MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 13.3 s] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 108 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 810 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 4 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (16) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __cil_tmp2_7HAT0, __disjvr_0HAT0, __retres1_6HAT0, b_128HAT0, b_51HAT0, b_76HAT0, count_5HAT0, lt_12HAT0, lt_13HAT0, tmp_11HAT0, x_8HAT0, y_9HAT0, z_10HAT0) -> l1(Result_4HATpost, __cil_tmp2_7HATpost, __disjvr_0HATpost, __retres1_6HATpost, b_128HATpost, b_51HATpost, b_76HATpost, count_5HATpost, lt_12HATpost, lt_13HATpost, tmp_11HATpost, x_8HATpost, y_9HATpost, z_10HATpost) :|: lt_13HAT1 = b_128HAT0 && 5 - lt_13HAT1 <= 0 && lt_13HATpost = lt_13HATpost && __retres1_6HATpost = 1 && __cil_tmp2_7HATpost = __retres1_6HATpost && Result_4HAT1 = __cil_tmp2_7HATpost && tmp_11HATpost = Result_4HAT1 && Result_4HATpost = Result_4HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && b_128HAT0 = b_128HATpost && b_51HAT0 = b_51HATpost && b_76HAT0 = b_76HATpost && count_5HAT0 = count_5HATpost && lt_12HAT0 = lt_12HATpost && x_8HAT0 = x_8HATpost && y_9HAT0 = y_9HATpost && z_10HAT0 = z_10HATpost l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> l2(x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27) :|: x28 = x4 && 0 <= 4 - x28 && x23 = x23 && x29 = x4 && x22 = x22 && x17 = 0 && x15 = x17 && x30 = x15 && x24 = x30 && x14 = x14 && x2 = x16 && x4 = x18 && x5 = x19 && x6 = x20 && x7 = x21 && x11 = x25 && x12 = x26 && x13 = x27 l3(x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58) :|: x44 = x58 && x43 = x57 && x42 = x56 && x41 = x55 && x40 = x54 && x39 = x53 && x38 = x52 && x37 = x51 && x36 = x50 && x35 = x49 && x34 = x48 && x33 = x47 && x32 = x46 && x45 = x45 && -1 * x42 + x43 <= 0 l3(x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72) -> l5(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86) :|: x72 = x86 && x71 = x85 && x70 = x84 && x69 = x83 && x68 = x82 && x67 = x81 && x66 = x80 && x65 = x79 && x64 = x78 && x63 = x77 && x62 = x76 && x61 = x75 && x60 = x74 && x59 = x73 && 0 <= -1 - x70 + x71 l2(x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l0(x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114) :|: x100 = x114 && x99 = x113 && x98 = x112 && x97 = x111 && x96 = x110 && x95 = x109 && x94 = x108 && x93 = x107 && x92 = x106 && x91 = x105 && x90 = x104 && x89 = x103 && x88 = x102 && x87 = x101 && 0 <= -1 - x99 + x100 && 0 <= x97 && x97 <= 0 l6(x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128) -> l2(x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) :|: 0 <= -1 - x127 + x128 && x143 = 0 && 0 <= 4 - x143 && x138 = x138 && x144 = 0 && x137 = x137 && x132 = 0 && x130 = x132 && x145 = x130 && x139 = x145 && x129 = x129 && x117 = x131 && x119 = x133 && x120 = x134 && x121 = x135 && x122 = x136 && x126 = x140 && x127 = x141 && x128 = x142 l6(x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l3(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173) :|: x159 = x173 && x158 = x172 && x156 = x170 && x155 = x169 && x154 = x168 && x153 = x167 && x152 = x166 && x151 = x165 && x150 = x164 && x149 = x163 && x148 = x162 && x147 = x161 && x146 = x160 && x171 = 1 + x157 && -1 * x158 + x159 <= 0 l1(x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187) -> l7(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201) :|: x187 = x201 && x186 = x200 && x185 = x199 && x184 = x198 && x183 = x197 && x182 = x196 && x181 = x195 && x180 = x194 && x179 = x193 && x178 = x192 && x177 = x191 && x176 = x190 && x175 = x189 && x174 = x188 && x190 = x176 l7(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) -> l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) :|: x215 = x229 && x213 = x227 && x212 = x226 && x211 = x225 && x210 = x224 && x209 = x223 && x208 = x222 && x207 = x221 && x206 = x220 && x205 = x219 && x204 = x218 && x203 = x217 && x202 = x216 && x228 = 1 + x214 l5(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) -> l2(x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257) :|: 0 <= -1 - x242 + x243 && x258 = 0 && 0 <= 4 - x258 && x253 = x253 && x259 = 0 && x252 = x252 && x247 = 0 && x245 = x247 && x260 = x245 && x254 = x260 && x244 = x244 && x232 = x246 && x234 = x248 && x235 = x249 && x236 = x250 && x237 = x251 && x241 = x255 && x242 = x256 && x243 = x257 l5(x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l3(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) :|: x274 = x288 && x273 = x287 && x271 = x285 && x270 = x284 && x269 = x283 && x268 = x282 && x267 = x281 && x266 = x280 && x265 = x279 && x264 = x278 && x263 = x277 && x262 = x276 && x261 = x275 && x286 = 1 + x272 && -1 * x273 + x274 <= 0 l8(x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302) -> l3(x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316) :|: x302 = x316 && x301 = x315 && x300 = x314 && x299 = x313 && x298 = x312 && x297 = x311 && x295 = x309 && x294 = x308 && x293 = x307 && x292 = x306 && x291 = x305 && x290 = x304 && x289 = x303 && x310 = x310 l9(x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330) -> l2(x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344) :|: x336 = -2 && x345 = -1 && 0 <= 4 - x345 && x340 = x340 && x346 = -1 && x339 = x339 && x334 = 0 && x332 = x334 && x347 = x332 && x341 = x347 && x331 = x331 && x319 = x333 && x321 = x335 && x323 = x337 && x324 = x338 && x328 = x342 && x329 = x343 && x330 = x344 l10(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361) -> l2(x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375) :|: x368 = -1 + x353 && x376 = x353 && 0 <= 4 - x376 && x371 = x371 && x377 = x353 && x370 = x370 && x365 = 0 && x363 = x365 && x378 = x363 && x372 = x378 && x362 = x362 && x350 = x364 && x352 = x366 && x353 = x367 && x355 = x369 && x359 = x373 && x360 = x374 && x361 = x375 l10(x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392) -> l1(x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) :|: x407 = x384 && 5 - x407 <= 0 && x402 = x402 && x396 = 1 && x394 = x396 && x408 = x394 && x403 = x408 && x393 = x393 && x381 = x395 && x383 = x397 && x384 = x398 && x385 = x399 && x386 = x400 && x387 = x401 && x390 = x404 && x391 = x405 && x392 = x406 l11(x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l2(x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436) :|: x427 = -2 && x437 = -1 && 0 <= 4 - x437 && x432 = x432 && x438 = -1 && x431 = x431 && x426 = 0 && x424 = x426 && x439 = x424 && x433 = x439 && x423 = x423 && x411 = x425 && x414 = x428 && x415 = x429 && x416 = x430 && x420 = x434 && x421 = x435 && x422 = x436 l12(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453) -> l8(x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) :|: x453 = x467 && x452 = x466 && x451 = x465 && x450 = x464 && x449 = x463 && x448 = x462 && x447 = x461 && x446 = x460 && x445 = x459 && x444 = x458 && x443 = x457 && x442 = x456 && x441 = x455 && x440 = x454 Start term: l12(Result_4HAT0, __cil_tmp2_7HAT0, __disjvr_0HAT0, __retres1_6HAT0, b_128HAT0, b_51HAT0, b_76HAT0, count_5HAT0, lt_12HAT0, lt_13HAT0, tmp_11HAT0, x_8HAT0, y_9HAT0, z_10HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, __cil_tmp2_7HAT0, __disjvr_0HAT0, __retres1_6HAT0, b_128HAT0, b_51HAT0, b_76HAT0, count_5HAT0, lt_12HAT0, lt_13HAT0, tmp_11HAT0, x_8HAT0, y_9HAT0, z_10HAT0) -> l1(Result_4HATpost, __cil_tmp2_7HATpost, __disjvr_0HATpost, __retres1_6HATpost, b_128HATpost, b_51HATpost, b_76HATpost, count_5HATpost, lt_12HATpost, lt_13HATpost, tmp_11HATpost, x_8HATpost, y_9HATpost, z_10HATpost) :|: lt_13HAT1 = b_128HAT0 && 5 - lt_13HAT1 <= 0 && lt_13HATpost = lt_13HATpost && __retres1_6HATpost = 1 && __cil_tmp2_7HATpost = __retres1_6HATpost && Result_4HAT1 = __cil_tmp2_7HATpost && tmp_11HATpost = Result_4HAT1 && Result_4HATpost = Result_4HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && b_128HAT0 = b_128HATpost && b_51HAT0 = b_51HATpost && b_76HAT0 = b_76HATpost && count_5HAT0 = count_5HATpost && lt_12HAT0 = lt_12HATpost && x_8HAT0 = x_8HATpost && y_9HAT0 = y_9HATpost && z_10HAT0 = z_10HATpost l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> l2(x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27) :|: x28 = x4 && 0 <= 4 - x28 && x23 = x23 && x29 = x4 && x22 = x22 && x17 = 0 && x15 = x17 && x30 = x15 && x24 = x30 && x14 = x14 && x2 = x16 && x4 = x18 && x5 = x19 && x6 = x20 && x7 = x21 && x11 = x25 && x12 = x26 && x13 = x27 l3(x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58) :|: x44 = x58 && x43 = x57 && x42 = x56 && x41 = x55 && x40 = x54 && x39 = x53 && x38 = x52 && x37 = x51 && x36 = x50 && x35 = x49 && x34 = x48 && x33 = x47 && x32 = x46 && x45 = x45 && -1 * x42 + x43 <= 0 l3(x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72) -> l5(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86) :|: x72 = x86 && x71 = x85 && x70 = x84 && x69 = x83 && x68 = x82 && x67 = x81 && x66 = x80 && x65 = x79 && x64 = x78 && x63 = x77 && x62 = x76 && x61 = x75 && x60 = x74 && x59 = x73 && 0 <= -1 - x70 + x71 l2(x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l0(x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114) :|: x100 = x114 && x99 = x113 && x98 = x112 && x97 = x111 && x96 = x110 && x95 = x109 && x94 = x108 && x93 = x107 && x92 = x106 && x91 = x105 && x90 = x104 && x89 = x103 && x88 = x102 && x87 = x101 && 0 <= -1 - x99 + x100 && 0 <= x97 && x97 <= 0 l6(x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128) -> l2(x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) :|: 0 <= -1 - x127 + x128 && x143 = 0 && 0 <= 4 - x143 && x138 = x138 && x144 = 0 && x137 = x137 && x132 = 0 && x130 = x132 && x145 = x130 && x139 = x145 && x129 = x129 && x117 = x131 && x119 = x133 && x120 = x134 && x121 = x135 && x122 = x136 && x126 = x140 && x127 = x141 && x128 = x142 l6(x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l3(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173) :|: x159 = x173 && x158 = x172 && x156 = x170 && x155 = x169 && x154 = x168 && x153 = x167 && x152 = x166 && x151 = x165 && x150 = x164 && x149 = x163 && x148 = x162 && x147 = x161 && x146 = x160 && x171 = 1 + x157 && -1 * x158 + x159 <= 0 l1(x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187) -> l7(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201) :|: x187 = x201 && x186 = x200 && x185 = x199 && x184 = x198 && x183 = x197 && x182 = x196 && x181 = x195 && x180 = x194 && x179 = x193 && x178 = x192 && x177 = x191 && x176 = x190 && x175 = x189 && x174 = x188 && x190 = x176 l7(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) -> l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) :|: x215 = x229 && x213 = x227 && x212 = x226 && x211 = x225 && x210 = x224 && x209 = x223 && x208 = x222 && x207 = x221 && x206 = x220 && x205 = x219 && x204 = x218 && x203 = x217 && x202 = x216 && x228 = 1 + x214 l5(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) -> l2(x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257) :|: 0 <= -1 - x242 + x243 && x258 = 0 && 0 <= 4 - x258 && x253 = x253 && x259 = 0 && x252 = x252 && x247 = 0 && x245 = x247 && x260 = x245 && x254 = x260 && x244 = x244 && x232 = x246 && x234 = x248 && x235 = x249 && x236 = x250 && x237 = x251 && x241 = x255 && x242 = x256 && x243 = x257 l5(x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l3(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) :|: x274 = x288 && x273 = x287 && x271 = x285 && x270 = x284 && x269 = x283 && x268 = x282 && x267 = x281 && x266 = x280 && x265 = x279 && x264 = x278 && x263 = x277 && x262 = x276 && x261 = x275 && x286 = 1 + x272 && -1 * x273 + x274 <= 0 l8(x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302) -> l3(x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316) :|: x302 = x316 && x301 = x315 && x300 = x314 && x299 = x313 && x298 = x312 && x297 = x311 && x295 = x309 && x294 = x308 && x293 = x307 && x292 = x306 && x291 = x305 && x290 = x304 && x289 = x303 && x310 = x310 l9(x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330) -> l2(x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344) :|: x336 = -2 && x345 = -1 && 0 <= 4 - x345 && x340 = x340 && x346 = -1 && x339 = x339 && x334 = 0 && x332 = x334 && x347 = x332 && x341 = x347 && x331 = x331 && x319 = x333 && x321 = x335 && x323 = x337 && x324 = x338 && x328 = x342 && x329 = x343 && x330 = x344 l10(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361) -> l2(x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375) :|: x368 = -1 + x353 && x376 = x353 && 0 <= 4 - x376 && x371 = x371 && x377 = x353 && x370 = x370 && x365 = 0 && x363 = x365 && x378 = x363 && x372 = x378 && x362 = x362 && x350 = x364 && x352 = x366 && x353 = x367 && x355 = x369 && x359 = x373 && x360 = x374 && x361 = x375 l10(x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392) -> l1(x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) :|: x407 = x384 && 5 - x407 <= 0 && x402 = x402 && x396 = 1 && x394 = x396 && x408 = x394 && x403 = x408 && x393 = x393 && x381 = x395 && x383 = x397 && x384 = x398 && x385 = x399 && x386 = x400 && x387 = x401 && x390 = x404 && x391 = x405 && x392 = x406 l11(x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l2(x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436) :|: x427 = -2 && x437 = -1 && 0 <= 4 - x437 && x432 = x432 && x438 = -1 && x431 = x431 && x426 = 0 && x424 = x426 && x439 = x424 && x433 = x439 && x423 = x423 && x411 = x425 && x414 = x428 && x415 = x429 && x416 = x430 && x420 = x434 && x421 = x435 && x422 = x436 l12(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453) -> l8(x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) :|: x453 = x467 && x452 = x466 && x451 = x465 && x450 = x464 && x449 = x463 && x448 = x462 && x447 = x461 && x446 = x460 && x445 = x459 && x444 = x458 && x443 = x457 && x442 = x456 && x441 = x455 && x440 = x454 Start term: l12(Result_4HAT0, __cil_tmp2_7HAT0, __disjvr_0HAT0, __retres1_6HAT0, b_128HAT0, b_51HAT0, b_76HAT0, count_5HAT0, lt_12HAT0, lt_13HAT0, tmp_11HAT0, x_8HAT0, y_9HAT0, z_10HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __cil_tmp2_7HAT0, __disjvr_0HAT0, __retres1_6HAT0, b_128HAT0, b_51HAT0, b_76HAT0, count_5HAT0, lt_12HAT0, lt_13HAT0, tmp_11HAT0, x_8HAT0, y_9HAT0, z_10HAT0) -> l1(Result_4HATpost, __cil_tmp2_7HATpost, __disjvr_0HATpost, __retres1_6HATpost, b_128HATpost, b_51HATpost, b_76HATpost, count_5HATpost, lt_12HATpost, lt_13HATpost, tmp_11HATpost, x_8HATpost, y_9HATpost, z_10HATpost) :|: lt_13HAT1 = b_128HAT0 && 5 - lt_13HAT1 <= 0 && lt_13HATpost = lt_13HATpost && __retres1_6HATpost = 1 && __cil_tmp2_7HATpost = __retres1_6HATpost && Result_4HAT1 = __cil_tmp2_7HATpost && tmp_11HATpost = Result_4HAT1 && Result_4HATpost = Result_4HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && b_128HAT0 = b_128HATpost && b_51HAT0 = b_51HATpost && b_76HAT0 = b_76HATpost && count_5HAT0 = count_5HATpost && lt_12HAT0 = lt_12HATpost && x_8HAT0 = x_8HATpost && y_9HAT0 = y_9HATpost && z_10HAT0 = z_10HATpost (2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> l2(x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27) :|: x28 = x4 && 0 <= 4 - x28 && x23 = x23 && x29 = x4 && x22 = x22 && x17 = 0 && x15 = x17 && x30 = x15 && x24 = x30 && x14 = x14 && x2 = x16 && x4 = x18 && x5 = x19 && x6 = x20 && x7 = x21 && x11 = x25 && x12 = x26 && x13 = x27 (3) l3(x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58) :|: x44 = x58 && x43 = x57 && x42 = x56 && x41 = x55 && x40 = x54 && x39 = x53 && x38 = x52 && x37 = x51 && x36 = x50 && x35 = x49 && x34 = x48 && x33 = x47 && x32 = x46 && x45 = x45 && -1 * x42 + x43 <= 0 (4) l3(x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72) -> l5(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86) :|: x72 = x86 && x71 = x85 && x70 = x84 && x69 = x83 && x68 = x82 && x67 = x81 && x66 = x80 && x65 = x79 && x64 = x78 && x63 = x77 && x62 = x76 && x61 = x75 && x60 = x74 && x59 = x73 && 0 <= -1 - x70 + x71 (5) l2(x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l0(x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114) :|: x100 = x114 && x99 = x113 && x98 = x112 && x97 = x111 && x96 = x110 && x95 = x109 && x94 = x108 && x93 = x107 && x92 = x106 && x91 = x105 && x90 = x104 && x89 = x103 && x88 = x102 && x87 = x101 && 0 <= -1 - x99 + x100 && 0 <= x97 && x97 <= 0 (6) l6(x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128) -> l2(x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) :|: 0 <= -1 - x127 + x128 && x143 = 0 && 0 <= 4 - x143 && x138 = x138 && x144 = 0 && x137 = x137 && x132 = 0 && x130 = x132 && x145 = x130 && x139 = x145 && x129 = x129 && x117 = x131 && x119 = x133 && x120 = x134 && x121 = x135 && x122 = x136 && x126 = x140 && x127 = x141 && x128 = x142 (7) l6(x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l3(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173) :|: x159 = x173 && x158 = x172 && x156 = x170 && x155 = x169 && x154 = x168 && x153 = x167 && x152 = x166 && x151 = x165 && x150 = x164 && x149 = x163 && x148 = x162 && x147 = x161 && x146 = x160 && x171 = 1 + x157 && -1 * x158 + x159 <= 0 (8) l1(x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187) -> l7(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201) :|: x187 = x201 && x186 = x200 && x185 = x199 && x184 = x198 && x183 = x197 && x182 = x196 && x181 = x195 && x180 = x194 && x179 = x193 && x178 = x192 && x177 = x191 && x176 = x190 && x175 = x189 && x174 = x188 && x190 = x176 (9) l7(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) -> l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) :|: x215 = x229 && x213 = x227 && x212 = x226 && x211 = x225 && x210 = x224 && x209 = x223 && x208 = x222 && x207 = x221 && x206 = x220 && x205 = x219 && x204 = x218 && x203 = x217 && x202 = x216 && x228 = 1 + x214 (10) l5(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) -> l2(x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257) :|: 0 <= -1 - x242 + x243 && x258 = 0 && 0 <= 4 - x258 && x253 = x253 && x259 = 0 && x252 = x252 && x247 = 0 && x245 = x247 && x260 = x245 && x254 = x260 && x244 = x244 && x232 = x246 && x234 = x248 && x235 = x249 && x236 = x250 && x237 = x251 && x241 = x255 && x242 = x256 && x243 = x257 (11) l5(x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l3(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) :|: x274 = x288 && x273 = x287 && x271 = x285 && x270 = x284 && x269 = x283 && x268 = x282 && x267 = x281 && x266 = x280 && x265 = x279 && x264 = x278 && x263 = x277 && x262 = x276 && x261 = x275 && x286 = 1 + x272 && -1 * x273 + x274 <= 0 (12) l8(x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302) -> l3(x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316) :|: x302 = x316 && x301 = x315 && x300 = x314 && x299 = x313 && x298 = x312 && x297 = x311 && x295 = x309 && x294 = x308 && x293 = x307 && x292 = x306 && x291 = x305 && x290 = x304 && x289 = x303 && x310 = x310 (13) l9(x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330) -> l2(x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344) :|: x336 = -2 && x345 = -1 && 0 <= 4 - x345 && x340 = x340 && x346 = -1 && x339 = x339 && x334 = 0 && x332 = x334 && x347 = x332 && x341 = x347 && x331 = x331 && x319 = x333 && x321 = x335 && x323 = x337 && x324 = x338 && x328 = x342 && x329 = x343 && x330 = x344 (14) l10(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361) -> l2(x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375) :|: x368 = -1 + x353 && x376 = x353 && 0 <= 4 - x376 && x371 = x371 && x377 = x353 && x370 = x370 && x365 = 0 && x363 = x365 && x378 = x363 && x372 = x378 && x362 = x362 && x350 = x364 && x352 = x366 && x353 = x367 && x355 = x369 && x359 = x373 && x360 = x374 && x361 = x375 (15) l10(x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392) -> l1(x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) :|: x407 = x384 && 5 - x407 <= 0 && x402 = x402 && x396 = 1 && x394 = x396 && x408 = x394 && x403 = x408 && x393 = x393 && x381 = x395 && x383 = x397 && x384 = x398 && x385 = x399 && x386 = x400 && x387 = x401 && x390 = x404 && x391 = x405 && x392 = x406 (16) l11(x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l2(x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436) :|: x427 = -2 && x437 = -1 && 0 <= 4 - x437 && x432 = x432 && x438 = -1 && x431 = x431 && x426 = 0 && x424 = x426 && x439 = x424 && x433 = x439 && x423 = x423 && x411 = x425 && x414 = x428 && x415 = x429 && x416 = x430 && x420 = x434 && x421 = x435 && x422 = x436 (17) l12(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453) -> l8(x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) :|: x453 = x467 && x452 = x466 && x451 = x465 && x450 = x464 && x449 = x463 && x448 = x462 && x447 = x461 && x446 = x460 && x445 = x459 && x444 = x458 && x443 = x457 && x442 = x456 && x441 = x455 && x440 = x454 Arcs: (1) -> (8) (2) -> (5) (4) -> (10), (11) (5) -> (1), (2) (6) -> (5) (7) -> (3), (4) (8) -> (9) (9) -> (6), (7) (10) -> (5) (11) -> (3), (4) (12) -> (3), (4) (13) -> (5) (14) -> (5) (15) -> (8) (16) -> (5) (17) -> (12) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(Result_4HAT0, __cil_tmp2_7HAT0, __disjvr_0HAT0, __retres1_6HAT0, b_128HAT0, b_51HAT0, b_76HAT0, count_5HAT0, lt_12HAT0, lt_13HAT0, tmp_11HAT0, x_8HAT0, y_9HAT0, z_10HAT0) -> l1(Result_4HATpost, __cil_tmp2_7HATpost, __disjvr_0HATpost, __retres1_6HATpost, b_128HATpost, b_51HATpost, b_76HATpost, count_5HATpost, lt_12HATpost, lt_13HATpost, tmp_11HATpost, x_8HATpost, y_9HATpost, z_10HATpost) :|: lt_13HAT1 = b_128HAT0 && 5 - lt_13HAT1 <= 0 && lt_13HATpost = lt_13HATpost && __retres1_6HATpost = 1 && __cil_tmp2_7HATpost = __retres1_6HATpost && Result_4HAT1 = __cil_tmp2_7HATpost && tmp_11HATpost = Result_4HAT1 && Result_4HATpost = Result_4HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && b_128HAT0 = b_128HATpost && b_51HAT0 = b_51HATpost && b_76HAT0 = b_76HATpost && count_5HAT0 = count_5HATpost && lt_12HAT0 = lt_12HATpost && x_8HAT0 = x_8HATpost && y_9HAT0 = y_9HATpost && z_10HAT0 = z_10HATpost (2) l2(x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100) -> l0(x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114) :|: x100 = x114 && x99 = x113 && x98 = x112 && x97 = x111 && x96 = x110 && x95 = x109 && x94 = x108 && x93 = x107 && x92 = x106 && x91 = x105 && x90 = x104 && x89 = x103 && x88 = x102 && x87 = x101 && 0 <= -1 - x99 + x100 && 0 <= x97 && x97 <= 0 (3) l5(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) -> l2(x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257) :|: 0 <= -1 - x242 + x243 && x258 = 0 && 0 <= 4 - x258 && x253 = x253 && x259 = 0 && x252 = x252 && x247 = 0 && x245 = x247 && x260 = x245 && x254 = x260 && x244 = x244 && x232 = x246 && x234 = x248 && x235 = x249 && x236 = x250 && x237 = x251 && x241 = x255 && x242 = x256 && x243 = x257 (4) l3(x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72) -> l5(x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86) :|: x72 = x86 && x71 = x85 && x70 = x84 && x69 = x83 && x68 = x82 && x67 = x81 && x66 = x80 && x65 = x79 && x64 = x78 && x63 = x77 && x62 = x76 && x61 = x75 && x60 = x74 && x59 = x73 && 0 <= -1 - x70 + x71 (5) l5(x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l3(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288) :|: x274 = x288 && x273 = x287 && x271 = x285 && x270 = x284 && x269 = x283 && x268 = x282 && x267 = x281 && x266 = x280 && x265 = x279 && x264 = x278 && x263 = x277 && x262 = x276 && x261 = x275 && x286 = 1 + x272 && -1 * x273 + x274 <= 0 (6) l6(x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) -> l3(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173) :|: x159 = x173 && x158 = x172 && x156 = x170 && x155 = x169 && x154 = x168 && x153 = x167 && x152 = x166 && x151 = x165 && x150 = x164 && x149 = x163 && x148 = x162 && x147 = x161 && x146 = x160 && x171 = 1 + x157 && -1 * x158 + x159 <= 0 (7) l6(x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128) -> l2(x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142) :|: 0 <= -1 - x127 + x128 && x143 = 0 && 0 <= 4 - x143 && x138 = x138 && x144 = 0 && x137 = x137 && x132 = 0 && x130 = x132 && x145 = x130 && x139 = x145 && x129 = x129 && x117 = x131 && x119 = x133 && x120 = x134 && x121 = x135 && x122 = x136 && x126 = x140 && x127 = x141 && x128 = x142 (8) l7(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) -> l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) :|: x215 = x229 && x213 = x227 && x212 = x226 && x211 = x225 && x210 = x224 && x209 = x223 && x208 = x222 && x207 = x221 && x206 = x220 && x205 = x219 && x204 = x218 && x203 = x217 && x202 = x216 && x228 = 1 + x214 (9) l1(x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187) -> l7(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201) :|: x187 = x201 && x186 = x200 && x185 = x199 && x184 = x198 && x183 = x197 && x182 = x196 && x181 = x195 && x180 = x194 && x179 = x193 && x178 = x192 && x177 = x191 && x176 = x190 && x175 = x189 && x174 = x188 && x190 = x176 (10) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> l2(x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27) :|: x28 = x4 && 0 <= 4 - x28 && x23 = x23 && x29 = x4 && x22 = x22 && x17 = 0 && x15 = x17 && x30 = x15 && x24 = x30 && x14 = x14 && x2 = x16 && x4 = x18 && x5 = x19 && x6 = x20 && x7 = x21 && x11 = x25 && x12 = x26 && x13 = x27 Arcs: (1) -> (9) (2) -> (1), (10) (3) -> (2) (4) -> (3), (5) (5) -> (4) (6) -> (4) (7) -> (2) (8) -> (6), (7) (9) -> (8) (10) -> (2) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l3(x275:0, x276:0, x277:0, x278:0, x279:0, x280:0, x281:0, x282:0, x283:0, x284:0, x285:0, x70:0, x287:0, x288:0) -> l3(x275:0, x276:0, x277:0, x278:0, x279:0, x280:0, x281:0, x282:0, x283:0, x284:0, x285:0, 1 + x70:0, x287:0, x288:0) :|: 0 <= -1 - x70:0 + x287:0 && 0 >= -1 * x287:0 + x288:0 l2(x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x100:0) -> l2(x14:0, 0, x103:0, 0, x105:0, x106:0, x107:0, x108:0, x22:0, x23:0, 0, x112:0, x113:0, x100:0) :|: x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> l2(x14, 0, x2, 0, x4, x5, x6, x7, x15, x16, 0, x11, 1 + x12, x13) :|: x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4 l3(x59:0, x60:0, x246:0, x62:0, x248:0, x249:0, x250:0, x251:0, x67:0, x68:0, x69:0, x255:0, x256:0, x257:0) -> l2(x244:0, 0, x246:0, 0, x248:0, x249:0, x250:0, x251:0, x252:0, x253:0, 0, x255:0, x256:0, x257:0) :|: 0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0 l2(x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30) -> l3(x31, 1, x19, 1, x21, x22, x23, x24, x25, x32, 1, 1 + x28, 1 + x29, x30) :|: 0 >= -1 * (1 + x29) + x30 && x27 < 1 && x27 > -1 && x21 > 4 && 0 <= -1 - x29 + x30 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l3(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l3(x5, x12, x13, x14) l2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l2(x5, x11, x12, x13, x14) ---------------------------------------- (8) Obligation: Rules: l3(x279:0, x70:0, x287:0, x288:0) -> l3(x279:0, 1 + x70:0, x287:0, x288:0) :|: 0 <= -1 - x70:0 + x287:0 && 0 >= -1 * x287:0 + x288:0 l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, 0, x112:0, x113:0, x100:0) :|: x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0 l2(x4, x10, x11, x12, x13) -> l2(x4, 0, x11, 1 + x12, x13) :|: x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4 l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, 0, x255:0, x256:0, x257:0) :|: 0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0 l2(x21, x27, x28, x29, x30) -> l3(x21, 1 + x28, 1 + x29, x30) :|: 0 >= -1 * (1 + x29) + x30 && x27 < 1 && x27 > -1 && x21 > 4 && 0 <= -1 - x29 + x30 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l3(VARIABLE, INTEGER, INTEGER, INTEGER) l2(VARIABLE, VARIABLE, VARIABLE, INTEGER, 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: l3(x279:0, x70:0, x287:0, x288:0) -> l3(x279:0, c, x287:0, x288:0) :|: c = 1 + x70:0 && (0 <= -1 - x70:0 + x287:0 && 0 >= -1 * x287:0 + x288:0) l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) l2(x4, x10, x11, x12, x13) -> l2(x4, c2, x11, c3, x13) :|: c3 = 1 + x12 && c2 = 0 && (x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4) l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) l2(x21, x27, x28, x29, x30) -> l3(x21, c5, c6, x30) :|: c6 = 1 + x29 && c5 = 1 + x28 && (0 >= -1 * (1 + x29) + x30 && x27 < 1 && x27 > -1 && x21 > 4 && 0 <= -1 - x29 + x30) Found the following polynomial interpretation: [l3(x, x1, x2, x3)] = -6 + x - x2 + x3 [l2(x4, x5, x6, x7, x8)] = -5 + x4 + c5*x5 The following rules are decreasing: l2(x21, x27, x28, x29, x30) -> l3(x21, c5, c6, x30) :|: c6 = 1 + x29 && c5 = 1 + x28 && (0 >= -1 * (1 + x29) + x30 && x27 < 1 && x27 > -1 && x21 > 4 && 0 <= -1 - x29 + x30) The following rules are bounded: l2(x4, x10, x11, x12, x13) -> l2(x4, c2, x11, c3, x13) :|: c3 = 1 + x12 && c2 = 0 && (x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4) l2(x21, x27, x28, x29, x30) -> l3(x21, c5, c6, x30) :|: c6 = 1 + x29 && c5 = 1 + x28 && (0 >= -1 * (1 + x29) + x30 && x27 < 1 && x27 > -1 && x21 > 4 && 0 <= -1 - x29 + x30) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l3(x279:0, x70:0, x287:0, x288:0) -> l3(x279:0, c, x287:0, x288:0) :|: c = 1 + x70:0 && (0 <= -1 - x70:0 + x287:0 && 0 >= -1 * x287:0 + x288:0) l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) l2(x4, x10, x11, x12, x13) -> l2(x4, c2, x11, c3, x13) :|: c3 = 1 + x12 && c2 = 0 && (x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4) l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) Found the following polynomial interpretation: [l3(x, x1, x2, x3)] = -x1 + x2 [l2(x4, x5, x6, x7, x8)] = 1 + c5*x5 The following rules are decreasing: l3(x279:0, x70:0, x287:0, x288:0) -> l3(x279:0, c, x287:0, x288:0) :|: c = 1 + x70:0 && (0 <= -1 - x70:0 + x287:0 && 0 >= -1 * x287:0 + x288:0) The following rules are bounded: l3(x279:0, x70:0, x287:0, x288:0) -> l3(x279:0, c, x287:0, x288:0) :|: c = 1 + x70:0 && (0 <= -1 - x70:0 + x287:0 && 0 >= -1 * x287:0 + x288:0) l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) l2(x4, x10, x11, x12, x13) -> l2(x4, c2, x11, c3, x13) :|: c3 = 1 + x12 && c2 = 0 && (x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4) l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) l2(x4, x10, x11, x12, x13) -> l2(x4, c2, x11, c3, x13) :|: c3 = 1 + x12 && c2 = 0 && (x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4) l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) Found the following polynomial interpretation: [l2(x, x1, x2, x3, x4)] = c1*x1 - x3 + x4 [l3(x5, x6, x7, x8)] = -x7 + x8 The following rules are decreasing: l2(x4, x10, x11, x12, x13) -> l2(x4, c2, x11, c3, x13) :|: c3 = 1 + x12 && c2 = 0 && (x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4) The following rules are bounded: l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) l2(x4, x10, x11, x12, x13) -> l2(x4, c2, x11, c3, x13) :|: c3 = 1 + x12 && c2 = 0 && (x10 > -1 && x10 < 1 && 0 <= -1 - x12 + x13 && 0 <= -1 - (1 + x12) + x13 && x4 > 4) l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof Rules: l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) Interpretation: [ l2 ] = 0 [ l3 ] = 1 The following rules are decreasing: l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) The following rules are bounded: l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) l3(x248:0, x255:0, x256:0, x257:0) -> l2(x248:0, c4, x255:0, x256:0, x257:0) :|: c4 = 0 && (0 <= -1 - x255:0 + x256:0 && 0 <= -1 - x256:0 + x257:0) - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof - IntTRS Rules: l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, c1, x112:0, x113:0, x100:0) :|: c1 = 0 && (x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0) ---------------------------------------- (10) Obligation: Rules: l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, 0, x112:0, x113:0, x100:0) :|: x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, 0, x112:0, x113:0, x100:0) :|: x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l2(x105:0, x111:0, x112:0, x113:0, x100:0) -> l2(x105:0, 0, x112:0, x113:0, x100:0) :|: x111:0 > -1 && x111:0 < 1 && x105:0 < 5 && 0 <= -1 - x113:0 + x100:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l2(x105:0:0, x111:0:0, x112:0:0, x113:0:0, x100:0:0) -> l2(x105:0:0, 0, x112:0:0, x113:0:0, x100:0:0) :|: x105:0:0 < 5 && 0 <= -1 - x113:0:0 + x100:0:0 && x111:0:0 < 1 && x111:0:0 > -1 ---------------------------------------- (15) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l2(x1, x2, x3, x4, x5) -> l2(x1, x2, x4, x5) ---------------------------------------- (16) Obligation: Rules: l2(x105:0:0, x111:0:0, x113:0:0, x100:0:0) -> l2(x105:0:0, 0, x113:0:0, x100:0:0) :|: x105:0:0 < 5 && 0 <= -1 - x113:0:0 + x100:0:0 && x111:0:0 < 1 && x111:0:0 > -1