MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 14.1 s] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 68 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 933 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 1 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, ___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, ___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 && 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) -> l2(x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) :|: x26 = x3 && 0 <= 4 - x26 && x21 = x21 && x27 = x3 && x20 = x20 && x15 = 0 && x14 = x15 && x28 = x14 && x22 = x28 && x13 = x13 && x3 = x16 && x4 = x17 && x5 = x18 && x6 = x19 && x10 = x23 && x11 = x24 && x12 = x25 l3(x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x41 = x54 && x40 = x53 && x39 = x52 && x38 = x51 && x37 = x50 && x36 = x49 && x35 = x48 && x34 = x47 && x33 = x46 && x32 = x45 && x31 = x44 && x30 = x43 && x42 = x42 && -1 * x39 + x40 <= 0 l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) -> l5(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: x67 = x80 && x66 = x79 && x65 = x78 && x64 = x77 && x63 = x76 && x62 = x75 && x61 = x74 && x60 = x73 && x59 = x72 && x58 = x71 && x57 = x70 && x56 = x69 && x55 = x68 && 0 <= -1 - x65 + x66 l2(x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93) -> l0(x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106) :|: x93 = x106 && x92 = x105 && x91 = x104 && x90 = x103 && x89 = x102 && x88 = x101 && x87 = x100 && x86 = x99 && x85 = x98 && x84 = x97 && x83 = x96 && x82 = x95 && x81 = x94 && 0 <= -1 - x92 + x93 && 0 <= x90 && x90 <= 0 l6(x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) -> l2(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132) :|: 0 <= -1 - x118 + x119 && x133 = 0 && 0 <= 4 - x133 && x128 = x128 && x134 = 0 && x127 = x127 && x122 = 0 && x121 = x122 && x135 = x121 && x129 = x135 && x120 = x120 && x110 = x123 && x111 = x124 && x112 = x125 && x113 = x126 && x117 = x130 && x118 = x131 && x119 = x132 l6(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) -> l3(x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x148 = x161 && x147 = x160 && x145 = x158 && x144 = x157 && x143 = x156 && x142 = x155 && x141 = x154 && x140 = x153 && x139 = x152 && x138 = x151 && x137 = x150 && x136 = x149 && x159 = 1 + x146 && -1 * x147 + x148 <= 0 l1(x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174) -> l7(x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187) :|: x174 = x187 && x173 = x186 && x172 = x185 && x171 = x184 && x170 = x183 && x169 = x182 && x168 = x181 && x167 = x180 && x166 = x179 && x165 = x178 && x164 = x177 && x163 = x176 && x162 = x175 && 1 + x171 <= 0 l1(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200) -> l7(x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213) :|: x200 = x213 && x199 = x212 && x198 = x211 && x197 = x210 && x196 = x209 && x195 = x208 && x194 = x207 && x193 = x206 && x192 = x205 && x191 = x204 && x190 = x203 && x189 = x202 && x188 = x201 && 1 <= x197 l7(x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226) -> l6(x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x226 = x239 && x224 = x237 && x223 = x236 && x222 = x235 && x221 = x234 && x220 = x233 && x219 = x232 && x218 = x231 && x217 = x230 && x216 = x229 && x215 = x228 && x214 = x227 && x238 = 1 + x225 l5(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l2(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265) :|: 0 <= -1 - x251 + x252 && x266 = 0 && 0 <= 4 - x266 && x261 = x261 && x267 = 0 && x260 = x260 && x255 = 0 && x254 = x255 && x268 = x254 && x262 = x268 && x253 = x253 && x243 = x256 && x244 = x257 && x245 = x258 && x246 = x259 && x250 = x263 && x251 = x264 && x252 = x265 l5(x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281) -> l3(x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294) :|: x281 = x294 && x280 = x293 && x278 = x291 && x277 = x290 && x276 = x289 && x275 = x288 && x274 = x287 && x273 = x286 && x272 = x285 && x271 = x284 && x270 = x283 && x269 = x282 && x292 = 1 + x279 && -1 * x280 + x281 <= 0 l8(x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) -> l3(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320) :|: x307 = x320 && x306 = x319 && x305 = x318 && x304 = x317 && x303 = x316 && x302 = x315 && x300 = x313 && x299 = x312 && x298 = x311 && x297 = x310 && x296 = x309 && x295 = x308 && x314 = x314 l9(x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333) -> l2(x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346) :|: x338 = 2 && x347 = 1 && 0 <= 4 - x347 && x342 = x342 && x348 = 1 && x341 = x341 && x336 = 0 && x335 = x336 && x349 = x335 && x343 = x349 && x334 = x334 && x324 = x337 && x326 = x339 && x327 = x340 && x331 = x344 && x332 = x345 && x333 = x346 l10(x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l2(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375) :|: x368 = 1 + x354 && x376 = x354 && 0 <= 4 - x376 && x371 = x371 && x377 = x354 && x370 = x370 && x365 = 0 && x364 = x365 && x378 = x364 && x372 = x378 && x363 = x363 && x353 = x366 && x354 = x367 && x356 = x369 && x360 = x373 && x361 = x374 && x362 = x375 l10(x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391) -> l1(x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404) :|: x405 = x383 && 5 - x405 <= 0 && x400 = x400 && x394 = 1 && x393 = x394 && x406 = x393 && x401 = x406 && x392 = x392 && x382 = x395 && x383 = x396 && x384 = x397 && x385 = x398 && x386 = x399 && x389 = x402 && x390 = x403 && x391 = x404 l11(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l2(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432) :|: x423 = 2 && x433 = 1 && 0 <= 4 - x433 && x428 = x428 && x434 = 1 && x427 = x427 && x422 = 0 && x421 = x422 && x435 = x421 && x429 = x435 && x420 = x420 && x411 = x424 && x412 = x425 && x413 = x426 && x417 = x430 && x418 = x431 && x419 = x432 l12(x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448) -> l8(x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x448 = x461 && x447 = x460 && x446 = x459 && x445 = x458 && x444 = x457 && x443 = x456 && x442 = x455 && x441 = x454 && x440 = x453 && x439 = x452 && x438 = x451 && x437 = x450 && x436 = x449 Start term: l12(Result_4HAT0, ___cil_tmp2_7HAT0, ___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, ___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, ___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 && 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) -> l2(x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) :|: x26 = x3 && 0 <= 4 - x26 && x21 = x21 && x27 = x3 && x20 = x20 && x15 = 0 && x14 = x15 && x28 = x14 && x22 = x28 && x13 = x13 && x3 = x16 && x4 = x17 && x5 = x18 && x6 = x19 && x10 = x23 && x11 = x24 && x12 = x25 l3(x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x41 = x54 && x40 = x53 && x39 = x52 && x38 = x51 && x37 = x50 && x36 = x49 && x35 = x48 && x34 = x47 && x33 = x46 && x32 = x45 && x31 = x44 && x30 = x43 && x42 = x42 && -1 * x39 + x40 <= 0 l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) -> l5(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: x67 = x80 && x66 = x79 && x65 = x78 && x64 = x77 && x63 = x76 && x62 = x75 && x61 = x74 && x60 = x73 && x59 = x72 && x58 = x71 && x57 = x70 && x56 = x69 && x55 = x68 && 0 <= -1 - x65 + x66 l2(x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93) -> l0(x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106) :|: x93 = x106 && x92 = x105 && x91 = x104 && x90 = x103 && x89 = x102 && x88 = x101 && x87 = x100 && x86 = x99 && x85 = x98 && x84 = x97 && x83 = x96 && x82 = x95 && x81 = x94 && 0 <= -1 - x92 + x93 && 0 <= x90 && x90 <= 0 l6(x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) -> l2(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132) :|: 0 <= -1 - x118 + x119 && x133 = 0 && 0 <= 4 - x133 && x128 = x128 && x134 = 0 && x127 = x127 && x122 = 0 && x121 = x122 && x135 = x121 && x129 = x135 && x120 = x120 && x110 = x123 && x111 = x124 && x112 = x125 && x113 = x126 && x117 = x130 && x118 = x131 && x119 = x132 l6(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) -> l3(x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x148 = x161 && x147 = x160 && x145 = x158 && x144 = x157 && x143 = x156 && x142 = x155 && x141 = x154 && x140 = x153 && x139 = x152 && x138 = x151 && x137 = x150 && x136 = x149 && x159 = 1 + x146 && -1 * x147 + x148 <= 0 l1(x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174) -> l7(x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187) :|: x174 = x187 && x173 = x186 && x172 = x185 && x171 = x184 && x170 = x183 && x169 = x182 && x168 = x181 && x167 = x180 && x166 = x179 && x165 = x178 && x164 = x177 && x163 = x176 && x162 = x175 && 1 + x171 <= 0 l1(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200) -> l7(x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213) :|: x200 = x213 && x199 = x212 && x198 = x211 && x197 = x210 && x196 = x209 && x195 = x208 && x194 = x207 && x193 = x206 && x192 = x205 && x191 = x204 && x190 = x203 && x189 = x202 && x188 = x201 && 1 <= x197 l7(x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226) -> l6(x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x226 = x239 && x224 = x237 && x223 = x236 && x222 = x235 && x221 = x234 && x220 = x233 && x219 = x232 && x218 = x231 && x217 = x230 && x216 = x229 && x215 = x228 && x214 = x227 && x238 = 1 + x225 l5(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l2(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265) :|: 0 <= -1 - x251 + x252 && x266 = 0 && 0 <= 4 - x266 && x261 = x261 && x267 = 0 && x260 = x260 && x255 = 0 && x254 = x255 && x268 = x254 && x262 = x268 && x253 = x253 && x243 = x256 && x244 = x257 && x245 = x258 && x246 = x259 && x250 = x263 && x251 = x264 && x252 = x265 l5(x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281) -> l3(x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294) :|: x281 = x294 && x280 = x293 && x278 = x291 && x277 = x290 && x276 = x289 && x275 = x288 && x274 = x287 && x273 = x286 && x272 = x285 && x271 = x284 && x270 = x283 && x269 = x282 && x292 = 1 + x279 && -1 * x280 + x281 <= 0 l8(x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) -> l3(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320) :|: x307 = x320 && x306 = x319 && x305 = x318 && x304 = x317 && x303 = x316 && x302 = x315 && x300 = x313 && x299 = x312 && x298 = x311 && x297 = x310 && x296 = x309 && x295 = x308 && x314 = x314 l9(x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333) -> l2(x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346) :|: x338 = 2 && x347 = 1 && 0 <= 4 - x347 && x342 = x342 && x348 = 1 && x341 = x341 && x336 = 0 && x335 = x336 && x349 = x335 && x343 = x349 && x334 = x334 && x324 = x337 && x326 = x339 && x327 = x340 && x331 = x344 && x332 = x345 && x333 = x346 l10(x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l2(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375) :|: x368 = 1 + x354 && x376 = x354 && 0 <= 4 - x376 && x371 = x371 && x377 = x354 && x370 = x370 && x365 = 0 && x364 = x365 && x378 = x364 && x372 = x378 && x363 = x363 && x353 = x366 && x354 = x367 && x356 = x369 && x360 = x373 && x361 = x374 && x362 = x375 l10(x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391) -> l1(x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404) :|: x405 = x383 && 5 - x405 <= 0 && x400 = x400 && x394 = 1 && x393 = x394 && x406 = x393 && x401 = x406 && x392 = x392 && x382 = x395 && x383 = x396 && x384 = x397 && x385 = x398 && x386 = x399 && x389 = x402 && x390 = x403 && x391 = x404 l11(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l2(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432) :|: x423 = 2 && x433 = 1 && 0 <= 4 - x433 && x428 = x428 && x434 = 1 && x427 = x427 && x422 = 0 && x421 = x422 && x435 = x421 && x429 = x435 && x420 = x420 && x411 = x424 && x412 = x425 && x413 = x426 && x417 = x430 && x418 = x431 && x419 = x432 l12(x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448) -> l8(x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x448 = x461 && x447 = x460 && x446 = x459 && x445 = x458 && x444 = x457 && x443 = x456 && x442 = x455 && x441 = x454 && x440 = x453 && x439 = x452 && x438 = x451 && x437 = x450 && x436 = x449 Start term: l12(Result_4HAT0, ___cil_tmp2_7HAT0, ___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, ___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, ___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 && 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) -> l2(x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) :|: x26 = x3 && 0 <= 4 - x26 && x21 = x21 && x27 = x3 && x20 = x20 && x15 = 0 && x14 = x15 && x28 = x14 && x22 = x28 && x13 = x13 && x3 = x16 && x4 = x17 && x5 = x18 && x6 = x19 && x10 = x23 && x11 = x24 && x12 = x25 (3) l3(x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41) -> l4(x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54) :|: x41 = x54 && x40 = x53 && x39 = x52 && x38 = x51 && x37 = x50 && x36 = x49 && x35 = x48 && x34 = x47 && x33 = x46 && x32 = x45 && x31 = x44 && x30 = x43 && x42 = x42 && -1 * x39 + x40 <= 0 (4) l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) -> l5(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: x67 = x80 && x66 = x79 && x65 = x78 && x64 = x77 && x63 = x76 && x62 = x75 && x61 = x74 && x60 = x73 && x59 = x72 && x58 = x71 && x57 = x70 && x56 = x69 && x55 = x68 && 0 <= -1 - x65 + x66 (5) l2(x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93) -> l0(x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106) :|: x93 = x106 && x92 = x105 && x91 = x104 && x90 = x103 && x89 = x102 && x88 = x101 && x87 = x100 && x86 = x99 && x85 = x98 && x84 = x97 && x83 = x96 && x82 = x95 && x81 = x94 && 0 <= -1 - x92 + x93 && 0 <= x90 && x90 <= 0 (6) l6(x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) -> l2(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132) :|: 0 <= -1 - x118 + x119 && x133 = 0 && 0 <= 4 - x133 && x128 = x128 && x134 = 0 && x127 = x127 && x122 = 0 && x121 = x122 && x135 = x121 && x129 = x135 && x120 = x120 && x110 = x123 && x111 = x124 && x112 = x125 && x113 = x126 && x117 = x130 && x118 = x131 && x119 = x132 (7) l6(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) -> l3(x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x148 = x161 && x147 = x160 && x145 = x158 && x144 = x157 && x143 = x156 && x142 = x155 && x141 = x154 && x140 = x153 && x139 = x152 && x138 = x151 && x137 = x150 && x136 = x149 && x159 = 1 + x146 && -1 * x147 + x148 <= 0 (8) l1(x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174) -> l7(x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187) :|: x174 = x187 && x173 = x186 && x172 = x185 && x171 = x184 && x170 = x183 && x169 = x182 && x168 = x181 && x167 = x180 && x166 = x179 && x165 = x178 && x164 = x177 && x163 = x176 && x162 = x175 && 1 + x171 <= 0 (9) l1(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200) -> l7(x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213) :|: x200 = x213 && x199 = x212 && x198 = x211 && x197 = x210 && x196 = x209 && x195 = x208 && x194 = x207 && x193 = x206 && x192 = x205 && x191 = x204 && x190 = x203 && x189 = x202 && x188 = x201 && 1 <= x197 (10) l7(x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226) -> l6(x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x226 = x239 && x224 = x237 && x223 = x236 && x222 = x235 && x221 = x234 && x220 = x233 && x219 = x232 && x218 = x231 && x217 = x230 && x216 = x229 && x215 = x228 && x214 = x227 && x238 = 1 + x225 (11) l5(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l2(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265) :|: 0 <= -1 - x251 + x252 && x266 = 0 && 0 <= 4 - x266 && x261 = x261 && x267 = 0 && x260 = x260 && x255 = 0 && x254 = x255 && x268 = x254 && x262 = x268 && x253 = x253 && x243 = x256 && x244 = x257 && x245 = x258 && x246 = x259 && x250 = x263 && x251 = x264 && x252 = x265 (12) l5(x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281) -> l3(x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294) :|: x281 = x294 && x280 = x293 && x278 = x291 && x277 = x290 && x276 = x289 && x275 = x288 && x274 = x287 && x273 = x286 && x272 = x285 && x271 = x284 && x270 = x283 && x269 = x282 && x292 = 1 + x279 && -1 * x280 + x281 <= 0 (13) l8(x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) -> l3(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320) :|: x307 = x320 && x306 = x319 && x305 = x318 && x304 = x317 && x303 = x316 && x302 = x315 && x300 = x313 && x299 = x312 && x298 = x311 && x297 = x310 && x296 = x309 && x295 = x308 && x314 = x314 (14) l9(x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333) -> l2(x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346) :|: x338 = 2 && x347 = 1 && 0 <= 4 - x347 && x342 = x342 && x348 = 1 && x341 = x341 && x336 = 0 && x335 = x336 && x349 = x335 && x343 = x349 && x334 = x334 && x324 = x337 && x326 = x339 && x327 = x340 && x331 = x344 && x332 = x345 && x333 = x346 (15) l10(x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) -> l2(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375) :|: x368 = 1 + x354 && x376 = x354 && 0 <= 4 - x376 && x371 = x371 && x377 = x354 && x370 = x370 && x365 = 0 && x364 = x365 && x378 = x364 && x372 = x378 && x363 = x363 && x353 = x366 && x354 = x367 && x356 = x369 && x360 = x373 && x361 = x374 && x362 = x375 (16) l10(x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391) -> l1(x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404) :|: x405 = x383 && 5 - x405 <= 0 && x400 = x400 && x394 = 1 && x393 = x394 && x406 = x393 && x401 = x406 && x392 = x392 && x382 = x395 && x383 = x396 && x384 = x397 && x385 = x398 && x386 = x399 && x389 = x402 && x390 = x403 && x391 = x404 (17) l11(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l2(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432) :|: x423 = 2 && x433 = 1 && 0 <= 4 - x433 && x428 = x428 && x434 = 1 && x427 = x427 && x422 = 0 && x421 = x422 && x435 = x421 && x429 = x435 && x420 = x420 && x411 = x424 && x412 = x425 && x413 = x426 && x417 = x430 && x418 = x431 && x419 = x432 (18) l12(x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448) -> l8(x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x448 = x461 && x447 = x460 && x446 = x459 && x445 = x458 && x444 = x457 && x443 = x456 && x442 = x455 && x441 = x454 && x440 = x453 && x439 = x452 && x438 = x451 && x437 = x450 && x436 = x449 Arcs: (1) -> (9) (2) -> (5) (4) -> (11), (12) (5) -> (1), (2) (6) -> (5) (7) -> (3), (4) (8) -> (10) (9) -> (10) (10) -> (6), (7) (11) -> (5) (12) -> (3), (4) (13) -> (3), (4) (14) -> (5) (15) -> (5) (16) -> (9) (17) -> (5) (18) -> (13) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(Result_4HAT0, ___cil_tmp2_7HAT0, ___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, ___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 && 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(x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93) -> l0(x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106) :|: x93 = x106 && x92 = x105 && x91 = x104 && x90 = x103 && x89 = x102 && x88 = x101 && x87 = x100 && x86 = x99 && x85 = x98 && x84 = x97 && x83 = x96 && x82 = x95 && x81 = x94 && 0 <= -1 - x92 + x93 && 0 <= x90 && x90 <= 0 (3) l5(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l2(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265) :|: 0 <= -1 - x251 + x252 && x266 = 0 && 0 <= 4 - x266 && x261 = x261 && x267 = 0 && x260 = x260 && x255 = 0 && x254 = x255 && x268 = x254 && x262 = x268 && x253 = x253 && x243 = x256 && x244 = x257 && x245 = x258 && x246 = x259 && x250 = x263 && x251 = x264 && x252 = x265 (4) l3(x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67) -> l5(x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80) :|: x67 = x80 && x66 = x79 && x65 = x78 && x64 = x77 && x63 = x76 && x62 = x75 && x61 = x74 && x60 = x73 && x59 = x72 && x58 = x71 && x57 = x70 && x56 = x69 && x55 = x68 && 0 <= -1 - x65 + x66 (5) l5(x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281) -> l3(x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294) :|: x281 = x294 && x280 = x293 && x278 = x291 && x277 = x290 && x276 = x289 && x275 = x288 && x274 = x287 && x273 = x286 && x272 = x285 && x271 = x284 && x270 = x283 && x269 = x282 && x292 = 1 + x279 && -1 * x280 + x281 <= 0 (6) l6(x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148) -> l3(x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x148 = x161 && x147 = x160 && x145 = x158 && x144 = x157 && x143 = x156 && x142 = x155 && x141 = x154 && x140 = x153 && x139 = x152 && x138 = x151 && x137 = x150 && x136 = x149 && x159 = 1 + x146 && -1 * x147 + x148 <= 0 (7) l6(x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) -> l2(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132) :|: 0 <= -1 - x118 + x119 && x133 = 0 && 0 <= 4 - x133 && x128 = x128 && x134 = 0 && x127 = x127 && x122 = 0 && x121 = x122 && x135 = x121 && x129 = x135 && x120 = x120 && x110 = x123 && x111 = x124 && x112 = x125 && x113 = x126 && x117 = x130 && x118 = x131 && x119 = x132 (8) l7(x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226) -> l6(x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x226 = x239 && x224 = x237 && x223 = x236 && x222 = x235 && x221 = x234 && x220 = x233 && x219 = x232 && x218 = x231 && x217 = x230 && x216 = x229 && x215 = x228 && x214 = x227 && x238 = 1 + x225 (9) l1(x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200) -> l7(x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213) :|: x200 = x213 && x199 = x212 && x198 = x211 && x197 = x210 && x196 = x209 && x195 = x208 && x194 = x207 && x193 = x206 && x192 = x205 && x191 = x204 && x190 = x203 && x189 = x202 && x188 = x201 && 1 <= x197 (10) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> l2(x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) :|: x26 = x3 && 0 <= 4 - x26 && x21 = x21 && x27 = x3 && x20 = x20 && x15 = 0 && x14 = x15 && x28 = x14 && x22 = x28 && x13 = x13 && x3 = x16 && x4 = x17 && x5 = x18 && x6 = x19 && x10 = x23 && x11 = x24 && x12 = x25 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(x55:0, x56:0, x57:0, x256:0, x257:0, x258:0, x259:0, x62:0, x63:0, x64:0, x263:0, x264:0, x265:0) -> l2(x253:0, 0, 0, x256:0, x257:0, x258:0, x259:0, x260:0, x261:0, 0, x263:0, x264:0, x265:0) :|: 0 <= -1 - x263:0 + x264:0 && 0 <= -1 - x264:0 + x265:0 l2(x81:0, x82:0, x83:0, x16:0, x17:0, x18:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0) -> l2(x13:0, 0, 0, x16:0, x17:0, x18:0, x100:0, x20:0, x21:0, 0, x104:0, x105:0, x106:0) :|: x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> l3(x13, 1, 1, x3, x4, x5, x6, x7, x14, 1, 1 + x10, 1 + x11, x12) :|: 0 >= -1 * (1 + x11) + x12 && x9 < 1 && x9 > -1 && x3 > 4 && 0 <= -1 - x11 + x12 l3(x282:0, x283:0, x284:0, x285:0, x286:0, x287:0, x288:0, x289:0, x290:0, x291:0, x65:0, x293:0, x294:0) -> l3(x282:0, x283:0, x284:0, x285:0, x286:0, x287:0, x288:0, x289:0, x290:0, x291:0, 1 + x65:0, x293:0, x294:0) :|: 0 <= -1 - x65:0 + x293:0 && 0 >= -1 * x293:0 + x294:0 l2(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27) -> l2(x28, 0, 0, x18, x19, x20, x21, x29, x30, 0, x25, 1 + x26, x27) :|: x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4 ---------------------------------------- (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) -> l3(x4, x11, x12, x13) l2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> l2(x4, x10, x11, x12, x13) ---------------------------------------- (8) Obligation: Rules: l3(x256:0, x263:0, x264:0, x265:0) -> l2(x256:0, 0, x263:0, x264:0, x265:0) :|: 0 <= -1 - x263:0 + x264:0 && 0 <= -1 - x264:0 + x265:0 l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, 0, x104:0, x105:0, x106:0) :|: x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0 l2(x3, x9, x10, x11, x12) -> l3(x3, 1 + x10, 1 + x11, x12) :|: 0 >= -1 * (1 + x11) + x12 && x9 < 1 && x9 > -1 && x3 > 4 && 0 <= -1 - x11 + x12 l3(x285:0, x65:0, x293:0, x294:0) -> l3(x285:0, 1 + x65:0, x293:0, x294:0) :|: 0 <= -1 - x65:0 + x293:0 && 0 >= -1 * x293:0 + x294:0 l2(x18, x24, x25, x26, x27) -> l2(x18, 0, x25, 1 + x26, x27) :|: x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4 ---------------------------------------- (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(x256:0, x263:0, x264:0, x265:0) -> l2(x256:0, c, x263:0, x264:0, x265:0) :|: c = 0 && (0 <= -1 - x263:0 + x264:0 && 0 <= -1 - x264:0 + x265:0) l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, c1, x104:0, x105:0, x106:0) :|: c1 = 0 && (x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0) l2(x3, x9, x10, x11, x12) -> l3(x3, c2, c3, x12) :|: c3 = 1 + x11 && c2 = 1 + x10 && (0 >= -1 * (1 + x11) + x12 && x9 < 1 && x9 > -1 && x3 > 4 && 0 <= -1 - x11 + x12) l3(x285:0, x65:0, x293:0, x294:0) -> l3(x285:0, c4, x293:0, x294:0) :|: c4 = 1 + x65:0 && (0 <= -1 - x65:0 + x293:0 && 0 >= -1 * x293:0 + x294:0) l2(x18, x24, x25, x26, x27) -> l2(x18, c5, x25, c6, x27) :|: c6 = 1 + x26 && c5 = 0 && (x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4) 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(x3, x9, x10, x11, x12) -> l3(x3, c2, c3, x12) :|: c3 = 1 + x11 && c2 = 1 + x10 && (0 >= -1 * (1 + x11) + x12 && x9 < 1 && x9 > -1 && x3 > 4 && 0 <= -1 - x11 + x12) The following rules are bounded: l2(x3, x9, x10, x11, x12) -> l3(x3, c2, c3, x12) :|: c3 = 1 + x11 && c2 = 1 + x10 && (0 >= -1 * (1 + x11) + x12 && x9 < 1 && x9 > -1 && x3 > 4 && 0 <= -1 - x11 + x12) l2(x18, x24, x25, x26, x27) -> l2(x18, c5, x25, c6, x27) :|: c6 = 1 + x26 && c5 = 0 && (x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4) - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof Rules: l3(x256:0, x263:0, x264:0, x265:0) -> l2(x256:0, c, x263:0, x264:0, x265:0) :|: c = 0 && (0 <= -1 - x263:0 + x264:0 && 0 <= -1 - x264:0 + x265:0) l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, c1, x104:0, x105:0, x106:0) :|: c1 = 0 && (x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0) l3(x285:0, x65:0, x293:0, x294:0) -> l3(x285:0, c4, x293:0, x294:0) :|: c4 = 1 + x65:0 && (0 <= -1 - x65:0 + x293:0 && 0 >= -1 * x293:0 + x294:0) l2(x18, x24, x25, x26, x27) -> l2(x18, c5, x25, c6, x27) :|: c6 = 1 + x26 && c5 = 0 && (x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4) Interpretation: [ l3 ] = -1*l3_2 + l3_3 [ l2 ] = 0 The following rules are decreasing: l3(x256:0, x263:0, x264:0, x265:0) -> l2(x256:0, c, x263:0, x264:0, x265:0) :|: c = 0 && (0 <= -1 - x263:0 + x264:0 && 0 <= -1 - x264:0 + x265:0) l3(x285:0, x65:0, x293:0, x294:0) -> l3(x285:0, c4, x293:0, x294:0) :|: c4 = 1 + x65:0 && (0 <= -1 - x65:0 + x293:0 && 0 >= -1 * x293:0 + x294:0) The following rules are bounded: l3(x256:0, x263:0, x264:0, x265:0) -> l2(x256:0, c, x263:0, x264:0, x265:0) :|: c = 0 && (0 <= -1 - x263:0 + x264:0 && 0 <= -1 - x264:0 + x265:0) l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, c1, x104:0, x105:0, x106:0) :|: c1 = 0 && (x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0) l3(x285:0, x65:0, x293:0, x294:0) -> l3(x285:0, c4, x293:0, x294:0) :|: c4 = 1 + x65:0 && (0 <= -1 - x65:0 + x293:0 && 0 >= -1 * x293:0 + x294:0) l2(x18, x24, x25, x26, x27) -> l2(x18, c5, x25, c6, x27) :|: c6 = 1 + x26 && c5 = 0 && (x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4) - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor Rules: l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, c1, x104:0, x105:0, x106:0) :|: c1 = 0 && (x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0) l2(x18, x24, x25, x26, x27) -> l2(x18, c5, x25, c6, x27) :|: c6 = 1 + x26 && c5 = 0 && (x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4) Found the following polynomial interpretation: [l2(x, x1, x2, x3, x4)] = c1*x1 - x3 + x4 The following rules are decreasing: l2(x18, x24, x25, x26, x27) -> l2(x18, c5, x25, c6, x27) :|: c6 = 1 + x26 && c5 = 0 && (x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4) The following rules are bounded: l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, c1, x104:0, x105:0, x106:0) :|: c1 = 0 && (x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0) l2(x18, x24, x25, x26, x27) -> l2(x18, c5, x25, c6, x27) :|: c6 = 1 + x26 && c5 = 0 && (x24 > -1 && x24 < 1 && 0 <= -1 - x26 + x27 && 0 <= -1 - (1 + x26) + x27 && x18 > 4) - IntTRS - PolynomialOrderProcessor - IntTRS - RankingReductionPairProof - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, c1, x104:0, x105:0, x106:0) :|: c1 = 0 && (x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0) ---------------------------------------- (10) Obligation: Rules: l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, 0, x104:0, x105:0, x106:0) :|: x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, 0, x104:0, x105:0, x106:0) :|: x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l2(x16:0, x103:0, x104:0, x105:0, x106:0) -> l2(x16:0, 0, x104:0, x105:0, x106:0) :|: x103:0 > -1 && x103:0 < 1 && x16:0 < 5 && 0 <= -1 - x105:0 + x106:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l2(x16:0:0, x103:0:0, x104:0:0, x105:0:0, x106:0:0) -> l2(x16:0:0, 0, x104:0:0, x105:0:0, x106:0:0) :|: x16:0:0 < 5 && 0 <= -1 - x105:0:0 + x106:0:0 && x103:0:0 < 1 && x103:0:0 > -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(x16:0:0, x103:0:0, x105:0:0, x106:0:0) -> l2(x16:0:0, 0, x105:0:0, x106:0:0) :|: x16:0:0 < 5 && 0 <= -1 - x105:0:0 + x106:0:0 && x103:0:0 < 1 && x103:0:0 > -1