MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 13.8 s] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 27 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 69 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(data16HAT0, data18HAT0, i6HAT0, ret17HAT0, ret28HAT0, ret_f19HAT0, ret_f212HAT0, ret_f215HAT0, tmpHAT0, val10HAT0, val13HAT0) -> l1(data16HATpost, data18HATpost, i6HATpost, ret17HATpost, ret28HATpost, ret_f19HATpost, ret_f212HATpost, ret_f215HATpost, tmpHATpost, val10HATpost, val13HATpost) :|: val13HAT0 = val13HATpost && val10HAT0 = val10HATpost && tmpHAT0 = tmpHATpost && ret_f215HAT0 = ret_f215HATpost && ret_f212HAT0 = ret_f212HATpost && ret_f19HAT0 = ret_f19HATpost && ret28HAT0 = ret28HATpost && ret17HAT0 = ret17HATpost && data18HAT0 = data18HATpost && data16HAT0 = data16HATpost && i6HATpost = i6HATpost l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x16 = 1 l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l3(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x29 = x40 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 && x41 = x27 l4(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l2(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x48 = x59 && x47 = x58 && x46 = x57 && x45 = x56 && x44 = x55 && x60 = x48 l5(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 && x82 = 0 && 0 <= x70 && x70 <= 0 l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l4(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x92 = x103 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && 1 <= x92 l5(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l4(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x110 = x121 && 1 + x114 <= 0 l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l0(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x155 = x166 && x154 = x165 l7(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l2(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 && x192 = x179 l8(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l1(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x198 = x209 && x211 = -1 + x200 && 0 <= x201 && x201 <= 0 l8(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l7(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x229 = x240 && x228 = x239 && x227 = x238 && x226 = x237 && x225 = x236 && x224 = x235 && x223 = x234 && x222 = x233 && x221 = x232 && x220 = x231 && 1 <= x223 l8(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l7(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x252 = x263 && x251 = x262 && x250 = x261 && x249 = x260 && x248 = x259 && x247 = x258 && x246 = x257 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 && 1 + x245 <= 0 l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l9(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x268 = x279 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 l10(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l8(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x294 = x305 && x293 = x304 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x300 = x303 && x303 = 0 && x297 = x306 && x306 = x306 l9(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) -> l5(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x317 = x328 && x316 = x327 && x314 = x325 && x313 = x324 && x311 = x322 && x310 = x321 && x308 = x319 && x323 = x326 && x326 = 0 && x320 = x329 && x329 = x329 && 0 <= x310 && x310 <= 0 l9(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l10(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 && 1 <= x332 l9(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l10(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x357 = x368 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && 1 + x354 <= 0 l11(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384) -> l6(x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x384 = x395 && x383 = x394 && x382 = x393 && x381 = x392 && x380 = x391 && x379 = x390 && x378 = x389 && x377 = x388 && x376 = x387 && x375 = x386 && x374 = x385 l12(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l11(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x406 = x417 && x405 = x416 && x404 = x415 && x403 = x414 && x402 = x413 && x401 = x412 && x400 = x411 && x399 = x410 && x398 = x409 && x397 = x408 && x396 = x407 Start term: l12(data16HAT0, data18HAT0, i6HAT0, ret17HAT0, ret28HAT0, ret_f19HAT0, ret_f212HAT0, ret_f215HAT0, tmpHAT0, val10HAT0, val13HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(data16HAT0, data18HAT0, i6HAT0, ret17HAT0, ret28HAT0, ret_f19HAT0, ret_f212HAT0, ret_f215HAT0, tmpHAT0, val10HAT0, val13HAT0) -> l1(data16HATpost, data18HATpost, i6HATpost, ret17HATpost, ret28HATpost, ret_f19HATpost, ret_f212HATpost, ret_f215HATpost, tmpHATpost, val10HATpost, val13HATpost) :|: val13HAT0 = val13HATpost && val10HAT0 = val10HATpost && tmpHAT0 = tmpHATpost && ret_f215HAT0 = ret_f215HATpost && ret_f212HAT0 = ret_f212HATpost && ret_f19HAT0 = ret_f19HATpost && ret28HAT0 = ret28HATpost && ret17HAT0 = ret17HATpost && data18HAT0 = data18HATpost && data16HAT0 = data16HATpost && i6HATpost = i6HATpost l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x16 = 1 l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l3(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x29 = x40 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 && x41 = x27 l4(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l2(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x48 = x59 && x47 = x58 && x46 = x57 && x45 = x56 && x44 = x55 && x60 = x48 l5(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 && x82 = 0 && 0 <= x70 && x70 <= 0 l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l4(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x92 = x103 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && 1 <= x92 l5(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l4(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x110 = x121 && 1 + x114 <= 0 l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l0(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x155 = x166 && x154 = x165 l7(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l2(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 && x192 = x179 l8(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l1(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x198 = x209 && x211 = -1 + x200 && 0 <= x201 && x201 <= 0 l8(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l7(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x229 = x240 && x228 = x239 && x227 = x238 && x226 = x237 && x225 = x236 && x224 = x235 && x223 = x234 && x222 = x233 && x221 = x232 && x220 = x231 && 1 <= x223 l8(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l7(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x252 = x263 && x251 = x262 && x250 = x261 && x249 = x260 && x248 = x259 && x247 = x258 && x246 = x257 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 && 1 + x245 <= 0 l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l9(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x268 = x279 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 l10(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l8(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x294 = x305 && x293 = x304 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x300 = x303 && x303 = 0 && x297 = x306 && x306 = x306 l9(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) -> l5(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x317 = x328 && x316 = x327 && x314 = x325 && x313 = x324 && x311 = x322 && x310 = x321 && x308 = x319 && x323 = x326 && x326 = 0 && x320 = x329 && x329 = x329 && 0 <= x310 && x310 <= 0 l9(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l10(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 && 1 <= x332 l9(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l10(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x357 = x368 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && 1 + x354 <= 0 l11(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384) -> l6(x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x384 = x395 && x383 = x394 && x382 = x393 && x381 = x392 && x380 = x391 && x379 = x390 && x378 = x389 && x377 = x388 && x376 = x387 && x375 = x386 && x374 = x385 l12(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l11(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x406 = x417 && x405 = x416 && x404 = x415 && x403 = x414 && x402 = x413 && x401 = x412 && x400 = x411 && x399 = x410 && x398 = x409 && x397 = x408 && x396 = x407 Start term: l12(data16HAT0, data18HAT0, i6HAT0, ret17HAT0, ret28HAT0, ret_f19HAT0, ret_f212HAT0, ret_f215HAT0, tmpHAT0, val10HAT0, val13HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(data16HAT0, data18HAT0, i6HAT0, ret17HAT0, ret28HAT0, ret_f19HAT0, ret_f212HAT0, ret_f215HAT0, tmpHAT0, val10HAT0, val13HAT0) -> l1(data16HATpost, data18HATpost, i6HATpost, ret17HATpost, ret28HATpost, ret_f19HATpost, ret_f212HATpost, ret_f215HATpost, tmpHATpost, val10HATpost, val13HATpost) :|: val13HAT0 = val13HATpost && val10HAT0 = val10HATpost && tmpHAT0 = tmpHATpost && ret_f215HAT0 = ret_f215HATpost && ret_f212HAT0 = ret_f212HATpost && ret_f19HAT0 = ret_f19HATpost && ret28HAT0 = ret28HATpost && ret17HAT0 = ret17HATpost && data18HAT0 = data18HATpost && data16HAT0 = data16HATpost && i6HATpost = i6HATpost (2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l2(x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) :|: x10 = x21 && x9 = x20 && x8 = x19 && x7 = x18 && x6 = x17 && x4 = x15 && x3 = x14 && x2 = x13 && x1 = x12 && x = x11 && x16 = 1 (3) l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l3(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x32 = x43 && x31 = x42 && x29 = x40 && x28 = x39 && x27 = x38 && x26 = x37 && x25 = x36 && x24 = x35 && x23 = x34 && x22 = x33 && x41 = x27 (4) l4(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) -> l2(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: x54 = x65 && x53 = x64 && x52 = x63 && x51 = x62 && x50 = x61 && x48 = x59 && x47 = x58 && x46 = x57 && x45 = x56 && x44 = x55 && x60 = x48 (5) l5(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76) -> l2(x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x76 = x87 && x75 = x86 && x74 = x85 && x73 = x84 && x72 = x83 && x70 = x81 && x69 = x80 && x68 = x79 && x67 = x78 && x66 = x77 && x82 = 0 && 0 <= x70 && x70 <= 0 (6) l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l4(x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) :|: x98 = x109 && x97 = x108 && x96 = x107 && x95 = x106 && x94 = x105 && x93 = x104 && x92 = x103 && x91 = x102 && x90 = x101 && x89 = x100 && x88 = x99 && 1 <= x92 (7) l5(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l4(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x120 = x131 && x119 = x130 && x118 = x129 && x117 = x128 && x116 = x127 && x115 = x126 && x114 = x125 && x113 = x124 && x112 = x123 && x111 = x122 && x110 = x121 && 1 + x114 <= 0 (8) l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) -> l0(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x142 = x153 && x141 = x152 && x140 = x151 && x139 = x150 && x138 = x149 && x137 = x148 && x136 = x147 && x135 = x146 && x134 = x145 && x133 = x144 && x132 = x143 (9) l6(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x164 = x175 && x163 = x174 && x162 = x173 && x161 = x172 && x160 = x171 && x159 = x170 && x158 = x169 && x157 = x168 && x156 = x167 && x155 = x166 && x154 = x165 (10) l7(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l2(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x186 = x197 && x185 = x196 && x184 = x195 && x183 = x194 && x182 = x193 && x180 = x191 && x179 = x190 && x178 = x189 && x177 = x188 && x176 = x187 && x192 = x179 (11) l8(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l1(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x198 = x209 && x211 = -1 + x200 && 0 <= x201 && x201 <= 0 (12) l8(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l7(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x230 = x241 && x229 = x240 && x228 = x239 && x227 = x238 && x226 = x237 && x225 = x236 && x224 = x235 && x223 = x234 && x222 = x233 && x221 = x232 && x220 = x231 && 1 <= x223 (13) l8(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l7(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x252 = x263 && x251 = x262 && x250 = x261 && x249 = x260 && x248 = x259 && x247 = x258 && x246 = x257 && x245 = x256 && x244 = x255 && x243 = x254 && x242 = x253 && 1 + x245 <= 0 (14) l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l9(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x268 = x279 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 (15) l10(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l8(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x294 = x305 && x293 = x304 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x300 = x303 && x303 = 0 && x297 = x306 && x306 = x306 (16) l9(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) -> l5(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x317 = x328 && x316 = x327 && x314 = x325 && x313 = x324 && x311 = x322 && x310 = x321 && x308 = x319 && x323 = x326 && x326 = 0 && x320 = x329 && x329 = x329 && 0 <= x310 && x310 <= 0 (17) l9(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l10(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 && 1 <= x332 (18) l9(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l10(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x357 = x368 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && 1 + x354 <= 0 (19) l11(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384) -> l6(x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x384 = x395 && x383 = x394 && x382 = x393 && x381 = x392 && x380 = x391 && x379 = x390 && x378 = x389 && x377 = x388 && x376 = x387 && x375 = x386 && x374 = x385 (20) l12(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l11(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x406 = x417 && x405 = x416 && x404 = x415 && x403 = x414 && x402 = x413 && x401 = x412 && x400 = x411 && x399 = x410 && x398 = x409 && x397 = x408 && x396 = x407 Arcs: (1) -> (14) (2) -> (3) (4) -> (3) (5) -> (3) (6) -> (4) (7) -> (4) (8) -> (1), (2) (10) -> (3) (11) -> (14) (12) -> (10) (13) -> (10) (14) -> (16), (17), (18) (15) -> (11) (16) -> (5) (17) -> (15) (18) -> (15) (19) -> (8), (9) (20) -> (19) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l9(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) :|: x274 = x285 && x273 = x284 && x272 = x283 && x271 = x282 && x270 = x281 && x269 = x280 && x268 = x279 && x267 = x278 && x266 = x277 && x265 = x276 && x264 = x275 (2) l8(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l1(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x208 = x219 && x207 = x218 && x206 = x217 && x205 = x216 && x204 = x215 && x203 = x214 && x202 = x213 && x201 = x212 && x199 = x210 && x198 = x209 && x211 = -1 + x200 && 0 <= x201 && x201 <= 0 (3) l10(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l8(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x296 = x307 && x294 = x305 && x293 = x304 && x291 = x302 && x290 = x301 && x288 = x299 && x287 = x298 && x300 = x303 && x303 = 0 && x297 = x306 && x306 = x306 (4) l9(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l10(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x362 = x373 && x361 = x372 && x360 = x371 && x359 = x370 && x358 = x369 && x357 = x368 && x356 = x367 && x355 = x366 && x354 = x365 && x353 = x364 && x352 = x363 && 1 + x354 <= 0 (5) l9(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l10(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x340 = x351 && x339 = x350 && x338 = x349 && x337 = x348 && x336 = x347 && x335 = x346 && x334 = x345 && x333 = x344 && x332 = x343 && x331 = x342 && x330 = x341 && 1 <= x332 Arcs: (1) -> (4), (5) (2) -> (1) (3) -> (2) (4) -> (3) (5) -> (3) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l10(x286:0, x210:0, x288:0, x289:0, x213:0, x214:0, x292:0, x216:0, x217:0, x295:0, x219:0) -> l10(x209:0, x210:0, -1 + x288:0, 0, x213:0, x214:0, 0, x216:0, x217:0, x209:0, x219:0) :|: x288:0 < 1 l10(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l10(x11, x1, -1 + x2, 0, x4, x5, 0, x7, x8, x11, x10) :|: x2 > 1 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l10(x3) ---------------------------------------- (8) Obligation: Rules: l10(x288:0) -> l10(-1 + x288:0) :|: x288:0 < 1 l10(x2) -> l10(-1 + x2) :|: x2 > 1 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l10(INTEGER) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: l10(x288:0) -> l10(c) :|: c = -1 + x288:0 && x288:0 < 1 l10(x2) -> l10(c1) :|: c1 = -1 + x2 && x2 > 1 Found the following polynomial interpretation: [l10(x)] = -1 + x The following rules are decreasing: l10(x288:0) -> l10(c) :|: c = -1 + x288:0 && x288:0 < 1 l10(x2) -> l10(c1) :|: c1 = -1 + x2 && x2 > 1 The following rules are bounded: l10(x2) -> l10(c1) :|: c1 = -1 + x2 && x2 > 1 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l10(x288:0) -> l10(c) :|: c = -1 + x288:0 && x288:0 < 1 ---------------------------------------- (10) Obligation: Rules: l10(x288:0) -> l10(-1 + x288:0) :|: x288:0 < 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l10(x288:0) -> l10(-1 + x288:0) :|: x288:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l10(x288:0) -> l10(-1 + x288:0) :|: x288:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated!