YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 17.0 s] (4) AND (5) IRSwT (6) IntTRSCompressionProof [EQUIVALENT, 7 ms] (7) IRSwT (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (9) IRSwT (10) TempFilterProof [SOUND, 28 ms] (11) IntTRS (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (13) IntTRS (14) RankingReductionPairProof [EQUIVALENT, 5 ms] (15) YES (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 14 ms] (18) IRSwT (19) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (20) IRSwT (21) TempFilterProof [SOUND, 24 ms] (22) IntTRS (23) RankingReductionPairProof [EQUIVALENT, 0 ms] (24) IntTRS (25) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (26) YES (27) IRSwT (28) IntTRSCompressionProof [EQUIVALENT, 7 ms] (29) IRSwT (30) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (31) IRSwT (32) TempFilterProof [SOUND, 36 ms] (33) IntTRS (34) RankingReductionPairProof [EQUIVALENT, 0 ms] (35) YES (36) IRSwT (37) IntTRSCompressionProof [EQUIVALENT, 8 ms] (38) IRSwT (39) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (40) IRSwT (41) TempFilterProof [SOUND, 9 ms] (42) IntTRS (43) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (44) YES ---------------------------------------- (0) Obligation: Rules: l0(__const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) -> l1(__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 l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && x4 <= x2 l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x17 = x25 && x16 = x24 && x26 = 1 + x18 && 1 + x18 <= x20 l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x33 = x41 && x32 = x40 && x42 = 1 + x34 l5(x48, x49, x50, x51, x52, x53, x54, x55) -> l3(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 l9(x80, x81, x82, x83, x84, x85, x86, x87) -> l4(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x81 = x89 && x80 = x88 && x90 = 0 && x81 <= x82 l9(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x111 = x111 && x110 = x110 && 1 + x98 <= x97 l10(x112, x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x114 = x122 && x113 = x121 && x112 = x120 && x123 = 1 + x115 l11(x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 l12(x144, x145, x146, x147, x148, x149, x150, x151) -> l7(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x145 = x153 && x144 = x152 && x154 = 1 + x146 && x145 <= x147 l12(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x175 = x175 && x174 = x174 && 1 + x163 <= x161 l8(x176, x177, x178, x179, x180, x181, x182, x183) -> l6(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x177 = x185 && x176 = x184 && x186 = 0 && x180 <= x178 l8(x192, x193, x194, x195, x196, x197, x198, x199) -> l11(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x194 = x202 && x193 = x201 && x192 = x200 && x203 = 0 && 1 + x194 <= x196 l13(x208, x209, x210, x211, x212, x213, x214, x215) -> l14(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x212 = x220 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 l6(x224, x225, x226, x227, x228, x229, x230, x231) -> l9(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l14(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 && x241 = x249 && x240 = x248 && x250 = 1 + x242 l15(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && 1 + x261 <= x258 l15(x272, x273, x274, x275, x276, x277, x278, x279) -> l13(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x278 = x286 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && 1 + x274 <= x277 l15(x288, x289, x290, x291, x292, x293, x294, x295) -> l14(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 && x293 <= x290 && x290 <= x293 l1(x304, x305, x306, x307, x308, x309, x310, x311) -> l7(x312, x313, x314, x315, x316, x317, x318, x319) :|: x311 = x319 && x310 = x318 && x309 = x317 && x308 = x316 && x307 = x315 && x305 = x313 && x304 = x312 && x314 = 0 && x308 <= x306 l1(x320, x321, x322, x323, x324, x325, x326, x327) -> l15(x328, x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x325 = x333 && x324 = x332 && x323 = x331 && x322 = x330 && x321 = x329 && x320 = x328 && 1 + x322 <= x324 l4(x336, x337, x338, x339, x340, x341, x342, x343) -> l2(x344, x345, x346, x347, x348, x349, x350, x351) :|: x343 = x351 && x342 = x350 && x341 = x349 && x340 = x348 && x339 = x347 && x338 = x346 && x337 = x345 && x336 = x344 l16(x352, x353, x354, x355, x356, x357, x358, x359) -> l0(x360, x361, x362, x363, x364, x365, x366, x367) :|: x359 = x367 && x358 = x366 && x355 = x363 && x352 = x360 && x362 = 0 && x365 = 0 && x361 = x352 && x364 = x352 l17(x368, x369, x370, x371, x372, x373, x374, x375) -> l16(x376, x377, x378, x379, x380, x381, x382, x383) :|: x375 = x383 && x374 = x382 && x373 = x381 && x372 = x380 && x371 = x379 && x370 = x378 && x369 = x377 && x368 = x376 Start term: l17(__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_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) -> l1(__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 l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && x4 <= x2 l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x17 = x25 && x16 = x24 && x26 = 1 + x18 && 1 + x18 <= x20 l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x33 = x41 && x32 = x40 && x42 = 1 + x34 l5(x48, x49, x50, x51, x52, x53, x54, x55) -> l3(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 l9(x80, x81, x82, x83, x84, x85, x86, x87) -> l4(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x81 = x89 && x80 = x88 && x90 = 0 && x81 <= x82 l9(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x111 = x111 && x110 = x110 && 1 + x98 <= x97 l10(x112, x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x114 = x122 && x113 = x121 && x112 = x120 && x123 = 1 + x115 l11(x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 l12(x144, x145, x146, x147, x148, x149, x150, x151) -> l7(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x145 = x153 && x144 = x152 && x154 = 1 + x146 && x145 <= x147 l12(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x175 = x175 && x174 = x174 && 1 + x163 <= x161 l8(x176, x177, x178, x179, x180, x181, x182, x183) -> l6(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x177 = x185 && x176 = x184 && x186 = 0 && x180 <= x178 l8(x192, x193, x194, x195, x196, x197, x198, x199) -> l11(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x194 = x202 && x193 = x201 && x192 = x200 && x203 = 0 && 1 + x194 <= x196 l13(x208, x209, x210, x211, x212, x213, x214, x215) -> l14(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x212 = x220 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 l6(x224, x225, x226, x227, x228, x229, x230, x231) -> l9(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 l14(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 && x241 = x249 && x240 = x248 && x250 = 1 + x242 l15(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && 1 + x261 <= x258 l15(x272, x273, x274, x275, x276, x277, x278, x279) -> l13(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x278 = x286 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && 1 + x274 <= x277 l15(x288, x289, x290, x291, x292, x293, x294, x295) -> l14(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 && x293 <= x290 && x290 <= x293 l1(x304, x305, x306, x307, x308, x309, x310, x311) -> l7(x312, x313, x314, x315, x316, x317, x318, x319) :|: x311 = x319 && x310 = x318 && x309 = x317 && x308 = x316 && x307 = x315 && x305 = x313 && x304 = x312 && x314 = 0 && x308 <= x306 l1(x320, x321, x322, x323, x324, x325, x326, x327) -> l15(x328, x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x325 = x333 && x324 = x332 && x323 = x331 && x322 = x330 && x321 = x329 && x320 = x328 && 1 + x322 <= x324 l4(x336, x337, x338, x339, x340, x341, x342, x343) -> l2(x344, x345, x346, x347, x348, x349, x350, x351) :|: x343 = x351 && x342 = x350 && x341 = x349 && x340 = x348 && x339 = x347 && x338 = x346 && x337 = x345 && x336 = x344 l16(x352, x353, x354, x355, x356, x357, x358, x359) -> l0(x360, x361, x362, x363, x364, x365, x366, x367) :|: x359 = x367 && x358 = x366 && x355 = x363 && x352 = x360 && x362 = 0 && x365 = 0 && x361 = x352 && x364 = x352 l17(x368, x369, x370, x371, x372, x373, x374, x375) -> l16(x376, x377, x378, x379, x380, x381, x382, x383) :|: x375 = x383 && x374 = x382 && x373 = x381 && x372 = x380 && x371 = x379 && x370 = x378 && x369 = x377 && x368 = x376 Start term: l17(__const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(__const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) -> l1(__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 (2) l2(x, x1, x2, x3, x4, x5, x6, x7) -> l3(x8, x9, x10, x11, x12, x13, x14, x15) :|: x7 = x15 && x6 = x14 && x5 = x13 && x4 = x12 && x3 = x11 && x2 = x10 && x1 = x9 && x = x8 && x4 <= x2 (3) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x17 = x25 && x16 = x24 && x26 = 1 + x18 && 1 + x18 <= x20 (4) l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x33 = x41 && x32 = x40 && x42 = 1 + x34 (5) l5(x48, x49, x50, x51, x52, x53, x54, x55) -> l3(x56, x57, x58, x59, x60, x61, x62, x63) :|: x55 = x63 && x54 = x62 && x53 = x61 && x52 = x60 && x51 = x59 && x50 = x58 && x49 = x57 && x48 = x56 (6) l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 (7) l9(x80, x81, x82, x83, x84, x85, x86, x87) -> l4(x88, x89, x90, x91, x92, x93, x94, x95) :|: x87 = x95 && x86 = x94 && x85 = x93 && x84 = x92 && x83 = x91 && x81 = x89 && x80 = x88 && x90 = 0 && x81 <= x82 (8) l9(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x111 = x111 && x110 = x110 && 1 + x98 <= x97 (9) l10(x112, x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x114 = x122 && x113 = x121 && x112 = x120 && x123 = 1 + x115 (10) l11(x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 (11) l12(x144, x145, x146, x147, x148, x149, x150, x151) -> l7(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x145 = x153 && x144 = x152 && x154 = 1 + x146 && x145 <= x147 (12) l12(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x175 = x175 && x174 = x174 && 1 + x163 <= x161 (13) l8(x176, x177, x178, x179, x180, x181, x182, x183) -> l6(x184, x185, x186, x187, x188, x189, x190, x191) :|: x183 = x191 && x182 = x190 && x181 = x189 && x180 = x188 && x179 = x187 && x177 = x185 && x176 = x184 && x186 = 0 && x180 <= x178 (14) l8(x192, x193, x194, x195, x196, x197, x198, x199) -> l11(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x194 = x202 && x193 = x201 && x192 = x200 && x203 = 0 && 1 + x194 <= x196 (15) l13(x208, x209, x210, x211, x212, x213, x214, x215) -> l14(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x212 = x220 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 (16) l6(x224, x225, x226, x227, x228, x229, x230, x231) -> l9(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) l14(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 && x241 = x249 && x240 = x248 && x250 = 1 + x242 (18) l15(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && 1 + x261 <= x258 (19) l15(x272, x273, x274, x275, x276, x277, x278, x279) -> l13(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x278 = x286 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && 1 + x274 <= x277 (20) l15(x288, x289, x290, x291, x292, x293, x294, x295) -> l14(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 && x293 <= x290 && x290 <= x293 (21) l1(x304, x305, x306, x307, x308, x309, x310, x311) -> l7(x312, x313, x314, x315, x316, x317, x318, x319) :|: x311 = x319 && x310 = x318 && x309 = x317 && x308 = x316 && x307 = x315 && x305 = x313 && x304 = x312 && x314 = 0 && x308 <= x306 (22) l1(x320, x321, x322, x323, x324, x325, x326, x327) -> l15(x328, x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x325 = x333 && x324 = x332 && x323 = x331 && x322 = x330 && x321 = x329 && x320 = x328 && 1 + x322 <= x324 (23) l4(x336, x337, x338, x339, x340, x341, x342, x343) -> l2(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) l16(x352, x353, x354, x355, x356, x357, x358, x359) -> l0(x360, x361, x362, x363, x364, x365, x366, x367) :|: x359 = x367 && x358 = x366 && x355 = x363 && x352 = x360 && x362 = 0 && x365 = 0 && x361 = x352 && x364 = x352 (25) l17(x368, x369, x370, x371, x372, x373, x374, x375) -> l16(x376, x377, x378, x379, x380, x381, x382, x383) :|: x375 = x383 && x374 = x382 && x373 = x381 && x372 = x380 && x371 = x379 && x370 = x378 && x369 = x377 && x368 = x376 Arcs: (1) -> (21), (22) (3) -> (23) (4) -> (16) (6) -> (13), (14) (7) -> (23) (8) -> (4), (5) (9) -> (10) (10) -> (11), (12) (11) -> (6) (12) -> (9) (13) -> (16) (14) -> (10) (15) -> (17) (16) -> (7), (8) (17) -> (1) (18) -> (15) (19) -> (15) (20) -> (17) (21) -> (6) (22) -> (18), (19), (20) (23) -> (2), (3) (24) -> (1) (25) -> (24) This digraph is fully evaluated! ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5) Obligation: Termination digraph: Nodes: (1) l0(__const_5HAT0, edgecountHAT0, iHAT0, jHAT0, nodecountHAT0, sourceHAT0, xHAT0, yHAT0) -> l1(__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 (2) l14(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 && x241 = x249 && x240 = x248 && x250 = 1 + x242 (3) l15(x288, x289, x290, x291, x292, x293, x294, x295) -> l14(x296, x297, x298, x299, x300, x301, x302, x303) :|: x295 = x303 && x294 = x302 && x293 = x301 && x292 = x300 && x291 = x299 && x290 = x298 && x289 = x297 && x288 = x296 && x293 <= x290 && x290 <= x293 (4) l13(x208, x209, x210, x211, x212, x213, x214, x215) -> l14(x216, x217, x218, x219, x220, x221, x222, x223) :|: x215 = x223 && x214 = x222 && x213 = x221 && x212 = x220 && x211 = x219 && x210 = x218 && x209 = x217 && x208 = x216 (5) l15(x272, x273, x274, x275, x276, x277, x278, x279) -> l13(x280, x281, x282, x283, x284, x285, x286, x287) :|: x279 = x287 && x278 = x286 && x277 = x285 && x276 = x284 && x275 = x283 && x274 = x282 && x273 = x281 && x272 = x280 && 1 + x274 <= x277 (6) l15(x256, x257, x258, x259, x260, x261, x262, x263) -> l13(x264, x265, x266, x267, x268, x269, x270, x271) :|: x263 = x271 && x262 = x270 && x261 = x269 && x260 = x268 && x259 = x267 && x258 = x266 && x257 = x265 && x256 = x264 && 1 + x261 <= x258 (7) l1(x320, x321, x322, x323, x324, x325, x326, x327) -> l15(x328, x329, x330, x331, x332, x333, x334, x335) :|: x327 = x335 && x326 = x334 && x325 = x333 && x324 = x332 && x323 = x331 && x322 = x330 && x321 = x329 && x320 = x328 && 1 + x322 <= x324 Arcs: (1) -> (7) (2) -> (1) (3) -> (2) (4) -> (2) (5) -> (4) (6) -> (4) (7) -> (3), (5), (6) This digraph is fully evaluated! ---------------------------------------- (6) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (7) Obligation: Rules: l15(__const_5HATpost:0, edgecountHATpost:0, x218:0, jHATpost:0, nodecountHATpost:0, sourceHATpost:0, x222:0, x223:0) -> l15(__const_5HATpost:0, edgecountHATpost:0, 1 + x218:0, jHATpost:0, nodecountHATpost:0, sourceHATpost:0, x222:0, x223:0) :|: sourceHATpost:0 >= 1 + x218:0 && nodecountHATpost:0 >= 1 + (1 + x218:0) l15(x, x1, x2, x3, x4, x2, x5, x6) -> l15(x, x1, 1 + x2, x3, x4, x2, x5, x6) :|: x4 >= 1 + (1 + x2) l15(x7, x8, x9, x10, x11, x12, x13, x14) -> l15(x7, x8, 1 + x9, x10, x11, x12, x13, x14) :|: x9 >= 1 + x12 && x11 >= 1 + (1 + x9) ---------------------------------------- (8) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l15(x1, x2, x3, x4, x5, x6, x7, x8) -> l15(x3, x5, x6) ---------------------------------------- (9) Obligation: Rules: l15(x218:0, nodecountHATpost:0, sourceHATpost:0) -> l15(1 + x218:0, nodecountHATpost:0, sourceHATpost:0) :|: sourceHATpost:0 >= 1 + x218:0 && nodecountHATpost:0 >= 1 + (1 + x218:0) l15(x2, x4, x2) -> l15(1 + x2, x4, x2) :|: x4 >= 1 + (1 + x2) l15(x9, x11, x12) -> l15(1 + x9, x11, x12) :|: x9 >= 1 + x12 && x11 >= 1 + (1 + x9) ---------------------------------------- (10) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l15(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (11) Obligation: Rules: l15(x218:0, nodecountHATpost:0, sourceHATpost:0) -> l15(c, nodecountHATpost:0, sourceHATpost:0) :|: c = 1 + x218:0 && (sourceHATpost:0 >= 1 + x218:0 && nodecountHATpost:0 >= 1 + (1 + x218:0)) l15(x2, x4, x2) -> l15(c1, x4, x2) :|: c1 = 1 + x2 && x4 >= 1 + (1 + x2) l15(x9, x11, x12) -> l15(c2, x11, x12) :|: c2 = 1 + x9 && (x9 >= 1 + x12 && x11 >= 1 + (1 + x9)) ---------------------------------------- (12) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l15(x, x1, x2)] = -x + x1 The following rules are decreasing: l15(x218:0, nodecountHATpost:0, sourceHATpost:0) -> l15(c, nodecountHATpost:0, sourceHATpost:0) :|: c = 1 + x218:0 && (sourceHATpost:0 >= 1 + x218:0 && nodecountHATpost:0 >= 1 + (1 + x218:0)) l15(x2, x4, x2) -> l15(c1, x4, x2) :|: c1 = 1 + x2 && x4 >= 1 + (1 + x2) l15(x9, x11, x12) -> l15(c2, x11, x12) :|: c2 = 1 + x9 && (x9 >= 1 + x12 && x11 >= 1 + (1 + x9)) The following rules are bounded: l15(x218:0, nodecountHATpost:0, sourceHATpost:0) -> l15(c, nodecountHATpost:0, sourceHATpost:0) :|: c = 1 + x218:0 && (sourceHATpost:0 >= 1 + x218:0 && nodecountHATpost:0 >= 1 + (1 + x218:0)) l15(x2, x4, x2) -> l15(c1, x4, x2) :|: c1 = 1 + x2 && x4 >= 1 + (1 + x2) ---------------------------------------- (13) Obligation: Rules: l15(x9, x11, x12) -> l15(c2, x11, x12) :|: c2 = 1 + x9 && (x9 >= 1 + x12 && x11 >= 1 + (1 + x9)) ---------------------------------------- (14) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l15 ] = -1*l15_1 + l15_2 The following rules are decreasing: l15(x9, x11, x12) -> l15(c2, x11, x12) :|: c2 = 1 + x9 && (x9 >= 1 + x12 && x11 >= 1 + (1 + x9)) The following rules are bounded: l15(x9, x11, x12) -> l15(c2, x11, x12) :|: c2 = 1 + x9 && (x9 >= 1 + x12 && x11 >= 1 + (1 + x9)) ---------------------------------------- (15) YES ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l7(x64, x65, x66, x67, x68, x69, x70, x71) -> l8(x72, x73, x74, x75, x76, x77, x78, x79) :|: x71 = x79 && x70 = x78 && x69 = x77 && x68 = x76 && x67 = x75 && x66 = x74 && x65 = x73 && x64 = x72 (2) l12(x144, x145, x146, x147, x148, x149, x150, x151) -> l7(x152, x153, x154, x155, x156, x157, x158, x159) :|: x151 = x159 && x150 = x158 && x149 = x157 && x148 = x156 && x147 = x155 && x145 = x153 && x144 = x152 && x154 = 1 + x146 && x145 <= x147 (3) l11(x128, x129, x130, x131, x132, x133, x134, x135) -> l12(x136, x137, x138, x139, x140, x141, x142, x143) :|: x135 = x143 && x134 = x142 && x133 = x141 && x132 = x140 && x131 = x139 && x130 = x138 && x129 = x137 && x128 = x136 (4) l8(x192, x193, x194, x195, x196, x197, x198, x199) -> l11(x200, x201, x202, x203, x204, x205, x206, x207) :|: x199 = x207 && x198 = x206 && x197 = x205 && x196 = x204 && x194 = x202 && x193 = x201 && x192 = x200 && x203 = 0 && 1 + x194 <= x196 (5) l10(x112, x113, x114, x115, x116, x117, x118, x119) -> l11(x120, x121, x122, x123, x124, x125, x126, x127) :|: x119 = x127 && x118 = x126 && x117 = x125 && x116 = x124 && x114 = x122 && x113 = x121 && x112 = x120 && x123 = 1 + x115 (6) l12(x160, x161, x162, x163, x164, x165, x166, x167) -> l10(x168, x169, x170, x171, x172, x173, x174, x175) :|: x165 = x173 && x164 = x172 && x163 = x171 && x162 = x170 && x161 = x169 && x160 = x168 && x175 = x175 && x174 = x174 && 1 + x163 <= x161 Arcs: (1) -> (4) (2) -> (1) (3) -> (2), (6) (4) -> (3) (5) -> (3) (6) -> (5) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l11(x128:0, x129:0, x130:0, x131:0, x132:0, x133:0, x134:0, x135:0) -> l11(x128:0, x129:0, 1 + x130:0, 0, x132:0, x133:0, x134:0, x135:0) :|: x131:0 >= x129:0 && x132:0 >= 1 + (1 + x130:0) l11(x, x1, x2, x3, x4, x5, x6, x7) -> l11(x, x1, x2, 1 + x3, x4, x5, x8, x9) :|: x1 >= 1 + x3 ---------------------------------------- (19) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l11(x1, x2, x3, x4, x5, x6, x7, x8) -> l11(x2, x3, x4, x5) ---------------------------------------- (20) Obligation: Rules: l11(x129:0, x130:0, x131:0, x132:0) -> l11(x129:0, 1 + x130:0, 0, x132:0) :|: x131:0 >= x129:0 && x132:0 >= 1 + (1 + x130:0) l11(x1, x2, x3, x4) -> l11(x1, x2, 1 + x3, x4) :|: x1 >= 1 + x3 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l11(INTEGER, VARIABLE, VARIABLE, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: l11(x129:0, x130:0, x131:0, x132:0) -> l11(x129:0, c, c1, x132:0) :|: c1 = 0 && c = 1 + x130:0 && (x131:0 >= x129:0 && x132:0 >= 1 + (1 + x130:0)) l11(x1, x2, x3, x4) -> l11(x1, x2, c2, x4) :|: c2 = 1 + x3 && x1 >= 1 + x3 ---------------------------------------- (23) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l11 ] = 2*l11_4 + -2*l11_2 The following rules are decreasing: l11(x129:0, x130:0, x131:0, x132:0) -> l11(x129:0, c, c1, x132:0) :|: c1 = 0 && c = 1 + x130:0 && (x131:0 >= x129:0 && x132:0 >= 1 + (1 + x130:0)) The following rules are bounded: l11(x129:0, x130:0, x131:0, x132:0) -> l11(x129:0, c, c1, x132:0) :|: c1 = 0 && c = 1 + x130:0 && (x131:0 >= x129:0 && x132:0 >= 1 + (1 + x130:0)) ---------------------------------------- (24) Obligation: Rules: l11(x1, x2, x3, x4) -> l11(x1, x2, c2, x4) :|: c2 = 1 + x3 && x1 >= 1 + x3 ---------------------------------------- (25) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l11(x, x1, x2, x3)] = x - x2 The following rules are decreasing: l11(x1, x2, x3, x4) -> l11(x1, x2, c2, x4) :|: c2 = 1 + x3 && x1 >= 1 + x3 The following rules are bounded: l11(x1, x2, x3, x4) -> l11(x1, x2, c2, x4) :|: c2 = 1 + x3 && x1 >= 1 + x3 ---------------------------------------- (26) YES ---------------------------------------- (27) Obligation: Termination digraph: Nodes: (1) l6(x224, x225, x226, x227, x228, x229, x230, x231) -> l9(x232, x233, x234, x235, x236, x237, x238, x239) :|: x231 = x239 && x230 = x238 && x229 = x237 && x228 = x236 && x227 = x235 && x226 = x234 && x225 = x233 && x224 = x232 (2) l5(x32, x33, x34, x35, x36, x37, x38, x39) -> l6(x40, x41, x42, x43, x44, x45, x46, x47) :|: x39 = x47 && x38 = x46 && x37 = x45 && x36 = x44 && x35 = x43 && x33 = x41 && x32 = x40 && x42 = 1 + x34 (3) l9(x96, x97, x98, x99, x100, x101, x102, x103) -> l5(x104, x105, x106, x107, x108, x109, x110, x111) :|: x101 = x109 && x100 = x108 && x99 = x107 && x98 = x106 && x97 = x105 && x96 = x104 && x111 = x111 && x110 = x110 && 1 + x98 <= x97 Arcs: (1) -> (3) (2) -> (1) (3) -> (2) This digraph is fully evaluated! ---------------------------------------- (28) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (29) Obligation: Rules: l5(x104:0, x105:0, x34:0, x107:0, x108:0, x109:0, x238:0, x239:0) -> l5(x104:0, x105:0, 1 + x34:0, x107:0, x108:0, x109:0, x110:0, x111:0) :|: x105:0 >= 1 + (1 + x34:0) ---------------------------------------- (30) 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) -> l5(x2, x3) ---------------------------------------- (31) Obligation: Rules: l5(x105:0, x34:0) -> l5(x105:0, 1 + x34:0) :|: x105:0 >= 1 + (1 + x34:0) ---------------------------------------- (32) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l5(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (33) Obligation: Rules: l5(x105:0, x34:0) -> l5(x105:0, c) :|: c = 1 + x34:0 && x105:0 >= 1 + (1 + x34:0) ---------------------------------------- (34) RankingReductionPairProof (EQUIVALENT) Interpretation: [ l5 ] = l5_1 + -1*l5_2 The following rules are decreasing: l5(x105:0, x34:0) -> l5(x105:0, c) :|: c = 1 + x34:0 && x105:0 >= 1 + (1 + x34:0) The following rules are bounded: l5(x105:0, x34:0) -> l5(x105:0, c) :|: c = 1 + x34:0 && x105:0 >= 1 + (1 + x34:0) ---------------------------------------- (35) YES ---------------------------------------- (36) Obligation: Termination digraph: Nodes: (1) l4(x336, x337, x338, x339, x340, x341, x342, x343) -> l2(x344, x345, x346, x347, x348, x349, x350, x351) :|: x343 = x351 && x342 = x350 && x341 = x349 && x340 = x348 && x339 = x347 && x338 = x346 && x337 = x345 && x336 = x344 (2) l2(x16, x17, x18, x19, x20, x21, x22, x23) -> l4(x24, x25, x26, x27, x28, x29, x30, x31) :|: x23 = x31 && x22 = x30 && x21 = x29 && x20 = x28 && x19 = x27 && x17 = x25 && x16 = x24 && x26 = 1 + x18 && 1 + x18 <= x20 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (37) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (38) Obligation: Rules: l4(x24:0, x25:0, x338:0, x27:0, x28:0, x29:0, x30:0, x31:0) -> l4(x24:0, x25:0, 1 + x338:0, x27:0, x28:0, x29:0, x30:0, x31:0) :|: x28:0 >= 1 + x338:0 ---------------------------------------- (39) 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(x3, x5) ---------------------------------------- (40) Obligation: Rules: l4(x338:0, x28:0) -> l4(1 + x338:0, x28:0) :|: x28:0 >= 1 + x338:0 ---------------------------------------- (41) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l4(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (42) Obligation: Rules: l4(x338:0, x28:0) -> l4(c, x28:0) :|: c = 1 + x338:0 && x28:0 >= 1 + x338:0 ---------------------------------------- (43) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l4(x, x1)] = -x + x1 The following rules are decreasing: l4(x338:0, x28:0) -> l4(c, x28:0) :|: c = 1 + x338:0 && x28:0 >= 1 + x338:0 The following rules are bounded: l4(x338:0, x28:0) -> l4(c, x28:0) :|: c = 1 + x338:0 && x28:0 >= 1 + x338:0 ---------------------------------------- (44) YES