YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 21.9 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 0 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 22 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 3 ms] (13) IntTRS (14) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (15) YES (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IRSwT (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (20) IRSwT (21) TempFilterProof [SOUND, 34 ms] (22) IntTRS (23) RankingReductionPairProof [EQUIVALENT, 7 ms] (24) YES ---------------------------------------- (0) Obligation: Rules: l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: oldX3HAT0 = oldX3HATpost && oldX2HAT0 = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX1HATpost <= 0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l0(x, x1, x2, x3, x4, x5) -> l1(x6, x7, x8, x9, x10, x11) :|: x3 = x9 && x2 = x8 && x11 = x7 && x10 = x6 && 0 <= x7 && x7 <= 0 && x7 = x5 && x6 = x4 l0(x12, x13, x14, x15, x16, x17) -> l2(x18, x19, x20, x21, x22, x23) :|: x15 = x21 && x14 = x20 && x23 = x19 && x22 = x18 && 1 <= x19 && 1 <= x19 && x19 = x17 && x18 = x16 l0(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x27 = x33 && x26 = x32 && x35 = x31 && x34 = x30 && 1 <= x31 && 1 + x31 <= 0 && x31 = x29 && x30 = x28 l3(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x38 = x44 && x47 = x43 && x46 = x42 && x43 = x41 && x42 = x40 l4(x48, x49, x50, x51, x52, x53) -> l5(x54, x55, x56, x57, x58, x59) :|: x59 = x57 && x58 = x56 && x57 = x57 && x56 = x56 && x55 = x53 && x54 = x52 l6(x60, x61, x62, x63, x64, x65) -> l5(x66, x67, x68, x69, x70, x71) :|: x71 = x69 && x70 = x68 && x69 = x69 && x68 = x68 && x67 = x65 && x66 = x64 l6(x72, x73, x74, x75, x76, x77) -> l7(x78, x79, x80, x81, x82, x83) :|: x75 = x81 && x74 = x80 && x83 = x79 && x82 = -1 + x78 && x79 = x77 && x78 = x76 l8(x84, x85, x86, x87, x88, x89) -> l4(x90, x91, x92, x93, x94, x95) :|: x87 = x93 && x86 = x92 && x95 = x91 && x94 = x90 && x90 <= 0 && x91 = x89 && x90 = x88 l8(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x98 = x104 && x107 = x103 && x106 = x102 && 1 <= x102 && x103 = x101 && x102 = x100 l9(x108, x109, x110, x111, x112, x113) -> l5(x114, x115, x116, x117, x118, x119) :|: x119 = x117 && x118 = x116 && x117 = x117 && x116 = x116 && x115 = x113 && x114 = x112 l9(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = -1 + x127 && x130 = x126 && x127 = x125 && x126 = x124 l10(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x135 = x141 && x134 = x140 && x143 = x139 && x142 = x138 && x139 <= 0 && x139 = x137 && x138 = x136 l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x147 = x153 && x146 = x152 && x155 = x151 && x154 = x150 && 1 <= x151 && x151 = x149 && x150 = x148 l1(x156, x157, x158, x159, x160, x161) -> l11(x162, x163, x164, x165, x166, x167) :|: x167 = x165 && x166 = x164 && x165 = x165 && x164 = x164 && x163 = x161 && x162 = x160 l2(x168, x169, x170, x171, x172, x173) -> l11(x174, x175, x176, x177, x178, x179) :|: x179 = x177 && x178 = x176 && x177 = x177 && x176 = x176 && x175 = x173 && x174 = x172 l2(x180, x181, x182, x183, x184, x185) -> l3(x186, x187, x188, x189, x190, x191) :|: x183 = x189 && x182 = x188 && x191 = -1 + x187 && x190 = x186 && x187 = x185 && x186 = x184 l7(x192, x193, x194, x195, x196, x197) -> l10(x198, x199, x200, x201, x202, x203) :|: x195 = x201 && x194 = x200 && x203 = x199 && x202 = x198 && x199 = x197 && x198 = x196 l12(x204, x205, x206, x207, x208, x209) -> l0(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x207 = x213 && x206 = x212 && x205 = x211 && x204 = x210 l12(x216, x217, x218, x219, x220, x221) -> l3(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x219 = x225 && x218 = x224 && x217 = x223 && x216 = x222 l12(x228, x229, x230, x231, x232, x233) -> l4(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x232 = x238 && x231 = x237 && x230 = x236 && x229 = x235 && x228 = x234 l12(x240, x241, x242, x243, x244, x245) -> l6(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x243 = x249 && x242 = x248 && x241 = x247 && x240 = x246 l12(x252, x253, x254, x255, x256, x257) -> l5(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x254 = x260 && x253 = x259 && x252 = x258 l12(x264, x265, x266, x267, x268, x269) -> l8(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x267 = x273 && x266 = x272 && x265 = x271 && x264 = x270 l12(x276, x277, x278, x279, x280, x281) -> l9(x282, x283, x284, x285, x286, x287) :|: x281 = x287 && x280 = x286 && x279 = x285 && x278 = x284 && x277 = x283 && x276 = x282 l12(x288, x289, x290, x291, x292, x293) -> l10(x294, x295, x296, x297, x298, x299) :|: x293 = x299 && x292 = x298 && x291 = x297 && x290 = x296 && x289 = x295 && x288 = x294 l12(x300, x301, x302, x303, x304, x305) -> l11(x306, x307, x308, x309, x310, x311) :|: x305 = x311 && x304 = x310 && x303 = x309 && x302 = x308 && x301 = x307 && x300 = x306 l12(x312, x313, x314, x315, x316, x317) -> l1(x318, x319, x320, x321, x322, x323) :|: x317 = x323 && x316 = x322 && x315 = x321 && x314 = x320 && x313 = x319 && x312 = x318 l12(x324, x325, x326, x327, x328, x329) -> l2(x330, x331, x332, x333, x334, x335) :|: x329 = x335 && x328 = x334 && x327 = x333 && x326 = x332 && x325 = x331 && x324 = x330 l12(x336, x337, x338, x339, x340, x341) -> l7(x342, x343, x344, x345, x346, x347) :|: x341 = x347 && x340 = x346 && x339 = x345 && x338 = x344 && x337 = x343 && x336 = x342 l13(x348, x349, x350, x351, x352, x353) -> l12(x354, x355, x356, x357, x358, x359) :|: x353 = x359 && x352 = x358 && x351 = x357 && x350 = x356 && x349 = x355 && x348 = x354 Start term: l13(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: oldX3HAT0 = oldX3HATpost && oldX2HAT0 = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX1HATpost <= 0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l0(x, x1, x2, x3, x4, x5) -> l1(x6, x7, x8, x9, x10, x11) :|: x3 = x9 && x2 = x8 && x11 = x7 && x10 = x6 && 0 <= x7 && x7 <= 0 && x7 = x5 && x6 = x4 l0(x12, x13, x14, x15, x16, x17) -> l2(x18, x19, x20, x21, x22, x23) :|: x15 = x21 && x14 = x20 && x23 = x19 && x22 = x18 && 1 <= x19 && 1 <= x19 && x19 = x17 && x18 = x16 l0(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x27 = x33 && x26 = x32 && x35 = x31 && x34 = x30 && 1 <= x31 && 1 + x31 <= 0 && x31 = x29 && x30 = x28 l3(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x38 = x44 && x47 = x43 && x46 = x42 && x43 = x41 && x42 = x40 l4(x48, x49, x50, x51, x52, x53) -> l5(x54, x55, x56, x57, x58, x59) :|: x59 = x57 && x58 = x56 && x57 = x57 && x56 = x56 && x55 = x53 && x54 = x52 l6(x60, x61, x62, x63, x64, x65) -> l5(x66, x67, x68, x69, x70, x71) :|: x71 = x69 && x70 = x68 && x69 = x69 && x68 = x68 && x67 = x65 && x66 = x64 l6(x72, x73, x74, x75, x76, x77) -> l7(x78, x79, x80, x81, x82, x83) :|: x75 = x81 && x74 = x80 && x83 = x79 && x82 = -1 + x78 && x79 = x77 && x78 = x76 l8(x84, x85, x86, x87, x88, x89) -> l4(x90, x91, x92, x93, x94, x95) :|: x87 = x93 && x86 = x92 && x95 = x91 && x94 = x90 && x90 <= 0 && x91 = x89 && x90 = x88 l8(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x98 = x104 && x107 = x103 && x106 = x102 && 1 <= x102 && x103 = x101 && x102 = x100 l9(x108, x109, x110, x111, x112, x113) -> l5(x114, x115, x116, x117, x118, x119) :|: x119 = x117 && x118 = x116 && x117 = x117 && x116 = x116 && x115 = x113 && x114 = x112 l9(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = -1 + x127 && x130 = x126 && x127 = x125 && x126 = x124 l10(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x135 = x141 && x134 = x140 && x143 = x139 && x142 = x138 && x139 <= 0 && x139 = x137 && x138 = x136 l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x147 = x153 && x146 = x152 && x155 = x151 && x154 = x150 && 1 <= x151 && x151 = x149 && x150 = x148 l1(x156, x157, x158, x159, x160, x161) -> l11(x162, x163, x164, x165, x166, x167) :|: x167 = x165 && x166 = x164 && x165 = x165 && x164 = x164 && x163 = x161 && x162 = x160 l2(x168, x169, x170, x171, x172, x173) -> l11(x174, x175, x176, x177, x178, x179) :|: x179 = x177 && x178 = x176 && x177 = x177 && x176 = x176 && x175 = x173 && x174 = x172 l2(x180, x181, x182, x183, x184, x185) -> l3(x186, x187, x188, x189, x190, x191) :|: x183 = x189 && x182 = x188 && x191 = -1 + x187 && x190 = x186 && x187 = x185 && x186 = x184 l7(x192, x193, x194, x195, x196, x197) -> l10(x198, x199, x200, x201, x202, x203) :|: x195 = x201 && x194 = x200 && x203 = x199 && x202 = x198 && x199 = x197 && x198 = x196 l12(x204, x205, x206, x207, x208, x209) -> l0(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x207 = x213 && x206 = x212 && x205 = x211 && x204 = x210 l12(x216, x217, x218, x219, x220, x221) -> l3(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x219 = x225 && x218 = x224 && x217 = x223 && x216 = x222 l12(x228, x229, x230, x231, x232, x233) -> l4(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x232 = x238 && x231 = x237 && x230 = x236 && x229 = x235 && x228 = x234 l12(x240, x241, x242, x243, x244, x245) -> l6(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x243 = x249 && x242 = x248 && x241 = x247 && x240 = x246 l12(x252, x253, x254, x255, x256, x257) -> l5(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x254 = x260 && x253 = x259 && x252 = x258 l12(x264, x265, x266, x267, x268, x269) -> l8(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x267 = x273 && x266 = x272 && x265 = x271 && x264 = x270 l12(x276, x277, x278, x279, x280, x281) -> l9(x282, x283, x284, x285, x286, x287) :|: x281 = x287 && x280 = x286 && x279 = x285 && x278 = x284 && x277 = x283 && x276 = x282 l12(x288, x289, x290, x291, x292, x293) -> l10(x294, x295, x296, x297, x298, x299) :|: x293 = x299 && x292 = x298 && x291 = x297 && x290 = x296 && x289 = x295 && x288 = x294 l12(x300, x301, x302, x303, x304, x305) -> l11(x306, x307, x308, x309, x310, x311) :|: x305 = x311 && x304 = x310 && x303 = x309 && x302 = x308 && x301 = x307 && x300 = x306 l12(x312, x313, x314, x315, x316, x317) -> l1(x318, x319, x320, x321, x322, x323) :|: x317 = x323 && x316 = x322 && x315 = x321 && x314 = x320 && x313 = x319 && x312 = x318 l12(x324, x325, x326, x327, x328, x329) -> l2(x330, x331, x332, x333, x334, x335) :|: x329 = x335 && x328 = x334 && x327 = x333 && x326 = x332 && x325 = x331 && x324 = x330 l12(x336, x337, x338, x339, x340, x341) -> l7(x342, x343, x344, x345, x346, x347) :|: x341 = x347 && x340 = x346 && x339 = x345 && x338 = x344 && x337 = x343 && x336 = x342 l13(x348, x349, x350, x351, x352, x353) -> l12(x354, x355, x356, x357, x358, x359) :|: x353 = x359 && x352 = x358 && x351 = x357 && x350 = x356 && x349 = x355 && x348 = x354 Start term: l13(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: oldX3HAT0 = oldX3HATpost && oldX2HAT0 = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX1HATpost <= 0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l0(x, x1, x2, x3, x4, x5) -> l1(x6, x7, x8, x9, x10, x11) :|: x3 = x9 && x2 = x8 && x11 = x7 && x10 = x6 && 0 <= x7 && x7 <= 0 && x7 = x5 && x6 = x4 (3) l0(x12, x13, x14, x15, x16, x17) -> l2(x18, x19, x20, x21, x22, x23) :|: x15 = x21 && x14 = x20 && x23 = x19 && x22 = x18 && 1 <= x19 && 1 <= x19 && x19 = x17 && x18 = x16 (4) l0(x24, x25, x26, x27, x28, x29) -> l2(x30, x31, x32, x33, x34, x35) :|: x27 = x33 && x26 = x32 && x35 = x31 && x34 = x30 && 1 <= x31 && 1 + x31 <= 0 && x31 = x29 && x30 = x28 (5) l3(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x38 = x44 && x47 = x43 && x46 = x42 && x43 = x41 && x42 = x40 (6) l4(x48, x49, x50, x51, x52, x53) -> l5(x54, x55, x56, x57, x58, x59) :|: x59 = x57 && x58 = x56 && x57 = x57 && x56 = x56 && x55 = x53 && x54 = x52 (7) l6(x60, x61, x62, x63, x64, x65) -> l5(x66, x67, x68, x69, x70, x71) :|: x71 = x69 && x70 = x68 && x69 = x69 && x68 = x68 && x67 = x65 && x66 = x64 (8) l6(x72, x73, x74, x75, x76, x77) -> l7(x78, x79, x80, x81, x82, x83) :|: x75 = x81 && x74 = x80 && x83 = x79 && x82 = -1 + x78 && x79 = x77 && x78 = x76 (9) l8(x84, x85, x86, x87, x88, x89) -> l4(x90, x91, x92, x93, x94, x95) :|: x87 = x93 && x86 = x92 && x95 = x91 && x94 = x90 && x90 <= 0 && x91 = x89 && x90 = x88 (10) l8(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x98 = x104 && x107 = x103 && x106 = x102 && 1 <= x102 && x103 = x101 && x102 = x100 (11) l9(x108, x109, x110, x111, x112, x113) -> l5(x114, x115, x116, x117, x118, x119) :|: x119 = x117 && x118 = x116 && x117 = x117 && x116 = x116 && x115 = x113 && x114 = x112 (12) l9(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = -1 + x127 && x130 = x126 && x127 = x125 && x126 = x124 (13) l10(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x135 = x141 && x134 = x140 && x143 = x139 && x142 = x138 && x139 <= 0 && x139 = x137 && x138 = x136 (14) l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x147 = x153 && x146 = x152 && x155 = x151 && x154 = x150 && 1 <= x151 && x151 = x149 && x150 = x148 (15) l1(x156, x157, x158, x159, x160, x161) -> l11(x162, x163, x164, x165, x166, x167) :|: x167 = x165 && x166 = x164 && x165 = x165 && x164 = x164 && x163 = x161 && x162 = x160 (16) l2(x168, x169, x170, x171, x172, x173) -> l11(x174, x175, x176, x177, x178, x179) :|: x179 = x177 && x178 = x176 && x177 = x177 && x176 = x176 && x175 = x173 && x174 = x172 (17) l2(x180, x181, x182, x183, x184, x185) -> l3(x186, x187, x188, x189, x190, x191) :|: x183 = x189 && x182 = x188 && x191 = -1 + x187 && x190 = x186 && x187 = x185 && x186 = x184 (18) l7(x192, x193, x194, x195, x196, x197) -> l10(x198, x199, x200, x201, x202, x203) :|: x195 = x201 && x194 = x200 && x203 = x199 && x202 = x198 && x199 = x197 && x198 = x196 (19) l12(x204, x205, x206, x207, x208, x209) -> l0(x210, x211, x212, x213, x214, x215) :|: x209 = x215 && x208 = x214 && x207 = x213 && x206 = x212 && x205 = x211 && x204 = x210 (20) l12(x216, x217, x218, x219, x220, x221) -> l3(x222, x223, x224, x225, x226, x227) :|: x221 = x227 && x220 = x226 && x219 = x225 && x218 = x224 && x217 = x223 && x216 = x222 (21) l12(x228, x229, x230, x231, x232, x233) -> l4(x234, x235, x236, x237, x238, x239) :|: x233 = x239 && x232 = x238 && x231 = x237 && x230 = x236 && x229 = x235 && x228 = x234 (22) l12(x240, x241, x242, x243, x244, x245) -> l6(x246, x247, x248, x249, x250, x251) :|: x245 = x251 && x244 = x250 && x243 = x249 && x242 = x248 && x241 = x247 && x240 = x246 (23) l12(x252, x253, x254, x255, x256, x257) -> l5(x258, x259, x260, x261, x262, x263) :|: x257 = x263 && x256 = x262 && x255 = x261 && x254 = x260 && x253 = x259 && x252 = x258 (24) l12(x264, x265, x266, x267, x268, x269) -> l8(x270, x271, x272, x273, x274, x275) :|: x269 = x275 && x268 = x274 && x267 = x273 && x266 = x272 && x265 = x271 && x264 = x270 (25) l12(x276, x277, x278, x279, x280, x281) -> l9(x282, x283, x284, x285, x286, x287) :|: x281 = x287 && x280 = x286 && x279 = x285 && x278 = x284 && x277 = x283 && x276 = x282 (26) l12(x288, x289, x290, x291, x292, x293) -> l10(x294, x295, x296, x297, x298, x299) :|: x293 = x299 && x292 = x298 && x291 = x297 && x290 = x296 && x289 = x295 && x288 = x294 (27) l12(x300, x301, x302, x303, x304, x305) -> l11(x306, x307, x308, x309, x310, x311) :|: x305 = x311 && x304 = x310 && x303 = x309 && x302 = x308 && x301 = x307 && x300 = x306 (28) l12(x312, x313, x314, x315, x316, x317) -> l1(x318, x319, x320, x321, x322, x323) :|: x317 = x323 && x316 = x322 && x315 = x321 && x314 = x320 && x313 = x319 && x312 = x318 (29) l12(x324, x325, x326, x327, x328, x329) -> l2(x330, x331, x332, x333, x334, x335) :|: x329 = x335 && x328 = x334 && x327 = x333 && x326 = x332 && x325 = x331 && x324 = x330 (30) l12(x336, x337, x338, x339, x340, x341) -> l7(x342, x343, x344, x345, x346, x347) :|: x341 = x347 && x340 = x346 && x339 = x345 && x338 = x344 && x337 = x343 && x336 = x342 (31) l13(x348, x349, x350, x351, x352, x353) -> l12(x354, x355, x356, x357, x358, x359) :|: x353 = x359 && x352 = x358 && x351 = x357 && x350 = x356 && x349 = x355 && x348 = x354 Arcs: (1) -> (15) (2) -> (15) (3) -> (16), (17) (5) -> (1), (2), (3) (8) -> (18) (9) -> (6) (10) -> (7), (8) (12) -> (18) (13) -> (9), (10) (14) -> (11), (12) (17) -> (5) (18) -> (13), (14) (19) -> (1), (2), (3) (20) -> (5) (21) -> (6) (22) -> (7), (8) (24) -> (9), (10) (25) -> (11), (12) (26) -> (13), (14) (28) -> (15) (29) -> (16), (17) (30) -> (18) (31) -> (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), (29), (30) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l6(x72, x73, x74, x75, x76, x77) -> l7(x78, x79, x80, x81, x82, x83) :|: x75 = x81 && x74 = x80 && x83 = x79 && x82 = -1 + x78 && x79 = x77 && x78 = x76 (2) l8(x96, x97, x98, x99, x100, x101) -> l6(x102, x103, x104, x105, x106, x107) :|: x99 = x105 && x98 = x104 && x107 = x103 && x106 = x102 && 1 <= x102 && x103 = x101 && x102 = x100 (3) l10(x132, x133, x134, x135, x136, x137) -> l8(x138, x139, x140, x141, x142, x143) :|: x135 = x141 && x134 = x140 && x143 = x139 && x142 = x138 && x139 <= 0 && x139 = x137 && x138 = x136 (4) l7(x192, x193, x194, x195, x196, x197) -> l10(x198, x199, x200, x201, x202, x203) :|: x195 = x201 && x194 = x200 && x203 = x199 && x202 = x198 && x199 = x197 && x198 = x196 (5) l9(x120, x121, x122, x123, x124, x125) -> l7(x126, x127, x128, x129, x130, x131) :|: x123 = x129 && x122 = x128 && x131 = -1 + x127 && x130 = x126 && x127 = x125 && x126 = x124 (6) l10(x144, x145, x146, x147, x148, x149) -> l9(x150, x151, x152, x153, x154, x155) :|: x147 = x153 && x146 = x152 && x155 = x151 && x154 = x150 && 1 <= x151 && x151 = x149 && x150 = x148 Arcs: (1) -> (4) (2) -> (1) (3) -> (2) (4) -> (3), (6) (5) -> (4) (6) -> (5) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l10(x144:0, x145:0, x128:0, x129:0, x126:0, x127:0) -> l10(x126:0, -1 + x127:0, x128:0, x129:0, x126:0, -1 + x127:0) :|: x127:0 > 0 l10(x132:0, x133:0, x104:0, x105:0, x102:0, x103:0) -> l10(-1 + x102:0, x103:0, x104:0, x105:0, -1 + x102:0, x103:0) :|: x103:0 < 1 && x102:0 > 0 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l10(x1, x2, x3, x4, x5, x6) -> l10(x5, x6) ---------------------------------------- (9) Obligation: Rules: l10(x126:0, x127:0) -> l10(x126:0, -1 + x127:0) :|: x127:0 > 0 l10(x102:0, x103:0) -> l10(-1 + x102:0, x103:0) :|: x103:0 < 1 && x102:0 > 0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l10(VARIABLE, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l10(x126:0, x127:0) -> l10(x126:0, c) :|: c = -1 + x127:0 && x127:0 > 0 l10(x102:0, x103:0) -> l10(c1, x103:0) :|: c1 = -1 + x102:0 && (x103:0 < 1 && x102:0 > 0) ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l10 ] = 2*l10_1 The following rules are decreasing: l10(x102:0, x103:0) -> l10(c1, x103:0) :|: c1 = -1 + x102:0 && (x103:0 < 1 && x102:0 > 0) The following rules are bounded: l10(x102:0, x103:0) -> l10(c1, x103:0) :|: c1 = -1 + x102:0 && (x103:0 < 1 && x102:0 > 0) ---------------------------------------- (13) Obligation: Rules: l10(x126:0, x127:0) -> l10(x126:0, c) :|: c = -1 + x127:0 && x127:0 > 0 ---------------------------------------- (14) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l10(x, x1)] = x1 The following rules are decreasing: l10(x126:0, x127:0) -> l10(x126:0, c) :|: c = -1 + x127:0 && x127:0 > 0 The following rules are bounded: l10(x126:0, x127:0) -> l10(x126:0, c) :|: c = -1 + x127:0 && x127:0 > 0 ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l0(x12, x13, x14, x15, x16, x17) -> l2(x18, x19, x20, x21, x22, x23) :|: x15 = x21 && x14 = x20 && x23 = x19 && x22 = x18 && 1 <= x19 && 1 <= x19 && x19 = x17 && x18 = x16 (2) l3(x36, x37, x38, x39, x40, x41) -> l0(x42, x43, x44, x45, x46, x47) :|: x39 = x45 && x38 = x44 && x47 = x43 && x46 = x42 && x43 = x41 && x42 = x40 (3) l2(x180, x181, x182, x183, x184, x185) -> l3(x186, x187, x188, x189, x190, x191) :|: x183 = x189 && x182 = x188 && x191 = -1 + x187 && x190 = x186 && x187 = x185 && x186 = x184 Arcs: (1) -> (3) (2) -> (1) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l3(x36:0, x37:0, x188:0, x189:0, x186:0, x187:0) -> l3(x186:0, x187:0, x188:0, x189:0, x186:0, -1 + x187:0) :|: x187:0 > 0 ---------------------------------------- (19) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l3(x1, x2, x3, x4, x5, x6) -> l3(x6) ---------------------------------------- (20) Obligation: Rules: l3(x187:0) -> l3(-1 + x187:0) :|: x187:0 > 0 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l3(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: l3(x187:0) -> l3(c) :|: c = -1 + x187:0 && x187:0 > 0 ---------------------------------------- (23) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l3 ] = l3_1 The following rules are decreasing: l3(x187:0) -> l3(c) :|: c = -1 + x187:0 && x187:0 > 0 The following rules are bounded: l3(x187:0) -> l3(c) :|: c = -1 + x187:0 && x187:0 > 0 ---------------------------------------- (24) YES