) :|: x43:0 > 0 && x44:0 > 0 && x29:0 > 0 && x28:0 > 0 && x44:0 <= x29:0 && x44:0 <= x28:0 && x43:0 <= x29:0 && x43:0 <= x28:0 && x42:0 - x30:0 <= x31:0 - x30:0 - 1 && x31:0 - 1 >= x30:0 f507_0_sort_GE(x100:0, x101:0, x102:0, x103:0, x104:0) -> f507_0_sort_GE'(x100:0, x101:0, x102:0, x103:0, x104:0) :|: x110:0 > 0 && x111:0 > 0 && x101:0 > 0 && x100:0 > 0 && x111:0 <= x101:0 && x111:0 <= x100:0 && x110:0 <= x101:0 && x110:0 <= x100:0 && x103:0 - (x109:0 + 1) <= x103:0 - x102:0 - 1 && x109:0 - x102:0 <= x103:0 - x102:0 - 1 && x103:0 - 1 >= x102:0 f507_0_sort_GE(x60:0, x61:0, x62:0, x64:0, x65:0) -> f507_0_sort_GE'(x60:0, x61:0, x62:0, x64:0, x65:0) :|: x76:0 > 0 && x77:0 > 0 && x61:0 > 0 && x60:0 > 0 && x77:0 <= x61:0 && x77:0 <= x60:0 && x76:0 <= x61:0 && x76:0 <= x60:0 && x64:0 - (x75:0 + 1) <= x64:0 - x62:0 - 1 && x75:0 - x62:0 >= x64:0 - x62:0 && x64:0 - 1 >= x62:0 f507_0_sort_GE'(x45:0, x46:0, x47:0, x48:0, x49:0) -> f507_0_sort_GE(x52:0, x53:0, x47:0, x55:0, x49:0) :|: x55:0 - x47:0 <= x48:0 - x47:0 - 1 && x48:0 - 1 >= x47:0 && x52:0 <= x45:0 && x52:0 <= x46:0 && x53:0 <= x45:0 && x53:0 <= x46:0 && x45:0 > 0 && x46:0 > 0 && x52:0 > 0 && x53:0 > 0 && x47:0 + x48:0 - 2 * x55:0 >= 0 && x47:0 + x48:0 - 2 * x55:0 <= 1 f507_0_sort_GE(x236:0, x237:0, x238:0, x239:0, x240:0) -> f507_0_sort_GE'(x236:0, x237:0, x238:0, x239:0, x240:0) :|: x237:0 > 0 && x251:0 > 0 && x236:0 > 0 && x251:0 <= x237:0 && x251:0 <= x236:0 && x240:0 > -1 && x239:0 - (x250:0 + 1) <= x239:0 - x238:0 - 1 && x250:0 - x238:0 >= x239:0 - x238:0 && x239:0 - 1 >= x238:0 f507_0_sort_GE(x133:0, x134:0, x135:0, x136:0, x137:0) -> f507_0_sort_GE'(x133:0, x134:0, x135:0, x136:0, x137:0) :|: x134:0 > 0 && x152:0 > 0 && x133:0 > 0 && x152:0 <= x134:0 && x152:0 <= x133:0 && x136:0 - (x151:0 + 1) >= x136:0 - x135:0 && x151:0 - x135:0 <= x136:0 - x135:0 - 1 && x136:0 - 1 >= x135:0 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f507_0_sort_GE'(INTEGER, INTEGER, INTEGER, INTEGER, VARIABLE) f507_0_sort_GE(INTEGER, INTEGER, INTEGER, INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: f507_0_sort_GE'(x112:0, x113:0, x117:0, x118:0, x119:0) -> f507_0_sort_GE(x122:0, x123:0, c, x118:0, x119:0) :|: c = x129:0 + 1 && (x117:0 + x118:0 - 2 * x129:0 <= 1 && x117:0 + x118:0 - 2 * x129:0 >= 0 && x123:0 > 0 && x122:0 > 0 && x113:0 > 0 && x112:0 > 0 && x123:0 <= x113:0 && x123:0 <= x112:0 && x122:0 <= x113:0 && x122:0 <= x112:0 && x118:0 - (x129:0 + 1) <= x118:0 - x117:0 - 1 && x129:0 - x117:0 <= x118:0 - x117:0 - 1 && x118:0 - 1 >= x117:0) f507_0_sort_GE(x170:0, x171:0, x172:0, x173:0, x174:0) -> f507_0_sort_GE'(x170:0, x171:0, x172:0, x173:0, x174:0) :|: x171:0 > 0 && x187:0 > 0 && x170:0 > 0 && x187:0 <= x171:0 && x187:0 <= x170:0 && x173:0 - (x186:0 + 1) <= x173:0 - x172:0 - 1 && x186:0 - x172:0 <= x173:0 - x172:0 - 1 && x173:0 - 1 >= x172:0 f507_0_sort_GE(x28:0, x29:0, x30:0, x31:0, x32:0) -> f507_0_sort_GE'(x28:0, x29:0, x30:0, x31:0, x32:0) :|: x43:0 > 0 && x44:0 > 0 && x29:0 > 0 && x28:0 > 0 && x44:0 <= x29:0 && x44:0 <= x28:0 && x43:0 <= x29:0 && x43:0 <= x28:0 && x42:0 - x30:0 <= x31:0 - x30:0 - 1 && x31:0 - 1 >= x30:0 f507_0_sort_GE(x100:0, x101:0, x102:0, x103:0, x104:0) -> f507_0_sort_GE'(x100:0, x101:0, x102:0, x103:0, x104:0) :|: x110:0 > 0 && x111:0 > 0 && x101:0 > 0 && x100:0 > 0 && x111:0 <= x101:0 && x111:0 <= x100:0 && x110:0 <= x101:0 && x110:0 <= x100:0 && x103:0 - (x109:0 + 1) <= x103:0 - x102:0 - 1 && x109:0 - x102:0 <= x103:0 - x102:0 - 1 && x103:0 - 1 >= x102:0 f507_0_sort_GE(x60:0, x61:0, x62:0, x64:0, x65:0) -> f507_0_sort_GE'(x60:0, x61:0, x62:0, x64:0, x65:0) :|: x76:0 > 0 && x77:0 > 0 && x61:0 > 0 && x60:0 > 0 && x77:0 <= x61:0 && x77:0 <= x60:0 && x76:0 <= x61:0 && x76:0 <= x60:0 && x64:0 - (x75:0 + 1) <= x64:0 - x62:0 - 1 && x75:0 - x62:0 >= x64:0 - x62:0 && x64:0 - 1 >= x62:0 f507_0_sort_GE'(x45:0, x46:0, x47:0, x48:0, x49:0) -> f507_0_sort_GE(x52:0, x53:0, x47:0, x55:0, x49:0) :|: x55:0 - x47:0 <= x48:0 - x47:0 - 1 && x48:0 - 1 >= x47:0 && x52:0 <= x45:0 && x52:0 <= x46:0 && x53:0 <= x45:0 && x53:0 <= x46:0 && x45:0 > 0 && x46:0 > 0 && x52:0 > 0 && x53:0 > 0 && x47:0 + x48:0 - 2 * x55:0 >= 0 && x47:0 + x48:0 - 2 * x55:0 <= 1 f507_0_sort_GE(x236:0, x237:0, x238:0, x239:0, x240:0) -> f507_0_sort_GE'(x236:0, x237:0, x238:0, x239:0, x240:0) :|: x237:0 > 0 && x251:0 > 0 && x236:0 > 0 && x251:0 <= x237:0 && x251:0 <= x236:0 && x240:0 > -1 && x239:0 - (x250:0 + 1) <= x239:0 - x238:0 - 1 && x250:0 - x238:0 >= x239:0 - x238:0 && x239:0 - 1 >= x238:0 f507_0_sort_GE(x133:0, x134:0, x135:0, x136:0, x137:0) -> f507_0_sort_GE'(x133:0, x134:0, x135:0, x136:0, x137:0) :|: x134:0 > 0 && x152:0 > 0 && x133:0 > 0 && x152:0 <= x134:0 && x152:0 <= x133:0 && x136:0 - (x151:0 + 1) >= x136:0 - x135:0 && x151:0 - x135:0 <= x136:0 - x135:0 - 1 && x136:0 - 1 >= x135:0 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f507_0_sort_GE' ] = 2*f507_0_sort_GE'_4 + -2*f507_0_sort_GE'_3 + -1 [ f507_0_sort_GE ] = 2*f507_0_sort_GE_4 + -2*f507_0_sort_GE_3 The following rules are decreasing: f507_0_sort_GE'(x112:0, x113:0, x117:0, x118:0, x119:0) -> f507_0_sort_GE(x122:0, x123:0, c, x118:0, x119:0) :|: c = x129:0 + 1 && (x117:0 + x118:0 - 2 * x129:0 <= 1 && x117:0 + x118:0 - 2 * x129:0 >= 0 && x123:0 > 0 && x122:0 > 0 && x113:0 > 0 && x112:0 > 0 && x123:0 <= x113:0 && x123:0 <= x112:0 && x122:0 <= x113:0 && x122:0 <= x112:0 && x118:0 - (x129:0 + 1) <= x118:0 - x117:0 - 1 && x129:0 - x117:0 <= x118:0 - x117:0 - 1 && x118:0 - 1 >= x117:0) f507_0_sort_GE(x170:0, x171:0, x172:0, x173:0, x174:0) -> f507_0_sort_GE'(x170:0, x171:0, x172:0, x173:0, x174:0) :|: x171:0 > 0 && x187:0 > 0 && x170:0 > 0 && x187:0 <= x171:0 && x187:0 <= x170:0 && x173:0 - (x186:0 + 1) <= x173:0 - x172:0 - 1 && x186:0 - x172:0 <= x173:0 - x172:0 - 1 && x173:0 - 1 >= x172:0 f507_0_sort_GE(x28:0, x29:0, x30:0, x31:0, x32:0) -> f507_0_sort_GE'(x28:0, x29:0, x30:0, x31:0, x32:0) :|: x43:0 > 0 && x44:0 > 0 && x29:0 > 0 && x28:0 > 0 && x44:0 <= x29:0 && x44:0 <= x28:0 && x43:0 <= x29:0 && x43:0 <= x28:0 && x42:0 - x30:0 <= x31:0 - x30:0 - 1 && x31:0 - 1 >= x30:0 f507_0_sort_GE(x100:0, x101:0, x102:0, x103:0, x104:0) -> f507_0_sort_GE'(x100:0, x101:0, x102:0, x103:0, x104:0) :|: x110:0 > 0 && x111:0 > 0 && x101:0 > 0 && x100:0 > 0 && x111:0 <= x101:0 && x111:0 <= x100:0 && x110:0 <= x101:0 && x110:0 <= x100:0 && x103:0 - (x109:0 + 1) <= x103:0 - x102:0 - 1 && x109:0 - x102:0 <= x103:0 - x102:0 - 1 && x103:0 - 1 >= x102:0 f507_0_sort_GE(x60:0, x61:0, x62:0, x64:0, x65:0) -> f507_0_sort_GE'(x60:0, x61:0, x62:0, x64:0, x65:0) :|: x76:0 > 0 && x77:0 > 0 && x61:0 > 0 && x60:0 > 0 && x77:0 <= x61:0 && x77:0 <= x60:0 && x76:0 <= x61:0 && x76:0 <= x60:0 && x64:0 - (x75:0 + 1) <= x64:0 - x62:0 - 1 && x75:0 - x62:0 >= x64:0 - x62:0 && x64:0 - 1 >= x62:0 f507_0_sort_GE'(x45:0, x46:0, x47:0, x48:0, x49:0) -> f507_0_sort_GE(x52:0, x53:0, x47:0, x55:0, x49:0) :|: x55:0 - x47:0 <= x48:0 - x47:0 - 1 && x48:0 - 1 >= x47:0 && x52:0 <= x45:0 && x52:0 <= x46:0 && x53:0 <= x45:0 && x53:0 <= x46:0 && x45:0 > 0 && x46:0 > 0 && x52:0 > 0 && x53:0 > 0 && x47:0 + x48:0 - 2 * x55:0 >= 0 && x47:0 + x48:0 - 2 * x55:0 <= 1 f507_0_sort_GE(x236:0, x237:0, x238:0, x239:0, x240:0) -> f507_0_sort_GE'(x236:0, x237:0, x238:0, x239:0, x240:0) :|: x237:0 > 0 && x251:0 > 0 && x236:0 > 0 && x251:0 <= x237:0 && x251:0 <= x236:0 && x240:0 > -1 && x239:0 - (x250:0 + 1) <= x239:0 - x238:0 - 1 && x250:0 - x238:0 >= x239:0 - x238:0 && x239:0 - 1 >= x238:0 f507_0_sort_GE(x133:0, x134:0, x135:0, x136:0, x137:0) -> f507_0_sort_GE'(x133:0, x134:0, x135:0, x136:0, x137:0) :|: x134:0 > 0 && x152:0 > 0 && x133:0 > 0 && x152:0 <= x134:0 && x152:0 <= x133:0 && x136:0 - (x151:0 + 1) >= x136:0 - x135:0 && x151:0 - x135:0 <= x136:0 - x135:0 - 1 && x136:0 - 1 >= x135:0 The following rules are bounded: f507_0_sort_GE'(x112:0, x113:0, x117:0, x118:0, x119:0) -> f507_0_sort_GE(x122:0, x123:0, c, x118:0, x119:0) :|: c = x129:0 + 1 && (x117:0 + x118:0 - 2 * x129:0 <= 1 && x117:0 + x118:0 - 2 * x129:0 >= 0 && x123:0 > 0 && x122:0 > 0 && x113:0 > 0 && x112:0 > 0 && x123:0 <= x113:0 && x123:0 <= x112:0 && x122:0 <= x113:0 && x122:0 <= x112:0 && x118:0 - (x129:0 + 1) <= x118:0 - x117:0 - 1 && x129:0 - x117:0 <= x118:0 - x117:0 - 1 && x118:0 - 1 >= x117:0) f507_0_sort_GE(x170:0, x171:0, x172:0, x173:0, x174:0) -> f507_0_sort_GE'(x170:0, x171:0, x172:0, x173:0, x174:0) :|: x171:0 > 0 && x187:0 > 0 && x170:0 > 0 && x187:0 <= x171:0 && x187:0 <= x170:0 && x173:0 - (x186:0 + 1) <= x173:0 - x172:0 - 1 && x186:0 - x172:0 <= x173:0 - x172:0 - 1 && x173:0 - 1 >= x172:0 f507_0_sort_GE(x28:0, x29:0, x30:0, x31:0, x32:0) -> f507_0_sort_GE'(x28:0, x29:0, x30:0, x31:0, x32:0) :|: x43:0 > 0 && x44:0 > 0 && x29:0 > 0 && x28:0 > 0 && x44:0 <= x29:0 && x44:0 <= x28:0 && x43:0 <= x29:0 && x43:0 <= x28:0 && x42:0 - x30:0 <= x31:0 - x30:0 - 1 && x31:0 - 1 >= x30:0 f507_0_sort_GE(x100:0, x101:0, x102:0, x103:0, x104:0) -> f507_0_sort_GE'(x100:0, x101:0, x102:0, x103:0, x104:0) :|: x110:0 > 0 && x111:0 > 0 && x101:0 > 0 && x100:0 > 0 && x111:0 <= x101:0 && x111:0 <= x100:0 && x110:0 <= x101:0 && x110:0 <= x100:0 && x103:0 - (x109:0 + 1) <= x103:0 - x102:0 - 1 && x109:0 - x102:0 <= x103:0 - x102:0 - 1 && x103:0 - 1 >= x102:0 f507_0_sort_GE(x60:0, x61:0, x62:0, x64:0, x65:0) -> f507_0_sort_GE'(x60:0, x61:0, x62:0, x64:0, x65:0) :|: x76:0 > 0 && x77:0 > 0 && x61:0 > 0 && x60:0 > 0 && x77:0 <= x61:0 && x77:0 <= x60:0 && x76:0 <= x61:0 && x76:0 <= x60:0 && x64:0 - (x75:0 + 1) <= x64:0 - x62:0 - 1 && x75:0 - x62:0 >= x64:0 - x62:0 && x64:0 - 1 >= x62:0 f507_0_sort_GE'(x45:0, x46:0, x47:0, x48:0, x49:0) -> f507_0_sort_GE(x52:0, x53:0, x47:0, x55:0, x49:0) :|: x55:0 - x47:0 <= x48:0 - x47:0 - 1 && x48:0 - 1 >= x47:0 && x52:0 <= x45:0 && x52:0 <= x46:0 && x53:0 <= x45:0 && x53:0 <= x46:0 && x45:0 > 0 && x46:0 > 0 && x52:0 > 0 && x53:0 > 0 && x47:0 + x48:0 - 2 * x55:0 >= 0 && x47:0 + x48:0 - 2 * x55:0 <= 1 f507_0_sort_GE(x236:0, x237:0, x238:0, x239:0, x240:0) -> f507_0_sort_GE'(x236:0, x237:0, x238:0, x239:0, x240:0) :|: x237:0 > 0 && x251:0 > 0 && x236:0 > 0 && x251:0 <= x237:0 && x251:0 <= x236:0 && x240:0 > -1 && x239:0 - (x250:0 + 1) <= x239:0 - x238:0 - 1 && x250:0 - x238:0 >= x239:0 - x238:0 && x239:0 - 1 >= x238:0 f507_0_sort_GE(x133:0, x134:0, x135:0, x136:0, x137:0) -> f507_0_sort_GE'(x133:0, x134:0, x135:0, x136:0, x137:0) :|: x134:0 > 0 && x152:0 > 0 && x133:0 > 0 && x152:0 <= x134:0 && x152:0 <= x133:0 && x136:0 - (x151:0 + 1) >= x136:0 - x135:0 && x151:0 - x135:0 <= x136:0 - x135:0 - 1 && x136:0 - 1 >= x135:0 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) f757_0_merge_GT(x294, x295, x296, x297, x298, x299, x300) -> f757_0_merge_GT(x301, x302, x303, x304, x305, x306, x307) :|: x300 = x307 && x299 = x306 && x297 + 1 = x305 && x297 + 1 = x304 && x295 = x302 && x294 = x301 && x297 = x298 && 0 <= x303 - 1 && 0 <= x296 - 1 && x303 <= x296 && x297 <= x300 - 1 && x297 <= x299 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: f757_0_merge_GT(x294:0, x295:0, x296:0, x297:0, x297:0, x299:0, x300:0) -> f757_0_merge_GT(x294:0, x295:0, x303:0, x297:0 + 1, x297:0 + 1, x299:0, x300:0) :|: x300:0 - 1 >= x297:0 && x299:0 >= x297:0 && x303:0 <= x296:0 && x303:0 > 0 && x296:0 > 0 ---------------------------------------- (26) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f757_0_merge_GT(x1, x2, x3, x4, x5, x6, x7) -> f757_0_merge_GT(x3, x4, x5, x6, x7) ---------------------------------------- (27) Obligation: Rules: f757_0_merge_GT(x296:0, x297:0, x297:0, x299:0, x300:0) -> f757_0_merge_GT(x303:0, x297:0 + 1, x297:0 + 1, x299:0, x300:0) :|: x300:0 - 1 >= x297:0 && x299:0 >= x297:0 && x303:0 <= x296:0 && x303:0 > 0 && x296:0 > 0 ---------------------------------------- (28) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f757_0_merge_GT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: f757_0_merge_GT(x296:0, x297:0, x297:0, x299:0, x300:0) -> f757_0_merge_GT(x303:0, c, c1, x299:0, x300:0) :|: c1 = x297:0 + 1 && c = x297:0 + 1 && (x300:0 - 1 >= x297:0 && x299:0 >= x297:0 && x303:0 <= x296:0 && x303:0 > 0 && x296:0 > 0) ---------------------------------------- (30) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f757_0_merge_GT(x, x1, x2, x3, x4)] = -x2 + x3 The following rules are decreasing: f757_0_merge_GT(x296:0, x297:0, x297:0, x299:0, x300:0) -> f757_0_merge_GT(x303:0, c, c1, x299:0, x300:0) :|: c1 = x297:0 + 1 && c = x297:0 + 1 && (x300:0 - 1 >= x297:0 && x299:0 >= x297:0 && x303:0 <= x296:0 && x303:0 > 0 && x296:0 > 0) The following rules are bounded: f757_0_merge_GT(x296:0, x297:0, x297:0, x299:0, x300:0) -> f757_0_merge_GT(x303:0, c, c1, x299:0, x300:0) :|: c1 = x297:0 + 1 && c = x297:0 + 1 && (x300:0 - 1 >= x297:0 && x299:0 >= x297:0 && x303:0 <= x296:0 && x303:0 > 0 && x296:0 > 0) ---------------------------------------- (31) YES ---------------------------------------- (32) Obligation: Termination digraph: Nodes: (1) f774_0_merge_GT(x308, x309, x310, x311, x312, x313, x314) -> f774_0_merge_GT(x315, x316, x317, x318, x319, x320, x321) :|: x313 = x320 && x312 = x319 && x311 + 1 = x318 && x309 = x316 && x308 = x315 && 0 <= x317 - 1 && 0 <= x310 - 1 && x317 <= x310 && x311 <= x313 - 1 && x311 <= x312 && x312 + x309 + 1 - x311 <= x313 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (33) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (34) Obligation: Rules: f774_0_merge_GT(x308:0, x309:0, x310:0, x311:0, x312:0, x313:0, x314:0) -> f774_0_merge_GT(x308:0, x309:0, x317:0, x311:0 + 1, x312:0, x313:0, x321:0) :|: x312:0 >= x311:0 && x313:0 - 1 >= x312:0 + x309:0 + 1 - x311:0 && x313:0 - 1 >= x311:0 && x317:0 <= x310:0 && x317:0 > 0 && x310:0 > 0 ---------------------------------------- (35) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f774_0_merge_GT(x1, x2, x3, x4, x5, x6, x7) -> f774_0_merge_GT(x2, x3, x4, x5, x6) ---------------------------------------- (36) Obligation: Rules: f774_0_merge_GT(x309:0, x310:0, x311:0, x312:0, x313:0) -> f774_0_merge_GT(x309:0, x317:0, x311:0 + 1, x312:0, x313:0) :|: x312:0 >= x311:0 && x313:0 - 1 >= x312:0 + x309:0 + 1 - x311:0 && x313:0 - 1 >= x311:0 && x317:0 <= x310:0 && x317:0 > 0 && x310:0 > 0 ---------------------------------------- (37) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f774_0_merge_GT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (38) Obligation: Rules: f774_0_merge_GT(x309:0, x310:0, x311:0, x312:0, x313:0) -> f774_0_merge_GT(x309:0, x317:0, c, x312:0, x313:0) :|: c = x311:0 + 1 && (x312:0 >= x311:0 && x313:0 - 1 >= x312:0 + x309:0 + 1 - x311:0 && x313:0 - 1 >= x311:0 && x317:0 <= x310:0 && x317:0 > 0 && x310:0 > 0) ---------------------------------------- (39) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f774_0_merge_GT ] = -1*f774_0_merge_GT_3 + f774_0_merge_GT_5 The following rules are decreasing: f774_0_merge_GT(x309:0, x310:0, x311:0, x312:0, x313:0) -> f774_0_merge_GT(x309:0, x317:0, c, x312:0, x313:0) :|: c = x311:0 + 1 && (x312:0 >= x311:0 && x313:0 - 1 >= x312:0 + x309:0 + 1 - x311:0 && x313:0 - 1 >= x311:0 && x317:0 <= x310:0 && x317:0 > 0 && x310:0 > 0) The following rules are bounded: f774_0_merge_GT(x309:0, x310:0, x311:0, x312:0, x313:0) -> f774_0_merge_GT(x309:0, x317:0, c, x312:0, x313:0) :|: c = x311:0 + 1 && (x312:0 >= x311:0 && x313:0 - 1 >= x312:0 + x309:0 + 1 - x311:0 && x313:0 - 1 >= x311:0 && x317:0 <= x310:0 && x317:0 > 0 && x310:0 > 0) ---------------------------------------- (40) YES ---------------------------------------- (41) Obligation: Termination digraph: Nodes: (1) f1440_0_merge_GT(x336, x337, x338, x339, x340, x341, x342) -> f1440_0_merge_GT(x343, x344, x345, x346, x347, x348, x349) :|: x339 <= x341 && x337 <= x342 - 1 && x338 <= x342 - 1 && x350 <= x351 && x339 <= x342 - 1 && x343 <= x336 && 0 <= x336 - 1 && 0 <= x343 - 1 && x339 = x340 && x337 = x344 && x338 - 1 = x345 && x339 + 1 = x346 && x339 + 1 = x347 && x341 = x348 && x342 = x349 (2) f1440_0_merge_GT(x352, x353, x354, x355, x356, x357, x358) -> f1440_0_merge_GT(x359, x360, x361, x362, x363, x364, x365) :|: x355 <= x357 && x353 <= x358 - 1 && x354 <= x358 - 1 && x366 <= x367 - 1 && x355 <= x358 - 1 && x359 <= x352 && 0 <= x352 - 1 && 0 <= x359 - 1 && x355 = x356 && x353 + 1 = x360 && x354 = x361 && x355 + 1 = x362 && x355 + 1 = x363 && x357 = x364 && x358 = x365 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (42) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (43) Obligation: Rules: f1440_0_merge_GT(x336:0, x337:0, x338:0, x339:0, x339:0, x341:0, x342:0) -> f1440_0_merge_GT(x343:0, x337:0, x338:0 - 1, x339:0 + 1, x339:0 + 1, x341:0, x342:0) :|: x336:0 > 0 && x343:0 > 0 && x343:0 <= x336:0 && x342:0 - 1 >= x339:0 && x351:0 >= x350:0 && x342:0 - 1 >= x338:0 && x342:0 - 1 >= x337:0 && x341:0 >= x339:0 f1440_0_merge_GT(x352:0, x353:0, x354:0, x355:0, x355:0, x357:0, x358:0) -> f1440_0_merge_GT(x359:0, x353:0 + 1, x354:0, x355:0 + 1, x355:0 + 1, x357:0, x358:0) :|: x352:0 > 0 && x359:0 > 0 && x359:0 <= x352:0 && x358:0 - 1 >= x355:0 && x367:0 - 1 >= x366:0 && x358:0 - 1 >= x354:0 && x358:0 - 1 >= x353:0 && x357:0 >= x355:0 ---------------------------------------- (44) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1440_0_merge_GT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (45) Obligation: Rules: f1440_0_merge_GT(x336:0, x337:0, x338:0, x339:0, x339:0, x341:0, x342:0) -> f1440_0_merge_GT(x343:0, x337:0, c, c1, c2, x341:0, x342:0) :|: c2 = x339:0 + 1 && (c1 = x339:0 + 1 && c = x338:0 - 1) && (x336:0 > 0 && x343:0 > 0 && x343:0 <= x336:0 && x342:0 - 1 >= x339:0 && x351:0 >= x350:0 && x342:0 - 1 >= x338:0 && x342:0 - 1 >= x337:0 && x341:0 >= x339:0) f1440_0_merge_GT(x352:0, x353:0, x354:0, x355:0, x355:0, x357:0, x358:0) -> f1440_0_merge_GT(x359:0, c3, x354:0, c4, c5, x357:0, x358:0) :|: c5 = x355:0 + 1 && (c4 = x355:0 + 1 && c3 = x353:0 + 1) && (x352:0 > 0 && x359:0 > 0 && x359:0 <= x352:0 && x358:0 - 1 >= x355:0 && x367:0 - 1 >= x366:0 && x358:0 - 1 >= x354:0 && x358:0 - 1 >= x353:0 && x357:0 >= x355:0) ---------------------------------------- (46) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f1440_0_merge_GT ] = -1*f1440_0_merge_GT_5 + f1440_0_merge_GT_6 The following rules are decreasing: f1440_0_merge_GT(x336:0, x337:0, x338:0, x339:0, x339:0, x341:0, x342:0) -> f1440_0_merge_GT(x343:0, x337:0, c, c1, c2, x341:0, x342:0) :|: c2 = x339:0 + 1 && (c1 = x339:0 + 1 && c = x338:0 - 1) && (x336:0 > 0 && x343:0 > 0 && x343:0 <= x336:0 && x342:0 - 1 >= x339:0 && x351:0 >= x350:0 && x342:0 - 1 >= x338:0 && x342:0 - 1 >= x337:0 && x341:0 >= x339:0) f1440_0_merge_GT(x352:0, x353:0, x354:0, x355:0, x355:0, x357:0, x358:0) -> f1440_0_merge_GT(x359:0, c3, x354:0, c4, c5, x357:0, x358:0) :|: c5 = x355:0 + 1 && (c4 = x355:0 + 1 && c3 = x353:0 + 1) && (x352:0 > 0 && x359:0 > 0 && x359:0 <= x352:0 && x358:0 - 1 >= x355:0 && x367:0 - 1 >= x366:0 && x358:0 - 1 >= x354:0 && x358:0 - 1 >= x353:0 && x357:0 >= x355:0) The following rules are bounded: f1440_0_merge_GT(x336:0, x337:0, x338:0, x339:0, x339:0, x341:0, x342:0) -> f1440_0_merge_GT(x343:0, x337:0, c, c1, c2, x341:0, x342:0) :|: c2 = x339:0 + 1 && (c1 = x339:0 + 1 && c = x338:0 - 1) && (x336:0 > 0 && x343:0 > 0 && x343:0 <= x336:0 && x342:0 - 1 >= x339:0 && x351:0 >= x350:0 && x342:0 - 1 >= x338:0 && x342:0 - 1 >= x337:0 && x341:0 >= x339:0) f1440_0_merge_GT(x352:0, x353:0, x354:0, x355:0, x355:0, x357:0, x358:0) -> f1440_0_merge_GT(x359:0, c3, x354:0, c4, c5, x357:0, x358:0) :|: c5 = x355:0 + 1 && (c4 = x355:0 + 1 && c3 = x353:0 + 1) && (x352:0 > 0 && x359:0 > 0 && x359:0 <= x352:0 && x358:0 - 1 >= x355:0 && x367:0 - 1 >= x366:0 && x358:0 - 1 >= x354:0 && x358:0 - 1 >= x353:0 && x357:0 >= x355:0) ---------------------------------------- (47) YES