YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 25.5 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 16 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 11 ms] (11) IntTRS (12) RankingReductionPairProof [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 8 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 33 ms] (20) IntTRS (21) RankingReductionPairProof [EQUIVALENT, 20 ms] (22) YES (23) IRSwT (24) IntTRSCompressionProof [EQUIVALENT, 9 ms] (25) IRSwT (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (27) IRSwT (28) TempFilterProof [SOUND, 7 ms] (29) IntTRS (30) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (31) YES ---------------------------------------- (0) Obligation: Rules: l0(__const_63HAT0, __const_7HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(__const_63HATpost, __const_7HATpost, oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: __const_7HAT0 = __const_7HATpost && __const_63HAT0 = __const_63HATpost && x1HATpost = oldX3HATpost && x0HATpost = oldX2HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = -1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 l3(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x21 = x29 && x20 = x28 && x17 = x25 && x16 = x24 && x31 = x27 && x30 = x26 && 1 + x27 <= 0 && x27 = x23 && x26 = x22 l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l2(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 0 <= x43 && x43 = x39 && x42 = x38 l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l5(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x49 = x57 && x48 = x56 && x63 = x60 && x62 = -1 + x58 && x60 = x60 && x59 = x55 && x58 = x54 l5(x64, x65, x66, x67, x68, x69, x70, x71) -> l3(x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x77 && x68 = x76 && x65 = x73 && x64 = x72 && x79 = x65 && x78 = x74 && 1 + x74 <= 0 && x75 = x71 && x74 = x70 l5(x80, x81, x82, x83, x84, x85, x86, x87) -> l4(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x81 = x89 && x80 = x88 && x95 = x92 && x94 = x90 && 0 <= x90 && x92 = x92 && x91 = x87 && x90 = x86 l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x97 = x105 && x96 = x104 && x111 = x108 && x110 = x97 && x108 = x108 && x107 = x103 && x106 = x102 l7(x112, x113, x114, x115, x116, x117, x118, x119) -> l8(x120, x121, x122, x123, x124, x125, x126, x127) :|: x113 = x121 && x112 = x120 && x127 = x125 && x126 = x124 && x125 = x125 && x124 = x124 && x123 = x119 && x122 = x118 l9(x128, x129, x130, x131, x132, x133, x134, x135) -> l10(x136, x137, x138, x139, x140, x141, x142, x143) :|: x133 = x141 && x129 = x137 && x128 = x136 && x143 = x140 && x142 = 1 + x138 && x140 = x140 && x139 = x135 && x138 = x134 l10(x144, x145, x146, x147, x148, x149, x150, x151) -> l7(x152, x153, x154, x155, x156, x157, x158, x159) :|: x149 = x157 && x148 = x156 && x145 = x153 && x144 = x152 && x159 = x155 && x158 = x154 && 1 + x144 <= x154 && x155 = x151 && x154 = x150 l10(x160, x161, x162, x163, x164, x165, x166, x167) -> l9(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x161 = x169 && x160 = x168 && x175 = x171 && x174 = x170 && x170 <= x160 && x171 = x167 && x170 = x166 l11(x176, x177, x178, x179, x180, x181, x182, x183) -> l10(x184, x185, x186, x187, x188, x189, x190, x191) :|: x181 = x189 && x180 = x188 && x177 = x185 && x176 = x184 && x191 = 0 && x190 = 0 && x187 = x183 && x186 = x182 l12(x192, x193, x194, x195, x196, x197, x198, x199) -> l11(x200, x201, x202, x203, x204, x205, x206, x207) :|: x193 = x201 && x192 = x200 && x207 = x205 && x206 = x204 && x205 = x205 && x204 = x204 && x203 = x199 && x202 = x198 l12(x208, x209, x210, x211, x212, x213, x214, x215) -> l6(x216, x217, x218, x219, x220, x221, x222, x223) :|: x209 = x217 && x208 = x216 && x223 = x221 && x222 = x220 && x221 = x221 && x220 = x220 && x219 = x215 && x218 = x214 l12(x224, x225, x226, x227, x228, x229, x230, x231) -> l1(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l12(x240, x241, x242, x243, x244, x245, x246, x247) -> l0(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x244 = x252 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 l12(x256, x257, x258, x259, x260, x261, x262, x263) -> l2(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 l12(x272, x273, x274, x275, x276, x277, x278, x279) -> l3(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x278 = x286 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 l12(x288, x289, x290, x291, x292, x293, x294, x295) -> l4(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 l12(x304, x305, x306, x307, x308, x309, x310, x311) -> l5(x312, x313, x314, x315, x316, x317, x318, x319) :|: x311 = x319 && x310 = x318 && x309 = x317 && x308 = x316 && x307 = x315 && x306 = x314 && x305 = x313 && x304 = x312 l12(x320, x321, x322, x323, x324, x325, x326, x327) -> l6(x328, x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x325 = x333 && x324 = x332 && x323 = x331 && x322 = x330 && x321 = x329 && x320 = x328 l12(x336, x337, x338, x339, x340, x341, x342, x343) -> l8(x344, x345, x346, x347, x348, x349, x350, x351) :|: x343 = x351 && x342 = x350 && x341 = x349 && x340 = x348 && x339 = x347 && x338 = x346 && x337 = x345 && x336 = x344 l12(x352, x353, x354, x355, x356, x357, x358, x359) -> l7(x360, x361, x362, x363, x364, x365, x366, x367) :|: x359 = x367 && x358 = x366 && x357 = x365 && x356 = x364 && x355 = x363 && x354 = x362 && x353 = x361 && x352 = x360 l12(x368, x369, x370, x371, x372, x373, x374, x375) -> l9(x376, x377, x378, x379, x380, x381, x382, x383) :|: x375 = x383 && x374 = x382 && x373 = x381 && x372 = x380 && x371 = x379 && x370 = x378 && x369 = x377 && x368 = x376 l12(x384, x385, x386, x387, x388, x389, x390, x391) -> l10(x392, x393, x394, x395, x396, x397, x398, x399) :|: x391 = x399 && x390 = x398 && x389 = x397 && x388 = x396 && x387 = x395 && x386 = x394 && x385 = x393 && x384 = x392 l12(x400, x401, x402, x403, x404, x405, x406, x407) -> l11(x408, x409, x410, x411, x412, x413, x414, x415) :|: x407 = x415 && x406 = x414 && x405 = x413 && x404 = x412 && x403 = x411 && x402 = x410 && x401 = x409 && x400 = x408 l13(x416, x417, x418, x419, x420, x421, x422, x423) -> l12(x424, x425, x426, x427, x428, x429, x430, x431) :|: x423 = x431 && x422 = x430 && x421 = x429 && x420 = x428 && x419 = x427 && x418 = x426 && x417 = x425 && x416 = x424 Start term: l13(__const_63HAT0, __const_7HAT0, 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(__const_63HAT0, __const_7HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(__const_63HATpost, __const_7HATpost, oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: __const_7HAT0 = __const_7HATpost && __const_63HAT0 = __const_63HATpost && x1HATpost = oldX3HATpost && x0HATpost = oldX2HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = -1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 l3(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x21 = x29 && x20 = x28 && x17 = x25 && x16 = x24 && x31 = x27 && x30 = x26 && 1 + x27 <= 0 && x27 = x23 && x26 = x22 l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l2(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 0 <= x43 && x43 = x39 && x42 = x38 l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l5(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x49 = x57 && x48 = x56 && x63 = x60 && x62 = -1 + x58 && x60 = x60 && x59 = x55 && x58 = x54 l5(x64, x65, x66, x67, x68, x69, x70, x71) -> l3(x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x77 && x68 = x76 && x65 = x73 && x64 = x72 && x79 = x65 && x78 = x74 && 1 + x74 <= 0 && x75 = x71 && x74 = x70 l5(x80, x81, x82, x83, x84, x85, x86, x87) -> l4(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x81 = x89 && x80 = x88 && x95 = x92 && x94 = x90 && 0 <= x90 && x92 = x92 && x91 = x87 && x90 = x86 l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x97 = x105 && x96 = x104 && x111 = x108 && x110 = x97 && x108 = x108 && x107 = x103 && x106 = x102 l7(x112, x113, x114, x115, x116, x117, x118, x119) -> l8(x120, x121, x122, x123, x124, x125, x126, x127) :|: x113 = x121 && x112 = x120 && x127 = x125 && x126 = x124 && x125 = x125 && x124 = x124 && x123 = x119 && x122 = x118 l9(x128, x129, x130, x131, x132, x133, x134, x135) -> l10(x136, x137, x138, x139, x140, x141, x142, x143) :|: x133 = x141 && x129 = x137 && x128 = x136 && x143 = x140 && x142 = 1 + x138 && x140 = x140 && x139 = x135 && x138 = x134 l10(x144, x145, x146, x147, x148, x149, x150, x151) -> l7(x152, x153, x154, x155, x156, x157, x158, x159) :|: x149 = x157 && x148 = x156 && x145 = x153 && x144 = x152 && x159 = x155 && x158 = x154 && 1 + x144 <= x154 && x155 = x151 && x154 = x150 l10(x160, x161, x162, x163, x164, x165, x166, x167) -> l9(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x161 = x169 && x160 = x168 && x175 = x171 && x174 = x170 && x170 <= x160 && x171 = x167 && x170 = x166 l11(x176, x177, x178, x179, x180, x181, x182, x183) -> l10(x184, x185, x186, x187, x188, x189, x190, x191) :|: x181 = x189 && x180 = x188 && x177 = x185 && x176 = x184 && x191 = 0 && x190 = 0 && x187 = x183 && x186 = x182 l12(x192, x193, x194, x195, x196, x197, x198, x199) -> l11(x200, x201, x202, x203, x204, x205, x206, x207) :|: x193 = x201 && x192 = x200 && x207 = x205 && x206 = x204 && x205 = x205 && x204 = x204 && x203 = x199 && x202 = x198 l12(x208, x209, x210, x211, x212, x213, x214, x215) -> l6(x216, x217, x218, x219, x220, x221, x222, x223) :|: x209 = x217 && x208 = x216 && x223 = x221 && x222 = x220 && x221 = x221 && x220 = x220 && x219 = x215 && x218 = x214 l12(x224, x225, x226, x227, x228, x229, x230, x231) -> l1(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l12(x240, x241, x242, x243, x244, x245, x246, x247) -> l0(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x244 = x252 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 l12(x256, x257, x258, x259, x260, x261, x262, x263) -> l2(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 l12(x272, x273, x274, x275, x276, x277, x278, x279) -> l3(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x278 = x286 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 l12(x288, x289, x290, x291, x292, x293, x294, x295) -> l4(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 l12(x304, x305, x306, x307, x308, x309, x310, x311) -> l5(x312, x313, x314, x315, x316, x317, x318, x319) :|: x311 = x319 && x310 = x318 && x309 = x317 && x308 = x316 && x307 = x315 && x306 = x314 && x305 = x313 && x304 = x312 l12(x320, x321, x322, x323, x324, x325, x326, x327) -> l6(x328, x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x325 = x333 && x324 = x332 && x323 = x331 && x322 = x330 && x321 = x329 && x320 = x328 l12(x336, x337, x338, x339, x340, x341, x342, x343) -> l8(x344, x345, x346, x347, x348, x349, x350, x351) :|: x343 = x351 && x342 = x350 && x341 = x349 && x340 = x348 && x339 = x347 && x338 = x346 && x337 = x345 && x336 = x344 l12(x352, x353, x354, x355, x356, x357, x358, x359) -> l7(x360, x361, x362, x363, x364, x365, x366, x367) :|: x359 = x367 && x358 = x366 && x357 = x365 && x356 = x364 && x355 = x363 && x354 = x362 && x353 = x361 && x352 = x360 l12(x368, x369, x370, x371, x372, x373, x374, x375) -> l9(x376, x377, x378, x379, x380, x381, x382, x383) :|: x375 = x383 && x374 = x382 && x373 = x381 && x372 = x380 && x371 = x379 && x370 = x378 && x369 = x377 && x368 = x376 l12(x384, x385, x386, x387, x388, x389, x390, x391) -> l10(x392, x393, x394, x395, x396, x397, x398, x399) :|: x391 = x399 && x390 = x398 && x389 = x397 && x388 = x396 && x387 = x395 && x386 = x394 && x385 = x393 && x384 = x392 l12(x400, x401, x402, x403, x404, x405, x406, x407) -> l11(x408, x409, x410, x411, x412, x413, x414, x415) :|: x407 = x415 && x406 = x414 && x405 = x413 && x404 = x412 && x403 = x411 && x402 = x410 && x401 = x409 && x400 = x408 l13(x416, x417, x418, x419, x420, x421, x422, x423) -> l12(x424, x425, x426, x427, x428, x429, x430, x431) :|: x423 = x431 && x422 = x430 && x421 = x429 && x420 = x428 && x419 = x427 && x418 = x426 && x417 = x425 && x416 = x424 Start term: l13(__const_63HAT0, __const_7HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_63HAT0, __const_7HAT0, oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, x0HAT0, x1HAT0) -> l1(__const_63HATpost, __const_7HATpost, oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, x0HATpost, x1HATpost) :|: __const_7HAT0 = __const_7HATpost && __const_63HAT0 = __const_63HATpost && x1HATpost = oldX3HATpost && x0HATpost = oldX2HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = oldX2HATpost && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = -1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 (3) l3(x16, x17, x18, x19, x20, x21, x22, x23) -> l0(x24, x25, x26, x27, x28, x29, x30, x31) :|: x21 = x29 && x20 = x28 && x17 = x25 && x16 = x24 && x31 = x27 && x30 = x26 && 1 + x27 <= 0 && x27 = x23 && x26 = x22 (4) l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l2(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 0 <= x43 && x43 = x39 && x42 = x38 (5) l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l5(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x49 = x57 && x48 = x56 && x63 = x60 && x62 = -1 + x58 && x60 = x60 && x59 = x55 && x58 = x54 (6) l5(x64, x65, x66, x67, x68, x69, x70, x71) -> l3(x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x77 && x68 = x76 && x65 = x73 && x64 = x72 && x79 = x65 && x78 = x74 && 1 + x74 <= 0 && x75 = x71 && x74 = x70 (7) l5(x80, x81, x82, x83, x84, x85, x86, x87) -> l4(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x81 = x89 && x80 = x88 && x95 = x92 && x94 = x90 && 0 <= x90 && x92 = x92 && x91 = x87 && x90 = x86 (8) l6(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x97 = x105 && x96 = x104 && x111 = x108 && x110 = x97 && x108 = x108 && x107 = x103 && x106 = x102 (9) l7(x112, x113, x114, x115, x116, x117, x118, x119) -> l8(x120, x121, x122, x123, x124, x125, x126, x127) :|: x113 = x121 && x112 = x120 && x127 = x125 && x126 = x124 && x125 = x125 && x124 = x124 && x123 = x119 && x122 = x118 (10) l9(x128, x129, x130, x131, x132, x133, x134, x135) -> l10(x136, x137, x138, x139, x140, x141, x142, x143) :|: x133 = x141 && x129 = x137 && x128 = x136 && x143 = x140 && x142 = 1 + x138 && x140 = x140 && x139 = x135 && x138 = x134 (11) l10(x144, x145, x146, x147, x148, x149, x150, x151) -> l7(x152, x153, x154, x155, x156, x157, x158, x159) :|: x149 = x157 && x148 = x156 && x145 = x153 && x144 = x152 && x159 = x155 && x158 = x154 && 1 + x144 <= x154 && x155 = x151 && x154 = x150 (12) l10(x160, x161, x162, x163, x164, x165, x166, x167) -> l9(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x161 = x169 && x160 = x168 && x175 = x171 && x174 = x170 && x170 <= x160 && x171 = x167 && x170 = x166 (13) l11(x176, x177, x178, x179, x180, x181, x182, x183) -> l10(x184, x185, x186, x187, x188, x189, x190, x191) :|: x181 = x189 && x180 = x188 && x177 = x185 && x176 = x184 && x191 = 0 && x190 = 0 && x187 = x183 && x186 = x182 (14) l12(x192, x193, x194, x195, x196, x197, x198, x199) -> l11(x200, x201, x202, x203, x204, x205, x206, x207) :|: x193 = x201 && x192 = x200 && x207 = x205 && x206 = x204 && x205 = x205 && x204 = x204 && x203 = x199 && x202 = x198 (15) l12(x208, x209, x210, x211, x212, x213, x214, x215) -> l6(x216, x217, x218, x219, x220, x221, x222, x223) :|: x209 = x217 && x208 = x216 && x223 = x221 && x222 = x220 && x221 = x221 && x220 = x220 && x219 = x215 && x218 = x214 (16) l12(x224, x225, x226, x227, x228, x229, x230, x231) -> l1(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 (17) l12(x240, x241, x242, x243, x244, x245, x246, x247) -> l0(x248, x249, x250, x251, x252, x253, x254, x255) :|: x247 = x255 && x246 = x254 && x245 = x253 && x244 = x252 && x243 = x251 && x242 = x250 && x241 = x249 && x240 = x248 (18) l12(x256, x257, x258, x259, x260, x261, x262, x263) -> l2(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 (19) l12(x272, x273, x274, x275, x276, x277, x278, x279) -> l3(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x278 = x286 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 (20) l12(x288, x289, x290, x291, x292, x293, x294, x295) -> l4(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 (21) l12(x304, x305, x306, x307, x308, x309, x310, x311) -> l5(x312, x313, x314, x315, x316, x317, x318, x319) :|: x311 = x319 && x310 = x318 && x309 = x317 && x308 = x316 && x307 = x315 && x306 = x314 && x305 = x313 && x304 = x312 (22) l12(x320, x321, x322, x323, x324, x325, x326, x327) -> l6(x328, x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x325 = x333 && x324 = x332 && x323 = x331 && x322 = x330 && x321 = x329 && x320 = x328 (23) l12(x336, x337, x338, x339, x340, x341, x342, x343) -> l8(x344, x345, x346, x347, x348, x349, x350, x351) :|: x343 = x351 && x342 = x350 && x341 = x349 && x340 = x348 && x339 = x347 && x338 = x346 && x337 = x345 && x336 = x344 (24) l12(x352, x353, x354, x355, x356, x357, x358, x359) -> l7(x360, x361, x362, x363, x364, x365, x366, x367) :|: x359 = x367 && x358 = x366 && x357 = x365 && x356 = x364 && x355 = x363 && x354 = x362 && x353 = x361 && x352 = x360 (25) l12(x368, x369, x370, x371, x372, x373, x374, x375) -> l9(x376, x377, x378, x379, x380, x381, x382, x383) :|: x375 = x383 && x374 = x382 && x373 = x381 && x372 = x380 && x371 = x379 && x370 = x378 && x369 = x377 && x368 = x376 (26) l12(x384, x385, x386, x387, x388, x389, x390, x391) -> l10(x392, x393, x394, x395, x396, x397, x398, x399) :|: x391 = x399 && x390 = x398 && x389 = x397 && x388 = x396 && x387 = x395 && x386 = x394 && x385 = x393 && x384 = x392 (27) l12(x400, x401, x402, x403, x404, x405, x406, x407) -> l11(x408, x409, x410, x411, x412, x413, x414, x415) :|: x407 = x415 && x406 = x414 && x405 = x413 && x404 = x412 && x403 = x411 && x402 = x410 && x401 = x409 && x400 = x408 (28) l13(x416, x417, x418, x419, x420, x421, x422, x423) -> l12(x424, x425, x426, x427, x428, x429, x430, x431) :|: x423 = x431 && x422 = x430 && x421 = x429 && x420 = x428 && x419 = x427 && x418 = x426 && x417 = x425 && x416 = x424 Arcs: (2) -> (3), (4) (3) -> (1) (4) -> (2) (5) -> (6), (7) (6) -> (3), (4) (7) -> (5) (8) -> (6), (7) (10) -> (11), (12) (11) -> (9) (12) -> (10) (13) -> (11), (12) (14) -> (13) (15) -> (8) (17) -> (1) (18) -> (2) (19) -> (3), (4) (20) -> (5) (21) -> (6), (7) (22) -> (8) (24) -> (9) (25) -> (10) (26) -> (11), (12) (27) -> (13) (28) -> (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l9(x128, x129, x130, x131, x132, x133, x134, x135) -> l10(x136, x137, x138, x139, x140, x141, x142, x143) :|: x133 = x141 && x129 = x137 && x128 = x136 && x143 = x140 && x142 = 1 + x138 && x140 = x140 && x139 = x135 && x138 = x134 (2) l10(x160, x161, x162, x163, x164, x165, x166, x167) -> l9(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x161 = x169 && x160 = x168 && x175 = x171 && x174 = x170 && x170 <= x160 && x171 = x167 && x170 = x166 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l9(x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0, x135:0) -> l9(x128:0, x129:0, 1 + x134:0, x140:0, x140:0, x133:0, 1 + x134:0, x140:0) :|: x128:0 >= 1 + x134:0 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l9(x1, x2, x3, x4, x5, x6, x7, x8) -> l9(x1, x7) ---------------------------------------- (9) Obligation: Rules: l9(x128:0, x134:0) -> l9(x128:0, 1 + x134:0) :|: x128:0 >= 1 + x134:0 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l9(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l9(x128:0, x134:0) -> l9(x128:0, c) :|: c = 1 + x134:0 && x128:0 >= 1 + x134:0 ---------------------------------------- (12) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l9 ] = l9_1 + -1*l9_2 The following rules are decreasing: l9(x128:0, x134:0) -> l9(x128:0, c) :|: c = 1 + x134:0 && x128:0 >= 1 + x134:0 The following rules are bounded: l9(x128:0, x134:0) -> l9(x128:0, c) :|: c = 1 + x134:0 && x128:0 >= 1 + x134:0 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) l4(x48, x49, x50, x51, x52, x53, x54, x55) -> l5(x56, x57, x58, x59, x60, x61, x62, x63) :|: x53 = x61 && x49 = x57 && x48 = x56 && x63 = x60 && x62 = -1 + x58 && x60 = x60 && x59 = x55 && x58 = x54 (2) l5(x80, x81, x82, x83, x84, x85, x86, x87) -> l4(x88, x89, x90, x91, x92, x93, x94, x95) :|: x85 = x93 && x81 = x89 && x80 = x88 && x95 = x92 && x94 = x90 && 0 <= x90 && x92 = x92 && x91 = x87 && x90 = x86 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: l4(x48:0, x49:0, x50:0, x51:0, x52:0, x53:0, x54:0, x55:0) -> l4(x48:0, x49:0, -1 + x54:0, x60:0, x92:0, x53:0, -1 + x54:0, x92:0) :|: x54:0 > 0 ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l4(x1, x2, x3, x4, x5, x6, x7, x8) -> l4(x7) ---------------------------------------- (18) Obligation: Rules: l4(x54:0) -> l4(-1 + x54:0) :|: x54:0 > 0 ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: l4(x54:0) -> l4(c) :|: c = -1 + x54:0 && x54:0 > 0 ---------------------------------------- (21) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l4 ] = l4_1 The following rules are decreasing: l4(x54:0) -> l4(c) :|: c = -1 + x54:0 && x54:0 > 0 The following rules are bounded: l4(x54:0) -> l4(c) :|: c = -1 + x54:0 && x54:0 > 0 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Termination digraph: Nodes: (1) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x5 = x13 && x4 = x12 && x1 = x9 && x = x8 && x15 = -1 + x11 && x14 = x10 && x11 = x7 && x10 = x6 (2) l3(x32, x33, x34, x35, x36, x37, x38, x39) -> l2(x40, x41, x42, x43, x44, x45, x46, x47) :|: x37 = x45 && x36 = x44 && x33 = x41 && x32 = x40 && x47 = x43 && x46 = x42 && 0 <= x43 && x43 = x39 && x42 = x38 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (24) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (25) Obligation: Rules: l2(x40:0, x1:0, x2:0, x3:0, x12:0, x13:0, x10:0, x11:0) -> l2(x40:0, x1:0, x10:0, -1 + x11:0, x12:0, x13:0, x10:0, -1 + x11:0) :|: x11:0 > 0 ---------------------------------------- (26) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x8) ---------------------------------------- (27) Obligation: Rules: l2(x11:0) -> l2(-1 + x11:0) :|: x11:0 > 0 ---------------------------------------- (28) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l2(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (29) Obligation: Rules: l2(x11:0) -> l2(c) :|: c = -1 + x11:0 && x11:0 > 0 ---------------------------------------- (30) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l2(x)] = x The following rules are decreasing: l2(x11:0) -> l2(c) :|: c = -1 + x11:0 && x11:0 > 0 The following rules are bounded: l2(x11:0) -> l2(c) :|: c = -1 + x11:0 && x11:0 > 0 ---------------------------------------- (31) YES