YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 21.3 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 14 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 19 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) YES (14) IRSwT (15) IntTRSCompressionProof [EQUIVALENT, 12 ms] (16) IRSwT (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (18) IRSwT (19) TempFilterProof [SOUND, 34 ms] (20) IntTRS (21) PolynomialOrderProcessor [EQUIVALENT, 10 ms] (22) IntTRS (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (24) YES (25) IRSwT (26) IntTRSCompressionProof [EQUIVALENT, 16 ms] (27) IRSwT (28) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (29) IRSwT (30) TempFilterProof [SOUND, 14 ms] (31) IntTRS (32) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (33) YES (34) IRSwT (35) IntTRSCompressionProof [EQUIVALENT, 7 ms] (36) IRSwT (37) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (38) IRSwT (39) TempFilterProof [SOUND, 4 ms] (40) IntTRS (41) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (42) YES ---------------------------------------- (0) Obligation: Rules: l0(__const_15HAT0, __const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) -> l1(__const_15HATpost, __const_5HATpost, edgecountHATpost, iHATpost, jHATpost, nodecountHATpost, sourceHATpost, xHATpost, yHATpost) :|: yHAT0 = yHATpost && xHAT0 = xHATpost && sourceHAT0 = sourceHATpost && nodecountHAT0 = nodecountHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost && edgecountHAT0 = edgecountHATpost && __const_5HAT0 = __const_5HATpost && __const_15HAT0 = __const_15HATpost && nodecountHAT0 <= iHAT0 l0(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x2 = x11 && x1 = x10 && x = x9 && x12 = 1 + x3 && 1 + x3 <= x5 l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x20 = x29 && x19 = x28 && x18 = x27 && x30 = 1 + x21 l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 l5(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x55 = x64 && x54 = x63 && x66 = 0 && x56 <= x57 l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l3(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 && x88 = x88 && 1 + x75 <= x74 l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l7(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x103 = 1 + x94 l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l9(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x111 && x110 <= x112 l8(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l6(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x143 = x143 && x142 = x142 && 1 + x130 <= x128 l10(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l4(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x146 = x155 && x145 = x154 && x144 = x153 && x156 = 0 && x149 <= x147 l10(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l7(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x167 = x176 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x175 = 0 && 1 + x165 <= x167 l11(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l12(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 l13(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l14(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207 l12(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l13(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x218 = x227 && x217 = x226 && x216 = x225 && x228 = 1 + x219 l15(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l11(x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x236 = x245 && x235 = x244 && x234 = x243 && 1 + x240 <= x237 l15(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l11(x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x254 = x263 && x253 = x262 && x252 = x261 && 1 + x255 <= x258 l15(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l12(x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x272 = x281 && x271 = x280 && x270 = x279 && x276 <= x273 && x273 <= x276 l14(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l9(x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x290 = x299 && x289 = x298 && x288 = x297 && x300 = 0 && x293 <= x291 l14(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l15(x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x308 = x317 && x307 = x316 && x306 = x315 && 1 + x309 <= x311 l9(x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l10(x333, x334, x335, x336, x337, x338, x339, x340, x341) :|: x332 = x341 && x331 = x340 && x330 = x339 && x329 = x338 && x328 = x337 && x327 = x336 && x326 = x335 && x325 = x334 && x324 = x333 l7(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l8(x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x345 = x354 && x344 = x353 && x343 = x352 && x342 = x351 l4(x360, x361, x362, x363, x364, x365, x366, x367, x368) -> l5(x369, x370, x371, x372, x373, x374, x375, x376, x377) :|: x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x363 = x372 && x362 = x371 && x361 = x370 && x360 = x369 l2(x378, x379, x380, x381, x382, x383, x384, x385, x386) -> l0(x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x386 = x395 && x385 = x394 && x384 = x393 && x383 = x392 && x382 = x391 && x381 = x390 && x380 = x389 && x379 = x388 && x378 = x387 l16(x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l13(x405, x406, x407, x408, x409, x410, x411, x412, x413) :|: x404 = x413 && x403 = x412 && x400 = x409 && x397 = x406 && x396 = x405 && x408 = 0 && x411 = 0 && x407 = x396 && x410 = x397 l17(x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l16(x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x422 = x431 && x421 = x430 && x420 = x429 && x419 = x428 && x418 = x427 && x417 = x426 && x416 = x425 && x415 = x424 && x414 = x423 Start term: l17(__const_15HAT0, __const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(__const_15HAT0, __const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) -> l1(__const_15HATpost, __const_5HATpost, edgecountHATpost, iHATpost, jHATpost, nodecountHATpost, sourceHATpost, xHATpost, yHATpost) :|: yHAT0 = yHATpost && xHAT0 = xHATpost && sourceHAT0 = sourceHATpost && nodecountHAT0 = nodecountHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost && edgecountHAT0 = edgecountHATpost && __const_5HAT0 = __const_5HATpost && __const_15HAT0 = __const_15HATpost && nodecountHAT0 <= iHAT0 l0(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x2 = x11 && x1 = x10 && x = x9 && x12 = 1 + x3 && 1 + x3 <= x5 l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x20 = x29 && x19 = x28 && x18 = x27 && x30 = 1 + x21 l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 l5(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x55 = x64 && x54 = x63 && x66 = 0 && x56 <= x57 l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l3(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 && x88 = x88 && 1 + x75 <= x74 l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l7(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x103 = 1 + x94 l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l9(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x111 && x110 <= x112 l8(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l6(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x143 = x143 && x142 = x142 && 1 + x130 <= x128 l10(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l4(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x146 = x155 && x145 = x154 && x144 = x153 && x156 = 0 && x149 <= x147 l10(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l7(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x167 = x176 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x175 = 0 && 1 + x165 <= x167 l11(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l12(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 l13(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l14(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207 l12(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l13(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x218 = x227 && x217 = x226 && x216 = x225 && x228 = 1 + x219 l15(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l11(x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x236 = x245 && x235 = x244 && x234 = x243 && 1 + x240 <= x237 l15(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l11(x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x254 = x263 && x253 = x262 && x252 = x261 && 1 + x255 <= x258 l15(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l12(x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x272 = x281 && x271 = x280 && x270 = x279 && x276 <= x273 && x273 <= x276 l14(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l9(x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x290 = x299 && x289 = x298 && x288 = x297 && x300 = 0 && x293 <= x291 l14(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l15(x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x308 = x317 && x307 = x316 && x306 = x315 && 1 + x309 <= x311 l9(x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l10(x333, x334, x335, x336, x337, x338, x339, x340, x341) :|: x332 = x341 && x331 = x340 && x330 = x339 && x329 = x338 && x328 = x337 && x327 = x336 && x326 = x335 && x325 = x334 && x324 = x333 l7(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l8(x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x345 = x354 && x344 = x353 && x343 = x352 && x342 = x351 l4(x360, x361, x362, x363, x364, x365, x366, x367, x368) -> l5(x369, x370, x371, x372, x373, x374, x375, x376, x377) :|: x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x363 = x372 && x362 = x371 && x361 = x370 && x360 = x369 l2(x378, x379, x380, x381, x382, x383, x384, x385, x386) -> l0(x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x386 = x395 && x385 = x394 && x384 = x393 && x383 = x392 && x382 = x391 && x381 = x390 && x380 = x389 && x379 = x388 && x378 = x387 l16(x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l13(x405, x406, x407, x408, x409, x410, x411, x412, x413) :|: x404 = x413 && x403 = x412 && x400 = x409 && x397 = x406 && x396 = x405 && x408 = 0 && x411 = 0 && x407 = x396 && x410 = x397 l17(x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l16(x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x422 = x431 && x421 = x430 && x420 = x429 && x419 = x428 && x418 = x427 && x417 = x426 && x416 = x425 && x415 = x424 && x414 = x423 Start term: l17(__const_15HAT0, __const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_15HAT0, __const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) -> l1(__const_15HATpost, __const_5HATpost, edgecountHATpost, iHATpost, jHATpost, nodecountHATpost, sourceHATpost, xHATpost, yHATpost) :|: yHAT0 = yHATpost && xHAT0 = xHATpost && sourceHAT0 = sourceHATpost && nodecountHAT0 = nodecountHATpost && jHAT0 = jHATpost && iHAT0 = iHATpost && edgecountHAT0 = edgecountHATpost && __const_5HAT0 = __const_5HATpost && __const_15HAT0 = __const_15HATpost && nodecountHAT0 <= iHAT0 (2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x2 = x11 && x1 = x10 && x = x9 && x12 = 1 + x3 && 1 + x3 <= x5 (3) l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x20 = x29 && x19 = x28 && x18 = x27 && x30 = 1 + x21 (4) l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x44 = x53 && x43 = x52 && x42 = x51 && x41 = x50 && x40 = x49 && x39 = x48 && x38 = x47 && x37 = x46 && x36 = x45 (5) l5(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x62 = x71 && x61 = x70 && x60 = x69 && x59 = x68 && x58 = x67 && x56 = x65 && x55 = x64 && x54 = x63 && x66 = 0 && x56 <= x57 (6) l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l3(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 && x88 = x88 && 1 + x75 <= x74 (7) l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l7(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x103 = 1 + x94 (8) l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l9(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x111 && x110 <= x112 (9) l8(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l6(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x143 = x143 && x142 = x142 && 1 + x130 <= x128 (10) l10(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l4(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x152 = x161 && x151 = x160 && x150 = x159 && x149 = x158 && x148 = x157 && x146 = x155 && x145 = x154 && x144 = x153 && x156 = 0 && x149 <= x147 (11) l10(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l7(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x167 = x176 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x175 = 0 && 1 + x165 <= x167 (12) l11(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l12(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 (13) l13(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l14(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207 (14) l12(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l13(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x218 = x227 && x217 = x226 && x216 = x225 && x228 = 1 + x219 (15) l15(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l11(x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x236 = x245 && x235 = x244 && x234 = x243 && 1 + x240 <= x237 (16) l15(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l11(x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x254 = x263 && x253 = x262 && x252 = x261 && 1 + x255 <= x258 (17) l15(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l12(x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x272 = x281 && x271 = x280 && x270 = x279 && x276 <= x273 && x273 <= x276 (18) l14(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l9(x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x290 = x299 && x289 = x298 && x288 = x297 && x300 = 0 && x293 <= x291 (19) l14(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l15(x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x308 = x317 && x307 = x316 && x306 = x315 && 1 + x309 <= x311 (20) l9(x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l10(x333, x334, x335, x336, x337, x338, x339, x340, x341) :|: x332 = x341 && x331 = x340 && x330 = x339 && x329 = x338 && x328 = x337 && x327 = x336 && x326 = x335 && x325 = x334 && x324 = x333 (21) l7(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l8(x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x345 = x354 && x344 = x353 && x343 = x352 && x342 = x351 (22) l4(x360, x361, x362, x363, x364, x365, x366, x367, x368) -> l5(x369, x370, x371, x372, x373, x374, x375, x376, x377) :|: x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x363 = x372 && x362 = x371 && x361 = x370 && x360 = x369 (23) l2(x378, x379, x380, x381, x382, x383, x384, x385, x386) -> l0(x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x386 = x395 && x385 = x394 && x384 = x393 && x383 = x392 && x382 = x391 && x381 = x390 && x380 = x389 && x379 = x388 && x378 = x387 (24) l16(x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l13(x405, x406, x407, x408, x409, x410, x411, x412, x413) :|: x404 = x413 && x403 = x412 && x400 = x409 && x397 = x406 && x396 = x405 && x408 = 0 && x411 = 0 && x407 = x396 && x410 = x397 (25) l17(x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l16(x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x422 = x431 && x421 = x430 && x420 = x429 && x419 = x428 && x418 = x427 && x417 = x426 && x416 = x425 && x415 = x424 && x414 = x423 Arcs: (2) -> (23) (3) -> (22) (5) -> (23) (6) -> (3), (4) (7) -> (21) (8) -> (20) (9) -> (7) (10) -> (22) (11) -> (21) (12) -> (14) (13) -> (18), (19) (14) -> (13) (15) -> (12) (16) -> (12) (17) -> (14) (18) -> (20) (19) -> (15), (16), (17) (20) -> (10), (11) (21) -> (8), (9) (22) -> (5), (6) (23) -> (1), (2) (24) -> (13) (25) -> (24) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l11(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l12(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x188 = x197 && x187 = x196 && x186 = x195 && x185 = x194 && x184 = x193 && x183 = x192 && x182 = x191 && x181 = x190 && x180 = x189 (2) l15(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l11(x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x254 = x263 && x253 = x262 && x252 = x261 && 1 + x255 <= x258 (3) l15(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l11(x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x236 = x245 && x235 = x244 && x234 = x243 && 1 + x240 <= x237 (4) l14(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l15(x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x308 = x317 && x307 = x316 && x306 = x315 && 1 + x309 <= x311 (5) l13(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l14(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207 (6) l12(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l13(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x218 = x227 && x217 = x226 && x216 = x225 && x228 = 1 + x219 (7) l15(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l12(x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x272 = x281 && x271 = x280 && x270 = x279 && x276 <= x273 && x273 <= x276 Arcs: (1) -> (6) (2) -> (1) (3) -> (1) (4) -> (2), (3), (7) (5) -> (4) (6) -> (5) (7) -> (6) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l13(x198:0, x199:0, x200:0, x201:0, x202:0, x203:0, x201:0, x205:0, x206:0) -> l13(x198:0, x199:0, x200:0, 1 + x201:0, x202:0, x203:0, x201:0, x205:0, x206:0) :|: x203:0 >= 1 + x201:0 l13(x189:0, x190:0, x191:0, x192:0, x193:0, x194:0, x195:0, x196:0, x197:0) -> l13(x189:0, x190:0, x191:0, 1 + x192:0, x193:0, x194:0, x195:0, x196:0, x197:0) :|: x194:0 >= 1 + x192:0 && x195:0 >= 1 + x192:0 l13(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l13(x, x1, x2, 1 + x3, x4, x5, x6, x7, x8) :|: x5 >= 1 + x3 && x3 >= 1 + x6 ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l13(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l13(x4, x6, x7) ---------------------------------------- (9) Obligation: Rules: l13(x201:0, x203:0, x201:0) -> l13(1 + x201:0, x203:0, x201:0) :|: x203:0 >= 1 + x201:0 l13(x192:0, x194:0, x195:0) -> l13(1 + x192:0, x194:0, x195:0) :|: x194:0 >= 1 + x192:0 && x195:0 >= 1 + x192:0 l13(x3, x5, x6) -> l13(1 + x3, x5, x6) :|: x5 >= 1 + x3 && x3 >= 1 + x6 ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l13(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l13(x201:0, x203:0, x201:0) -> l13(c, x203:0, x201:0) :|: c = 1 + x201:0 && x203:0 >= 1 + x201:0 l13(x192:0, x194:0, x195:0) -> l13(c1, x194:0, x195:0) :|: c1 = 1 + x192:0 && (x194:0 >= 1 + x192:0 && x195:0 >= 1 + x192:0) l13(x3, x5, x6) -> l13(c2, x5, x6) :|: c2 = 1 + x3 && (x5 >= 1 + x3 && x3 >= 1 + x6) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l13(x, x1, x2)] = -x + x1 The following rules are decreasing: l13(x201:0, x203:0, x201:0) -> l13(c, x203:0, x201:0) :|: c = 1 + x201:0 && x203:0 >= 1 + x201:0 l13(x192:0, x194:0, x195:0) -> l13(c1, x194:0, x195:0) :|: c1 = 1 + x192:0 && (x194:0 >= 1 + x192:0 && x195:0 >= 1 + x192:0) l13(x3, x5, x6) -> l13(c2, x5, x6) :|: c2 = 1 + x3 && (x5 >= 1 + x3 && x3 >= 1 + x6) The following rules are bounded: l13(x201:0, x203:0, x201:0) -> l13(c, x203:0, x201:0) :|: c = 1 + x201:0 && x203:0 >= 1 + x201:0 l13(x192:0, x194:0, x195:0) -> l13(c1, x194:0, x195:0) :|: c1 = 1 + x192:0 && (x194:0 >= 1 + x192:0 && x195:0 >= 1 + x192:0) l13(x3, x5, x6) -> l13(c2, x5, x6) :|: c2 = 1 + x3 && (x5 >= 1 + x3 && x3 >= 1 + x6) ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Termination digraph: Nodes: (1) l6(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l7(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x98 = x107 && x97 = x106 && x96 = x105 && x95 = x104 && x93 = x102 && x92 = x101 && x91 = x100 && x90 = x99 && x103 = 1 + x94 (2) l8(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l6(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x132 = x141 && x131 = x140 && x130 = x139 && x129 = x138 && x128 = x137 && x127 = x136 && x126 = x135 && x143 = x143 && x142 = x142 && 1 + x130 <= x128 (3) l7(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l8(x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x345 = x354 && x344 = x353 && x343 = x352 && x342 = x351 (4) l10(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l7(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x170 = x179 && x169 = x178 && x168 = x177 && x167 = x176 && x165 = x174 && x164 = x173 && x163 = x172 && x162 = x171 && x175 = 0 && 1 + x165 <= x167 (5) l9(x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l10(x333, x334, x335, x336, x337, x338, x339, x340, x341) :|: x332 = x341 && x331 = x340 && x330 = x339 && x329 = x338 && x328 = x337 && x327 = x336 && x326 = x335 && x325 = x334 && x324 = x333 (6) l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l9(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x116 = x125 && x115 = x124 && x114 = x123 && x113 = x122 && x112 = x121 && x110 = x119 && x109 = x118 && x108 = x117 && x120 = 1 + x111 && x110 <= x112 Arcs: (1) -> (3) (2) -> (1) (3) -> (2), (6) (4) -> (3) (5) -> (4) (6) -> (5) This digraph is fully evaluated! ---------------------------------------- (15) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (16) Obligation: Rules: l8(x126:0, x100:0, x101:0, x102:0, x130:0, x104:0, x105:0, x133:0, x134:0) -> l8(x126:0, x100:0, x101:0, x102:0, 1 + x130:0, x104:0, x105:0, x106:0, x107:0) :|: x101:0 >= 1 + x130:0 l8(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0) -> l8(x108:0, x109:0, x110:0, 1 + x111:0, 0, x113:0, x114:0, x115:0, x116:0) :|: x112:0 >= x110:0 && x113:0 >= 1 + (1 + x111:0) ---------------------------------------- (17) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l8(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l8(x3, x4, x5, x6) ---------------------------------------- (18) Obligation: Rules: l8(x101:0, x102:0, x130:0, x104:0) -> l8(x101:0, x102:0, 1 + x130:0, x104:0) :|: x101:0 >= 1 + x130:0 l8(x110:0, x111:0, x112:0, x113:0) -> l8(x110:0, 1 + x111:0, 0, x113:0) :|: x112:0 >= x110:0 && x113:0 >= 1 + (1 + x111:0) ---------------------------------------- (19) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l8(INTEGER, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (20) Obligation: Rules: l8(x101:0, x102:0, x130:0, x104:0) -> l8(x101:0, x102:0, c, x104:0) :|: c = 1 + x130:0 && x101:0 >= 1 + x130:0 l8(x110:0, x111:0, x112:0, x113:0) -> l8(x110:0, c1, c2, x113:0) :|: c2 = 0 && c1 = 1 + x111:0 && (x112:0 >= x110:0 && x113:0 >= 1 + (1 + x111:0)) ---------------------------------------- (21) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l8(x, x1, x2, x3)] = -1 - x1 + x3 The following rules are decreasing: l8(x110:0, x111:0, x112:0, x113:0) -> l8(x110:0, c1, c2, x113:0) :|: c2 = 0 && c1 = 1 + x111:0 && (x112:0 >= x110:0 && x113:0 >= 1 + (1 + x111:0)) The following rules are bounded: l8(x110:0, x111:0, x112:0, x113:0) -> l8(x110:0, c1, c2, x113:0) :|: c2 = 0 && c1 = 1 + x111:0 && (x112:0 >= x110:0 && x113:0 >= 1 + (1 + x111:0)) ---------------------------------------- (22) Obligation: Rules: l8(x101:0, x102:0, x130:0, x104:0) -> l8(x101:0, x102:0, c, x104:0) :|: c = 1 + x130:0 && x101:0 >= 1 + x130:0 ---------------------------------------- (23) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l8(x, x1, x2, x3)] = x - x2 The following rules are decreasing: l8(x101:0, x102:0, x130:0, x104:0) -> l8(x101:0, x102:0, c, x104:0) :|: c = 1 + x130:0 && x101:0 >= 1 + x130:0 The following rules are bounded: l8(x101:0, x102:0, x130:0, x104:0) -> l8(x101:0, x102:0, c, x104:0) :|: c = 1 + x130:0 && x101:0 >= 1 + x130:0 ---------------------------------------- (24) YES ---------------------------------------- (25) Obligation: Termination digraph: Nodes: (1) l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x26 = x35 && x25 = x34 && x24 = x33 && x23 = x32 && x22 = x31 && x20 = x29 && x19 = x28 && x18 = x27 && x30 = 1 + x21 (2) l5(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l3(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x78 = x87 && x77 = x86 && x76 = x85 && x75 = x84 && x74 = x83 && x73 = x82 && x72 = x81 && x89 = x89 && x88 = x88 && 1 + x75 <= x74 (3) l4(x360, x361, x362, x363, x364, x365, x366, x367, x368) -> l5(x369, x370, x371, x372, x373, x374, x375, x376, x377) :|: x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x363 = x372 && x362 = x371 && x361 = x370 && x360 = x369 Arcs: (1) -> (3) (2) -> (1) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (26) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (27) Obligation: Rules: l5(x27:0, x28:0, x29:0, x75:0, x31:0, x32:0, x33:0, x79:0, x80:0) -> l5(x27:0, x28:0, x29:0, 1 + x75:0, x31:0, x32:0, x33:0, x34:0, x35:0) :|: x29:0 >= 1 + x75:0 ---------------------------------------- (28) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l5(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l5(x3, x4) ---------------------------------------- (29) Obligation: Rules: l5(x29:0, x75:0) -> l5(x29:0, 1 + x75:0) :|: x29:0 >= 1 + x75:0 ---------------------------------------- (30) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l5(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (31) Obligation: Rules: l5(x29:0, x75:0) -> l5(x29:0, c) :|: c = 1 + x75:0 && x29:0 >= 1 + x75:0 ---------------------------------------- (32) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l5(x, x1)] = x - x1 The following rules are decreasing: l5(x29:0, x75:0) -> l5(x29:0, c) :|: c = 1 + x75:0 && x29:0 >= 1 + x75:0 The following rules are bounded: l5(x29:0, x75:0) -> l5(x29:0, c) :|: c = 1 + x75:0 && x29:0 >= 1 + x75:0 ---------------------------------------- (33) YES ---------------------------------------- (34) Obligation: Termination digraph: Nodes: (1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x8 = x17 && x7 = x16 && x6 = x15 && x5 = x14 && x4 = x13 && x2 = x11 && x1 = x10 && x = x9 && x12 = 1 + x3 && 1 + x3 <= x5 (2) l2(x378, x379, x380, x381, x382, x383, x384, x385, x386) -> l0(x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x386 = x395 && x385 = x394 && x384 = x393 && x383 = x392 && x382 = x391 && x381 = x390 && x380 = x389 && x379 = x388 && x378 = x387 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (35) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (36) Obligation: Rules: l0(x387:0, x10:0, x11:0, x3:0, x13:0, x14:0, x15:0, x16:0, x17:0) -> l0(x387:0, x10:0, x11:0, 1 + x3:0, x13:0, x14:0, x15:0, x16:0, x17:0) :|: x14:0 >= 1 + x3:0 ---------------------------------------- (37) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l0(x4, x6) ---------------------------------------- (38) Obligation: Rules: l0(x3:0, x14:0) -> l0(1 + x3:0, x14:0) :|: x14:0 >= 1 + x3:0 ---------------------------------------- (39) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (40) Obligation: Rules: l0(x3:0, x14:0) -> l0(c, x14:0) :|: c = 1 + x3:0 && x14:0 >= 1 + x3:0 ---------------------------------------- (41) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l0(x, x1)] = -x + x1 The following rules are decreasing: l0(x3:0, x14:0) -> l0(c, x14:0) :|: c = 1 + x3:0 && x14:0 >= 1 + x3:0 The following rules are bounded: l0(x3:0, x14:0) -> l0(c, x14:0) :|: c = 1 + x3:0 && x14:0 >= 1 + x3:0 ---------------------------------------- (42) YES