MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 22.8 s] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 40 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 397 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, __disjvr_3HAT0, __disjvr_4HAT0, __disjvr_5HAT0, __disjvr_6HAT0, w_5HAT0, x_6HAT0) -> l2(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, __disjvr_3HATpost, __disjvr_4HATpost, __disjvr_5HATpost, __disjvr_6HATpost, w_5HATpost, x_6HATpost) :|: __disjvr_6HAT0 = __disjvr_6HATpost && __disjvr_5HAT0 = __disjvr_5HATpost && __disjvr_4HAT0 = __disjvr_4HATpost && __disjvr_3HAT0 = __disjvr_3HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && w_5HATpost = 1 + w_5HAT0 && x_6HATpost = 1 + x_6HAT0 && 0 <= 2 - w_5HAT0 && 2 - x_6HAT0 <= 0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l3(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x11 = x1 l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x32 = x22 l1(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x40 = x50 l0(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l5(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72 && x61 = x71 && x60 = x70 && x78 = 1 + x68 && x79 = 1 + x69 && 0 <= 2 - x68 && 2 - x69 <= 0 l5(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && x93 = x83 l6(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l4(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x107 = x117 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x100 = x110 && x118 = 1 && 2 <= x108 && x108 <= 2 l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l0(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 l0(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x142 = x152 && x141 = x151 && x140 = x150 && x158 = 1 + x148 && x159 = 1 + x149 && 0 <= 1 - x149 l8(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170 && x174 = x164 l9(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l7(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190 && x195 = x185 l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) -> l0(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x209 = x219 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x204 = x214 && x203 = x213 && x202 = x212 && x201 = x211 && x200 = x210 l0(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l11(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x222 = x232 && x221 = x231 && x220 = x230 && x238 = 1 + x228 && x239 = 1 + x229 && 0 <= 1 - x229 l11(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249) -> l12(x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) :|: x249 = x259 && x248 = x258 && x247 = x257 && x246 = x256 && x245 = x255 && x244 = x254 && x243 = x253 && x242 = x252 && x241 = x251 && x240 = x250 && x256 = x246 l12(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l10(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x269 = x279 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x262 = x272 && x261 = x271 && x260 = x270 && x278 = 1 && 2 <= x268 && x268 <= 2 l10(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289) -> l0(x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x283 = x293 && x282 = x292 && x281 = x291 && x280 = x290 l0(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309) -> l14(x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x302 = x312 && x301 = x311 && x300 = x310 && 2 <= x319 && x319 <= 2 && x318 = 1 + x308 && x319 = 1 + x309 && 0 <= 1 - x309 l14(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l13(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x324 = x334 && x323 = x333 && x322 = x332 && x321 = x331 && x320 = x330 && x337 = x327 l13(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349) -> l0(x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x343 = x353 && x342 = x352 && x341 = x351 && x340 = x350 l0(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369) -> l15(x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) :|: 0 <= 1 - x369 && x379 = 1 + x369 && x380 = 1 + x368 && x379 <= 2 && 2 <= x379 && x380 <= 2 && 2 <= x380 && x378 = 1 && x360 = x370 && x361 = x371 && x362 = x372 && x363 = x373 && x364 = x374 && x365 = x375 && x366 = x376 && x367 = x377 l15(x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l0(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400) :|: x390 = x400 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x384 = x394 && x383 = x393 && x382 = x392 && x381 = x391 l0(x401, x402, x403, x404, x405, x406, x407, x408, x409, x410) -> l16(x411, x412, x413, x414, x415, x416, x417, x418, x419, x420) :|: x410 = x420 && x409 = x419 && x408 = x418 && x407 = x417 && x406 = x416 && x405 = x415 && x404 = x414 && x403 = x413 && x402 = x412 && x411 = x411 && 3 - x409 <= 0 && 2 - x410 <= 0 l17(x421, x422, x423, x424, x425, x426, x427, x428, x429, x430) -> l0(x431, x432, x433, x434, x435, x436, x437, x438, x439, x440) :|: x430 = x440 && x429 = x439 && x428 = x438 && x427 = x437 && x426 = x436 && x425 = x435 && x424 = x434 && x423 = x433 && x422 = x432 && x421 = x431 l18(x441, x442, x443, x444, x445, x446, x447, x448, x449, x450) -> l17(x451, x452, x453, x454, x455, x456, x457, x458, x459, x460) :|: x450 = x460 && x449 = x459 && x448 = x458 && x447 = x457 && x446 = x456 && x445 = x455 && x444 = x454 && x443 = x453 && x442 = x452 && x441 = x451 Start term: l18(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, __disjvr_3HAT0, __disjvr_4HAT0, __disjvr_5HAT0, __disjvr_6HAT0, w_5HAT0, x_6HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, __disjvr_3HAT0, __disjvr_4HAT0, __disjvr_5HAT0, __disjvr_6HAT0, w_5HAT0, x_6HAT0) -> l2(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, __disjvr_3HATpost, __disjvr_4HATpost, __disjvr_5HATpost, __disjvr_6HATpost, w_5HATpost, x_6HATpost) :|: __disjvr_6HAT0 = __disjvr_6HATpost && __disjvr_5HAT0 = __disjvr_5HATpost && __disjvr_4HAT0 = __disjvr_4HATpost && __disjvr_3HAT0 = __disjvr_3HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && w_5HATpost = 1 + w_5HAT0 && x_6HATpost = 1 + x_6HAT0 && 0 <= 2 - w_5HAT0 && 2 - x_6HAT0 <= 0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l3(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x11 = x1 l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x32 = x22 l1(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x40 = x50 l0(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l5(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72 && x61 = x71 && x60 = x70 && x78 = 1 + x68 && x79 = 1 + x69 && 0 <= 2 - x68 && 2 - x69 <= 0 l5(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && x93 = x83 l6(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l4(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x107 = x117 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x100 = x110 && x118 = 1 && 2 <= x108 && x108 <= 2 l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l0(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 l0(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x142 = x152 && x141 = x151 && x140 = x150 && x158 = 1 + x148 && x159 = 1 + x149 && 0 <= 1 - x149 l8(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170 && x174 = x164 l9(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l7(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190 && x195 = x185 l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) -> l0(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x209 = x219 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x204 = x214 && x203 = x213 && x202 = x212 && x201 = x211 && x200 = x210 l0(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l11(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x222 = x232 && x221 = x231 && x220 = x230 && x238 = 1 + x228 && x239 = 1 + x229 && 0 <= 1 - x229 l11(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249) -> l12(x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) :|: x249 = x259 && x248 = x258 && x247 = x257 && x246 = x256 && x245 = x255 && x244 = x254 && x243 = x253 && x242 = x252 && x241 = x251 && x240 = x250 && x256 = x246 l12(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l10(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x269 = x279 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x262 = x272 && x261 = x271 && x260 = x270 && x278 = 1 && 2 <= x268 && x268 <= 2 l10(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289) -> l0(x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x283 = x293 && x282 = x292 && x281 = x291 && x280 = x290 l0(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309) -> l14(x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x302 = x312 && x301 = x311 && x300 = x310 && 2 <= x319 && x319 <= 2 && x318 = 1 + x308 && x319 = 1 + x309 && 0 <= 1 - x309 l14(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l13(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x324 = x334 && x323 = x333 && x322 = x332 && x321 = x331 && x320 = x330 && x337 = x327 l13(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349) -> l0(x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x343 = x353 && x342 = x352 && x341 = x351 && x340 = x350 l0(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369) -> l15(x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) :|: 0 <= 1 - x369 && x379 = 1 + x369 && x380 = 1 + x368 && x379 <= 2 && 2 <= x379 && x380 <= 2 && 2 <= x380 && x378 = 1 && x360 = x370 && x361 = x371 && x362 = x372 && x363 = x373 && x364 = x374 && x365 = x375 && x366 = x376 && x367 = x377 l15(x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l0(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400) :|: x390 = x400 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x384 = x394 && x383 = x393 && x382 = x392 && x381 = x391 l0(x401, x402, x403, x404, x405, x406, x407, x408, x409, x410) -> l16(x411, x412, x413, x414, x415, x416, x417, x418, x419, x420) :|: x410 = x420 && x409 = x419 && x408 = x418 && x407 = x417 && x406 = x416 && x405 = x415 && x404 = x414 && x403 = x413 && x402 = x412 && x411 = x411 && 3 - x409 <= 0 && 2 - x410 <= 0 l17(x421, x422, x423, x424, x425, x426, x427, x428, x429, x430) -> l0(x431, x432, x433, x434, x435, x436, x437, x438, x439, x440) :|: x430 = x440 && x429 = x439 && x428 = x438 && x427 = x437 && x426 = x436 && x425 = x435 && x424 = x434 && x423 = x433 && x422 = x432 && x421 = x431 l18(x441, x442, x443, x444, x445, x446, x447, x448, x449, x450) -> l17(x451, x452, x453, x454, x455, x456, x457, x458, x459, x460) :|: x450 = x460 && x449 = x459 && x448 = x458 && x447 = x457 && x446 = x456 && x445 = x455 && x444 = x454 && x443 = x453 && x442 = x452 && x441 = x451 Start term: l18(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, __disjvr_3HAT0, __disjvr_4HAT0, __disjvr_5HAT0, __disjvr_6HAT0, w_5HAT0, x_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, __disjvr_3HAT0, __disjvr_4HAT0, __disjvr_5HAT0, __disjvr_6HAT0, w_5HAT0, x_6HAT0) -> l2(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, __disjvr_3HATpost, __disjvr_4HATpost, __disjvr_5HATpost, __disjvr_6HATpost, w_5HATpost, x_6HATpost) :|: __disjvr_6HAT0 = __disjvr_6HATpost && __disjvr_5HAT0 = __disjvr_5HATpost && __disjvr_4HAT0 = __disjvr_4HATpost && __disjvr_3HAT0 = __disjvr_3HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && w_5HATpost = 1 + w_5HAT0 && x_6HATpost = 1 + x_6HAT0 && 0 <= 2 - w_5HAT0 && 2 - x_6HAT0 <= 0 (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l3(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x11 = x1 (3) l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x32 = x22 (4) l1(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x40 = x50 (5) l0(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l5(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72 && x61 = x71 && x60 = x70 && x78 = 1 + x68 && x79 = 1 + x69 && 0 <= 2 - x68 && 2 - x69 <= 0 (6) l5(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && x93 = x83 (7) l6(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l4(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x107 = x117 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x100 = x110 && x118 = 1 && 2 <= x108 && x108 <= 2 (8) l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l0(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 (9) l0(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x142 = x152 && x141 = x151 && x140 = x150 && x158 = 1 + x148 && x159 = 1 + x149 && 0 <= 1 - x149 (10) l8(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170 && x174 = x164 (11) l9(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l7(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190 && x195 = x185 (12) l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) -> l0(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x209 = x219 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x204 = x214 && x203 = x213 && x202 = x212 && x201 = x211 && x200 = x210 (13) l0(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l11(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x222 = x232 && x221 = x231 && x220 = x230 && x238 = 1 + x228 && x239 = 1 + x229 && 0 <= 1 - x229 (14) l11(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249) -> l12(x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) :|: x249 = x259 && x248 = x258 && x247 = x257 && x246 = x256 && x245 = x255 && x244 = x254 && x243 = x253 && x242 = x252 && x241 = x251 && x240 = x250 && x256 = x246 (15) l12(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l10(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x269 = x279 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x262 = x272 && x261 = x271 && x260 = x270 && x278 = 1 && 2 <= x268 && x268 <= 2 (16) l10(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289) -> l0(x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x283 = x293 && x282 = x292 && x281 = x291 && x280 = x290 (17) l0(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309) -> l14(x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x302 = x312 && x301 = x311 && x300 = x310 && 2 <= x319 && x319 <= 2 && x318 = 1 + x308 && x319 = 1 + x309 && 0 <= 1 - x309 (18) l14(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l13(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x324 = x334 && x323 = x333 && x322 = x332 && x321 = x331 && x320 = x330 && x337 = x327 (19) l13(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349) -> l0(x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x343 = x353 && x342 = x352 && x341 = x351 && x340 = x350 (20) l0(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369) -> l15(x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) :|: 0 <= 1 - x369 && x379 = 1 + x369 && x380 = 1 + x368 && x379 <= 2 && 2 <= x379 && x380 <= 2 && 2 <= x380 && x378 = 1 && x360 = x370 && x361 = x371 && x362 = x372 && x363 = x373 && x364 = x374 && x365 = x375 && x366 = x376 && x367 = x377 (21) l15(x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l0(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400) :|: x390 = x400 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x384 = x394 && x383 = x393 && x382 = x392 && x381 = x391 (22) l0(x401, x402, x403, x404, x405, x406, x407, x408, x409, x410) -> l16(x411, x412, x413, x414, x415, x416, x417, x418, x419, x420) :|: x410 = x420 && x409 = x419 && x408 = x418 && x407 = x417 && x406 = x416 && x405 = x415 && x404 = x414 && x403 = x413 && x402 = x412 && x411 = x411 && 3 - x409 <= 0 && 2 - x410 <= 0 (23) l17(x421, x422, x423, x424, x425, x426, x427, x428, x429, x430) -> l0(x431, x432, x433, x434, x435, x436, x437, x438, x439, x440) :|: x430 = x440 && x429 = x439 && x428 = x438 && x427 = x437 && x426 = x436 && x425 = x435 && x424 = x434 && x423 = x433 && x422 = x432 && x421 = x431 (24) l18(x441, x442, x443, x444, x445, x446, x447, x448, x449, x450) -> l17(x451, x452, x453, x454, x455, x456, x457, x458, x459, x460) :|: x450 = x460 && x449 = x459 && x448 = x458 && x447 = x457 && x446 = x456 && x445 = x455 && x444 = x454 && x443 = x453 && x442 = x452 && x441 = x451 Arcs: (1) -> (2) (2) -> (3) (3) -> (4) (4) -> (1), (5), (9), (13), (17), (20), (22) (5) -> (6) (6) -> (7) (7) -> (8) (8) -> (1), (5), (9), (13), (17), (20), (22) (9) -> (10) (10) -> (11) (11) -> (12) (12) -> (1), (5), (9), (13), (17), (20), (22) (13) -> (14) (14) -> (15) (15) -> (16) (16) -> (1), (5), (9), (13), (17), (20), (22) (17) -> (18) (18) -> (19) (19) -> (1), (5), (9), (13), (17), (20), (22) (20) -> (21) (21) -> (1), (5), (9), (13), (17), (20), (22) (23) -> (1), (5), (9), (13), (17), (20), (22) (24) -> (23) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(Result_4HAT0, __disjvr_0HAT0, __disjvr_1HAT0, __disjvr_2HAT0, __disjvr_3HAT0, __disjvr_4HAT0, __disjvr_5HAT0, __disjvr_6HAT0, w_5HAT0, x_6HAT0) -> l2(Result_4HATpost, __disjvr_0HATpost, __disjvr_1HATpost, __disjvr_2HATpost, __disjvr_3HATpost, __disjvr_4HATpost, __disjvr_5HATpost, __disjvr_6HATpost, w_5HATpost, x_6HATpost) :|: __disjvr_6HAT0 = __disjvr_6HATpost && __disjvr_5HAT0 = __disjvr_5HATpost && __disjvr_4HAT0 = __disjvr_4HATpost && __disjvr_3HAT0 = __disjvr_3HATpost && __disjvr_2HAT0 = __disjvr_2HATpost && __disjvr_1HAT0 = __disjvr_1HATpost && __disjvr_0HAT0 = __disjvr_0HATpost && Result_4HAT0 = Result_4HATpost && w_5HATpost = 1 + w_5HAT0 && x_6HATpost = 1 + x_6HAT0 && 0 <= 2 - w_5HAT0 && 2 - x_6HAT0 <= 0 (2) l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l0(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x129 = x139 && x128 = x138 && x127 = x137 && x126 = x136 && x125 = x135 && x124 = x134 && x123 = x133 && x122 = x132 && x121 = x131 && x120 = x130 (3) l6(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l4(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x107 = x117 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x100 = x110 && x118 = 1 && 2 <= x108 && x108 <= 2 (4) l5(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l6(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x87 = x97 && x86 = x96 && x85 = x95 && x84 = x94 && x83 = x93 && x82 = x92 && x81 = x91 && x80 = x90 && x93 = x83 (5) l0(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l5(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x67 = x77 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72 && x61 = x71 && x60 = x70 && x78 = 1 + x68 && x79 = 1 + x69 && 0 <= 2 - x68 && 2 - x69 <= 0 (6) l7(x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) -> l0(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x209 = x219 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x204 = x214 && x203 = x213 && x202 = x212 && x201 = x211 && x200 = x210 (7) l9(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189) -> l7(x190, x191, x192, x193, x194, x195, x196, x197, x198, x199) :|: x189 = x199 && x188 = x198 && x187 = x197 && x186 = x196 && x185 = x195 && x184 = x194 && x183 = x193 && x182 = x192 && x181 = x191 && x180 = x190 && x195 = x185 (8) l8(x160, x161, x162, x163, x164, x165, x166, x167, x168, x169) -> l9(x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x169 = x179 && x168 = x178 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x161 = x171 && x160 = x170 && x174 = x164 (9) l0(x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) -> l8(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159) :|: x147 = x157 && x146 = x156 && x145 = x155 && x144 = x154 && x143 = x153 && x142 = x152 && x141 = x151 && x140 = x150 && x158 = 1 + x148 && x159 = 1 + x149 && 0 <= 1 - x149 (10) l10(x280, x281, x282, x283, x284, x285, x286, x287, x288, x289) -> l0(x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x283 = x293 && x282 = x292 && x281 = x291 && x280 = x290 (11) l12(x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l10(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279) :|: x269 = x279 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x262 = x272 && x261 = x271 && x260 = x270 && x278 = 1 && 2 <= x268 && x268 <= 2 (12) l11(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249) -> l12(x250, x251, x252, x253, x254, x255, x256, x257, x258, x259) :|: x249 = x259 && x248 = x258 && x247 = x257 && x246 = x256 && x245 = x255 && x244 = x254 && x243 = x253 && x242 = x252 && x241 = x251 && x240 = x250 && x256 = x246 (13) l0(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229) -> l11(x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x222 = x232 && x221 = x231 && x220 = x230 && x238 = 1 + x228 && x239 = 1 + x229 && 0 <= 1 - x229 (14) l13(x340, x341, x342, x343, x344, x345, x346, x347, x348, x349) -> l0(x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x343 = x353 && x342 = x352 && x341 = x351 && x340 = x350 (15) l14(x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l13(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339) :|: x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x324 = x334 && x323 = x333 && x322 = x332 && x321 = x331 && x320 = x330 && x337 = x327 (16) l0(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309) -> l14(x310, x311, x312, x313, x314, x315, x316, x317, x318, x319) :|: x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x302 = x312 && x301 = x311 && x300 = x310 && 2 <= x319 && x319 <= 2 && x318 = 1 + x308 && x319 = 1 + x309 && 0 <= 1 - x309 (17) l15(x381, x382, x383, x384, x385, x386, x387, x388, x389, x390) -> l0(x391, x392, x393, x394, x395, x396, x397, x398, x399, x400) :|: x390 = x400 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x384 = x394 && x383 = x393 && x382 = x392 && x381 = x391 (18) l0(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369) -> l15(x370, x371, x372, x373, x374, x375, x376, x377, x378, x379) :|: 0 <= 1 - x369 && x379 = 1 + x369 && x380 = 1 + x368 && x379 <= 2 && 2 <= x379 && x380 <= 2 && 2 <= x380 && x378 = 1 && x360 = x370 && x361 = x371 && x362 = x372 && x363 = x373 && x364 = x374 && x365 = x375 && x366 = x376 && x367 = x377 (19) l1(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l0(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x47 = x57 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x40 = x50 (20) l3(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l1(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x27 = x37 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x32 = x22 (21) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l3(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x7 = x17 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x = x10 && x11 = x1 Arcs: (1) -> (21) (2) -> (1), (5), (9), (13), (16), (18) (3) -> (2) (4) -> (3) (5) -> (4) (6) -> (1), (5), (9), (13), (16), (18) (7) -> (6) (8) -> (7) (9) -> (8) (10) -> (1), (5), (9), (13), (16), (18) (11) -> (10) (12) -> (11) (13) -> (12) (14) -> (1), (5), (9), (13), (16), (18) (15) -> (14) (16) -> (15) (17) -> (1), (5), (9), (13), (16), (18) (18) -> (17) (19) -> (1), (5), (9), (13), (16), (18) (20) -> (19) (21) -> (20) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l0(x140:0, x141:0, x142:0, x143:0, x144:0, x145:0, x146:0, x147:0, x148:0, x149:0) -> l0(x140:0, x141:0, x142:0, x143:0, x144:0, x145:0, x146:0, x147:0, 1 + x148:0, 1 + x149:0) :|: x149:0 < 2 l0(x360:0, x361:0, x362:0, x363:0, x364:0, x365:0, x366:0, x367:0, x368:0, x369:0) -> l0(x360:0, x361:0, x362:0, x363:0, x364:0, x365:0, x366:0, x367:0, 1, 1 + x369:0) :|: x368:0 < 2 && x368:0 > 0 && x369:0 < 2 && x369:0 > 0 l0(x300:0, x301:0, x302:0, x303:0, x304:0, x305:0, x306:0, x307:0, x308:0, x309:0) -> l0(x300:0, x301:0, x302:0, x303:0, x304:0, x305:0, x306:0, x307:0, 1 + x308:0, 1 + x309:0) :|: x309:0 > 0 && x309:0 < 2 l0(Result_4HAT0:0, __disjvr_0HAT0:0, __disjvr_1HAT0:0, __disjvr_2HAT0:0, __disjvr_3HAT0:0, __disjvr_4HAT0:0, __disjvr_5HAT0:0, __disjvr_6HAT0:0, w_5HAT0:0, x_6HAT0:0) -> l0(Result_4HAT0:0, __disjvr_0HAT0:0, __disjvr_1HAT0:0, __disjvr_2HAT0:0, __disjvr_3HAT0:0, __disjvr_4HAT0:0, __disjvr_5HAT0:0, __disjvr_6HAT0:0, 1 + w_5HAT0:0, 1 + x_6HAT0:0) :|: x_6HAT0:0 > 1 && w_5HAT0:0 < 3 l0(x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, x68:0, x69:0) -> l0(x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, 1, 1 + x69:0) :|: x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2 l0(x220:0, x221:0, x222:0, x223:0, x224:0, x225:0, x226:0, x227:0, x228:0, x229:0) -> l0(x220:0, x221:0, x222:0, x223:0, x224:0, x225:0, x226:0, x227:0, 1, 1 + x229:0) :|: x228:0 < 2 && x228:0 > 0 && x229:0 < 2 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l0(x9, x10) ---------------------------------------- (8) Obligation: Rules: l0(x148:0, x149:0) -> l0(1 + x148:0, 1 + x149:0) :|: x149:0 < 2 l0(x368:0, x369:0) -> l0(1, 1 + x369:0) :|: x368:0 < 2 && x368:0 > 0 && x369:0 < 2 && x369:0 > 0 l0(x308:0, x309:0) -> l0(1 + x308:0, 1 + x309:0) :|: x309:0 > 0 && x309:0 < 2 l0(w_5HAT0:0, x_6HAT0:0) -> l0(1 + w_5HAT0:0, 1 + x_6HAT0:0) :|: x_6HAT0:0 > 1 && w_5HAT0:0 < 3 l0(x68:0, x69:0) -> l0(1, 1 + x69:0) :|: x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2 l0(x228:0, x229:0) -> l0(1, 1 + x229:0) :|: x228:0 < 2 && x228:0 > 0 && x229:0 < 2 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l0(VARIABLE, 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: l0(x148:0, x149:0) -> l0(c, c1) :|: c1 = 1 + x149:0 && c = 1 + x148:0 && x149:0 < 2 l0(x368:0, x369:0) -> l0(c2, c3) :|: c3 = 1 + x369:0 && c2 = 1 && (x368:0 < 2 && x368:0 > 0 && x369:0 < 2 && x369:0 > 0) l0(x308:0, x309:0) -> l0(c4, c5) :|: c5 = 1 + x309:0 && c4 = 1 + x308:0 && (x309:0 > 0 && x309:0 < 2) l0(w_5HAT0:0, x_6HAT0:0) -> l0(c6, c7) :|: c7 = 1 + x_6HAT0:0 && c6 = 1 + w_5HAT0:0 && (x_6HAT0:0 > 1 && w_5HAT0:0 < 3) l0(x68:0, x69:0) -> l0(c8, c9) :|: c9 = 1 + x69:0 && c8 = 1 && (x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2) l0(x228:0, x229:0) -> l0(c10, c11) :|: c11 = 1 + x229:0 && c10 = 1 && (x228:0 < 2 && x228:0 > 0 && x229:0 < 2) Found the following polynomial interpretation: [l0(x, x1)] = 1 - x The following rules are decreasing: l0(x148:0, x149:0) -> l0(c, c1) :|: c1 = 1 + x149:0 && c = 1 + x148:0 && x149:0 < 2 l0(x308:0, x309:0) -> l0(c4, c5) :|: c5 = 1 + x309:0 && c4 = 1 + x308:0 && (x309:0 > 0 && x309:0 < 2) l0(w_5HAT0:0, x_6HAT0:0) -> l0(c6, c7) :|: c7 = 1 + x_6HAT0:0 && c6 = 1 + w_5HAT0:0 && (x_6HAT0:0 > 1 && w_5HAT0:0 < 3) The following rules are bounded: l0(x368:0, x369:0) -> l0(c2, c3) :|: c3 = 1 + x369:0 && c2 = 1 && (x368:0 < 2 && x368:0 > 0 && x369:0 < 2 && x369:0 > 0) l0(x68:0, x69:0) -> l0(c8, c9) :|: c9 = 1 + x69:0 && c8 = 1 && (x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2) l0(x228:0, x229:0) -> l0(c10, c11) :|: c11 = 1 + x229:0 && c10 = 1 && (x228:0 < 2 && x228:0 > 0 && x229:0 < 2) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l0(x368:0, x369:0) -> l0(c2, c3) :|: c3 = 1 + x369:0 && c2 = 1 && (x368:0 < 2 && x368:0 > 0 && x369:0 < 2 && x369:0 > 0) l0(x68:0, x69:0) -> l0(c8, c9) :|: c9 = 1 + x69:0 && c8 = 1 && (x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2) l0(x228:0, x229:0) -> l0(c10, c11) :|: c11 = 1 + x229:0 && c10 = 1 && (x228:0 < 2 && x228:0 > 0 && x229:0 < 2) Found the following polynomial interpretation: [l0(x, x1)] = x - x1 The following rules are decreasing: l0(x368:0, x369:0) -> l0(c2, c3) :|: c3 = 1 + x369:0 && c2 = 1 && (x368:0 < 2 && x368:0 > 0 && x369:0 < 2 && x369:0 > 0) l0(x68:0, x69:0) -> l0(c8, c9) :|: c9 = 1 + x69:0 && c8 = 1 && (x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2) l0(x228:0, x229:0) -> l0(c10, c11) :|: c11 = 1 + x229:0 && c10 = 1 && (x228:0 < 2 && x228:0 > 0 && x229:0 < 2) The following rules are bounded: l0(x368:0, x369:0) -> l0(c2, c3) :|: c3 = 1 + x369:0 && c2 = 1 && (x368:0 < 2 && x368:0 > 0 && x369:0 < 2 && x369:0 > 0) l0(x228:0, x229:0) -> l0(c10, c11) :|: c11 = 1 + x229:0 && c10 = 1 && (x228:0 < 2 && x228:0 > 0 && x229:0 < 2) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - IntTRS Rules: l0(x68:0, x69:0) -> l0(c8, c9) :|: c9 = 1 + x69:0 && c8 = 1 && (x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor Rules: l0(x148:0, x149:0) -> l0(c, c1) :|: c1 = 1 + x149:0 && c = 1 + x148:0 && x149:0 < 2 l0(x308:0, x309:0) -> l0(c4, c5) :|: c5 = 1 + x309:0 && c4 = 1 + x308:0 && (x309:0 > 0 && x309:0 < 2) l0(w_5HAT0:0, x_6HAT0:0) -> l0(c6, c7) :|: c7 = 1 + x_6HAT0:0 && c6 = 1 + w_5HAT0:0 && (x_6HAT0:0 > 1 && w_5HAT0:0 < 3) Found the following polynomial interpretation: [l0(x, x1)] = 2 - 2*x + x1 The following rules are decreasing: l0(x148:0, x149:0) -> l0(c, c1) :|: c1 = 1 + x149:0 && c = 1 + x148:0 && x149:0 < 2 l0(x308:0, x309:0) -> l0(c4, c5) :|: c5 = 1 + x309:0 && c4 = 1 + x308:0 && (x309:0 > 0 && x309:0 < 2) l0(w_5HAT0:0, x_6HAT0:0) -> l0(c6, c7) :|: c7 = 1 + x_6HAT0:0 && c6 = 1 + w_5HAT0:0 && (x_6HAT0:0 > 1 && w_5HAT0:0 < 3) The following rules are bounded: l0(w_5HAT0:0, x_6HAT0:0) -> l0(c6, c7) :|: c7 = 1 + x_6HAT0:0 && c6 = 1 + w_5HAT0:0 && (x_6HAT0:0 > 1 && w_5HAT0:0 < 3) - IntTRS - PolynomialOrderProcessor - AND - IntTRS - IntTRS - IntTRS - PolynomialOrderProcessor - IntTRS - PolynomialOrderProcessor Rules: l0(x148:0, x149:0) -> l0(c, c1) :|: c1 = 1 + x149:0 && c = 1 + x148:0 && x149:0 < 2 l0(x308:0, x309:0) -> l0(c4, c5) :|: c5 = 1 + x309:0 && c4 = 1 + x308:0 && (x309:0 > 0 && x309:0 < 2) Found the following polynomial interpretation: [l0(x, x1)] = 1 - x1 The following rules are decreasing: l0(x148:0, x149:0) -> l0(c, c1) :|: c1 = 1 + x149:0 && c = 1 + x148:0 && x149:0 < 2 l0(x308:0, x309:0) -> l0(c4, c5) :|: c5 = 1 + x309:0 && c4 = 1 + x308:0 && (x309:0 > 0 && x309:0 < 2) The following rules are bounded: l0(x148:0, x149:0) -> l0(c, c1) :|: c1 = 1 + x149:0 && c = 1 + x148:0 && x149:0 < 2 l0(x308:0, x309:0) -> l0(c4, c5) :|: c5 = 1 + x309:0 && c4 = 1 + x308:0 && (x309:0 > 0 && x309:0 < 2) ---------------------------------------- (10) Obligation: Rules: l0(x68:0, x69:0) -> l0(1, 1 + x69:0) :|: x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(x68:0, x69:0) -> l0(1, 1 + x69:0) :|: x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) l0(x68:0, x69:0) -> l0(1, 1 + x69:0) :|: x68:0 < 3 && x69:0 > 1 && x68:0 > 0 && x68:0 < 2 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: l0(x68:0:0, x69:0:0) -> l0(1, 1 + x69:0:0) :|: x68:0:0 > 0 && x68:0:0 < 2 && x69:0:0 > 1 && x68:0:0 < 3