YES
proof of prog.inttrs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given IRSwT could be proven:

(0) IRSwT
(1) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(2) IRSwT
(3) IRSwTTerminationDigraphProof [EQUIVALENT, 7020 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 23 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 8 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 30 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 15 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 82 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) TempFilterProof [SOUND, 29 ms]
        (29) IntTRS
        (30) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (31) YES


----------------------------------------

(0)
Obligation:
Rules:
l0(__const_64HAT0, __const_7HAT0, ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0) -> l1(__const_64HATpost, __const_7HATpost, ctr23HATpost, iHATpost, seedHATpost, tmp05HATpost, tmp1013HATpost, tmp1114HATpost, tmp1215HATpost, tmp1316HATpost, tmp16HATpost, tmp27HATpost, tmp38HATpost, tmp49HATpost, tmp510HATpost, tmp611HATpost, tmp712HATpost, z117HATpost, z218HATpost, z319HATpost, z420HATpost, z521HATpost) :|: z521HAT0 = z521HATpost && z420HAT0 = z420HATpost && z319HAT0 = z319HATpost && z218HAT0 = z218HATpost && z117HAT0 = z117HATpost && tmp712HAT0 = tmp712HATpost && tmp611HAT0 = tmp611HATpost && tmp510HAT0 = tmp510HATpost && tmp49HAT0 = tmp49HATpost && tmp38HAT0 = tmp38HATpost && tmp27HAT0 = tmp27HATpost && tmp16HAT0 = tmp16HATpost && tmp1316HAT0 = tmp1316HATpost && tmp1215HAT0 = tmp1215HATpost && tmp1114HAT0 = tmp1114HATpost && tmp1013HAT0 = tmp1013HATpost && tmp05HAT0 = tmp05HATpost && seedHAT0 = seedHATpost && iHAT0 = iHATpost && __const_7HAT0 = __const_7HATpost && __const_64HAT0 = __const_64HATpost && ctr23HATpost = __const_7HAT0 && __const_64HAT0 <= iHAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x21 = x43 && x20 = x42 && x19 = x41 && x18 = x40 && x17 = x39 && x16 = x38 && x15 = x37 && x14 = x36 && x13 = x35 && x12 = x34 && x11 = x33 && x10 = x32 && x9 = x31 && x8 = x30 && x7 = x29 && x6 = x28 && x5 = x27 && x2 = x24 && x1 = x23 && x = x22 && x25 = 1 + x3 && x26 = x26 && 1 + x3 <= x
l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x65 = x87 && x64 = x86 && x63 = x85 && x62 = x84 && x61 = x83 && x60 = x82 && x59 = x81 && x58 = x80 && x57 = x79 && x56 = x78 && x55 = x77 && x54 = x76 && x53 = x75 && x52 = x74 && x51 = x73 && x50 = x72 && x49 = x71 && x48 = x70 && x47 = x69 && x46 = x68 && x45 = x67 && x44 = x66 && 1 + x46 <= 0
l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l5(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: 0 <= x90 && x115 = x115 && x132 = x132 && x120 = x120 && x133 = x133 && x121 = x121 && x134 = x134 && x122 = x122 && x135 = x135 && x116 = x115 + x122 && x119 = x115 - x122 && x117 = x120 + x121 && x118 = x120 - x121 && x136 = x136 && x137 = x135 + x132 && x138 = x134 + x133 && x139 = x135 + x133 && x140 = x134 + x132 && x131 = x131 && x123 = x123 && x124 = x124 && x125 = x125 && x126 = x126 && x127 = x127 && x128 = x128 && x141 = x141 && x142 = x142 && x129 = x141 + x131 && x130 = x142 + x131 && x112 = -1 + x90 && x88 = x110 && x89 = x111 && x91 = x113 && x92 = x114
l2(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l0(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) :|: x164 = x186 && x163 = x185 && x162 = x184 && x161 = x183 && x160 = x182 && x159 = x181 && x158 = x180 && x157 = x179 && x156 = x178 && x155 = x177 && x154 = x176 && x153 = x175 && x152 = x174 && x151 = x173 && x150 = x172 && x149 = x171 && x148 = x170 && x147 = x169 && x146 = x168 && x145 = x167 && x144 = x166 && x143 = x165
l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) :|: x208 = x230 && x207 = x229 && x206 = x228 && x205 = x227 && x204 = x226 && x203 = x225 && x202 = x224 && x201 = x223 && x200 = x222 && x199 = x221 && x198 = x220 && x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209
l5(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l3(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) :|: x252 = x274 && x251 = x273 && x250 = x272 && x249 = x271 && x248 = x270 && x247 = x269 && x246 = x268 && x245 = x267 && x244 = x266 && x243 = x265 && x242 = x264 && x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253
l6(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l5(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) :|: x296 = x318 && x295 = x317 && x294 = x316 && x293 = x315 && x292 = x314 && x291 = x313 && x290 = x312 && x289 = x311 && x288 = x310 && x287 = x309 && x286 = x308 && x285 = x307 && x284 = x306 && x283 = x305 && x282 = x304 && x281 = x303 && x280 = x302 && x279 = x301 && x278 = x300 && x276 = x298 && x275 = x297 && x299 = x276 && 1 + x277 <= 0
l6(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l1(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: 0 <= x321 && x346 = x346 && x363 = x363 && x351 = x351 && x364 = x364 && x352 = x352 && x365 = x365 && x353 = x353 && x366 = x366 && x347 = x346 + x353 && x350 = x346 - x353 && x348 = x351 + x352 && x349 = x351 - x352 && x367 = x367 && x368 = x366 + x363 && x369 = x365 + x364 && x370 = x366 + x364 && x371 = x365 + x363 && x362 = x362 && x354 = x354 && x355 = x355 && x356 = x356 && x357 = x357 && x358 = x358 && x359 = x359 && x372 = x372 && x373 = x373 && x360 = x372 + x362 && x361 = x373 + x362 && x343 = -1 + x321 && x319 = x341 && x320 = x342 && x322 = x344 && x323 = x345
l7(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) -> l2(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x395 = x417 && x394 = x416 && x393 = x415 && x392 = x414 && x391 = x413 && x390 = x412 && x389 = x411 && x388 = x410 && x387 = x409 && x386 = x408 && x385 = x407 && x384 = x406 && x383 = x405 && x382 = x404 && x381 = x403 && x380 = x402 && x379 = x401 && x376 = x398 && x375 = x397 && x374 = x396 && x399 = 0 && x400 = 0
l8(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) -> l7(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x439 = x461 && x438 = x460 && x437 = x459 && x436 = x458 && x435 = x457 && x434 = x456 && x433 = x455 && x432 = x454 && x431 = x453 && x430 = x452 && x429 = x451 && x428 = x450 && x427 = x449 && x426 = x448 && x425 = x447 && x424 = x446 && x423 = x445 && x422 = x444 && x421 = x443 && x420 = x442 && x419 = x441 && x418 = x440
Start term: l8(__const_64HAT0, __const_7HAT0, ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0)

----------------------------------------

(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(2)
Obligation:
Rules:
l0(__const_64HAT0, __const_7HAT0, ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0) -> l1(__const_64HATpost, __const_7HATpost, ctr23HATpost, iHATpost, seedHATpost, tmp05HATpost, tmp1013HATpost, tmp1114HATpost, tmp1215HATpost, tmp1316HATpost, tmp16HATpost, tmp27HATpost, tmp38HATpost, tmp49HATpost, tmp510HATpost, tmp611HATpost, tmp712HATpost, z117HATpost, z218HATpost, z319HATpost, z420HATpost, z521HATpost) :|: z521HAT0 = z521HATpost && z420HAT0 = z420HATpost && z319HAT0 = z319HATpost && z218HAT0 = z218HATpost && z117HAT0 = z117HATpost && tmp712HAT0 = tmp712HATpost && tmp611HAT0 = tmp611HATpost && tmp510HAT0 = tmp510HATpost && tmp49HAT0 = tmp49HATpost && tmp38HAT0 = tmp38HATpost && tmp27HAT0 = tmp27HATpost && tmp16HAT0 = tmp16HATpost && tmp1316HAT0 = tmp1316HATpost && tmp1215HAT0 = tmp1215HATpost && tmp1114HAT0 = tmp1114HATpost && tmp1013HAT0 = tmp1013HATpost && tmp05HAT0 = tmp05HATpost && seedHAT0 = seedHATpost && iHAT0 = iHATpost && __const_7HAT0 = __const_7HATpost && __const_64HAT0 = __const_64HATpost && ctr23HATpost = __const_7HAT0 && __const_64HAT0 <= iHAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x21 = x43 && x20 = x42 && x19 = x41 && x18 = x40 && x17 = x39 && x16 = x38 && x15 = x37 && x14 = x36 && x13 = x35 && x12 = x34 && x11 = x33 && x10 = x32 && x9 = x31 && x8 = x30 && x7 = x29 && x6 = x28 && x5 = x27 && x2 = x24 && x1 = x23 && x = x22 && x25 = 1 + x3 && x26 = x26 && 1 + x3 <= x
l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x65 = x87 && x64 = x86 && x63 = x85 && x62 = x84 && x61 = x83 && x60 = x82 && x59 = x81 && x58 = x80 && x57 = x79 && x56 = x78 && x55 = x77 && x54 = x76 && x53 = x75 && x52 = x74 && x51 = x73 && x50 = x72 && x49 = x71 && x48 = x70 && x47 = x69 && x46 = x68 && x45 = x67 && x44 = x66 && 1 + x46 <= 0
l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l5(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: 0 <= x90 && x115 = x115 && x132 = x132 && x120 = x120 && x133 = x133 && x121 = x121 && x134 = x134 && x122 = x122 && x135 = x135 && x116 = x115 + x122 && x119 = x115 - x122 && x117 = x120 + x121 && x118 = x120 - x121 && x136 = x136 && x137 = x135 + x132 && x138 = x134 + x133 && x139 = x135 + x133 && x140 = x134 + x132 && x131 = x131 && x123 = x123 && x124 = x124 && x125 = x125 && x126 = x126 && x127 = x127 && x128 = x128 && x141 = x141 && x142 = x142 && x129 = x141 + x131 && x130 = x142 + x131 && x112 = -1 + x90 && x88 = x110 && x89 = x111 && x91 = x113 && x92 = x114
l2(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l0(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) :|: x164 = x186 && x163 = x185 && x162 = x184 && x161 = x183 && x160 = x182 && x159 = x181 && x158 = x180 && x157 = x179 && x156 = x178 && x155 = x177 && x154 = x176 && x153 = x175 && x152 = x174 && x151 = x173 && x150 = x172 && x149 = x171 && x148 = x170 && x147 = x169 && x146 = x168 && x145 = x167 && x144 = x166 && x143 = x165
l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) :|: x208 = x230 && x207 = x229 && x206 = x228 && x205 = x227 && x204 = x226 && x203 = x225 && x202 = x224 && x201 = x223 && x200 = x222 && x199 = x221 && x198 = x220 && x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209
l5(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l3(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) :|: x252 = x274 && x251 = x273 && x250 = x272 && x249 = x271 && x248 = x270 && x247 = x269 && x246 = x268 && x245 = x267 && x244 = x266 && x243 = x265 && x242 = x264 && x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253
l6(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l5(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) :|: x296 = x318 && x295 = x317 && x294 = x316 && x293 = x315 && x292 = x314 && x291 = x313 && x290 = x312 && x289 = x311 && x288 = x310 && x287 = x309 && x286 = x308 && x285 = x307 && x284 = x306 && x283 = x305 && x282 = x304 && x281 = x303 && x280 = x302 && x279 = x301 && x278 = x300 && x276 = x298 && x275 = x297 && x299 = x276 && 1 + x277 <= 0
l6(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l1(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: 0 <= x321 && x346 = x346 && x363 = x363 && x351 = x351 && x364 = x364 && x352 = x352 && x365 = x365 && x353 = x353 && x366 = x366 && x347 = x346 + x353 && x350 = x346 - x353 && x348 = x351 + x352 && x349 = x351 - x352 && x367 = x367 && x368 = x366 + x363 && x369 = x365 + x364 && x370 = x366 + x364 && x371 = x365 + x363 && x362 = x362 && x354 = x354 && x355 = x355 && x356 = x356 && x357 = x357 && x358 = x358 && x359 = x359 && x372 = x372 && x373 = x373 && x360 = x372 + x362 && x361 = x373 + x362 && x343 = -1 + x321 && x319 = x341 && x320 = x342 && x322 = x344 && x323 = x345
l7(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) -> l2(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x395 = x417 && x394 = x416 && x393 = x415 && x392 = x414 && x391 = x413 && x390 = x412 && x389 = x411 && x388 = x410 && x387 = x409 && x386 = x408 && x385 = x407 && x384 = x406 && x383 = x405 && x382 = x404 && x381 = x403 && x380 = x402 && x379 = x401 && x376 = x398 && x375 = x397 && x374 = x396 && x399 = 0 && x400 = 0
l8(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) -> l7(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x439 = x461 && x438 = x460 && x437 = x459 && x436 = x458 && x435 = x457 && x434 = x456 && x433 = x455 && x432 = x454 && x431 = x453 && x430 = x452 && x429 = x451 && x428 = x450 && x427 = x449 && x426 = x448 && x425 = x447 && x424 = x446 && x423 = x445 && x422 = x444 && x421 = x443 && x420 = x442 && x419 = x441 && x418 = x440
Start term: l8(__const_64HAT0, __const_7HAT0, ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0)

----------------------------------------

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(__const_64HAT0, __const_7HAT0, ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0) -> l1(__const_64HATpost, __const_7HATpost, ctr23HATpost, iHATpost, seedHATpost, tmp05HATpost, tmp1013HATpost, tmp1114HATpost, tmp1215HATpost, tmp1316HATpost, tmp16HATpost, tmp27HATpost, tmp38HATpost, tmp49HATpost, tmp510HATpost, tmp611HATpost, tmp712HATpost, z117HATpost, z218HATpost, z319HATpost, z420HATpost, z521HATpost) :|: z521HAT0 = z521HATpost && z420HAT0 = z420HATpost && z319HAT0 = z319HATpost && z218HAT0 = z218HATpost && z117HAT0 = z117HATpost && tmp712HAT0 = tmp712HATpost && tmp611HAT0 = tmp611HATpost && tmp510HAT0 = tmp510HATpost && tmp49HAT0 = tmp49HATpost && tmp38HAT0 = tmp38HATpost && tmp27HAT0 = tmp27HATpost && tmp16HAT0 = tmp16HATpost && tmp1316HAT0 = tmp1316HATpost && tmp1215HAT0 = tmp1215HATpost && tmp1114HAT0 = tmp1114HATpost && tmp1013HAT0 = tmp1013HATpost && tmp05HAT0 = tmp05HATpost && seedHAT0 = seedHATpost && iHAT0 = iHATpost && __const_7HAT0 = __const_7HATpost && __const_64HAT0 = __const_64HATpost && ctr23HATpost = __const_7HAT0 && __const_64HAT0 <= iHAT0
(2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x21 = x43 && x20 = x42 && x19 = x41 && x18 = x40 && x17 = x39 && x16 = x38 && x15 = x37 && x14 = x36 && x13 = x35 && x12 = x34 && x11 = x33 && x10 = x32 && x9 = x31 && x8 = x30 && x7 = x29 && x6 = x28 && x5 = x27 && x2 = x24 && x1 = x23 && x = x22 && x25 = 1 + x3 && x26 = x26 && 1 + x3 <= x
(3) l3(x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) -> l4(x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87) :|: x65 = x87 && x64 = x86 && x63 = x85 && x62 = x84 && x61 = x83 && x60 = x82 && x59 = x81 && x58 = x80 && x57 = x79 && x56 = x78 && x55 = x77 && x54 = x76 && x53 = x75 && x52 = x74 && x51 = x73 && x50 = x72 && x49 = x71 && x48 = x70 && x47 = x69 && x46 = x68 && x45 = x67 && x44 = x66 && 1 + x46 <= 0
(4) l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l5(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: 0 <= x90 && x115 = x115 && x132 = x132 && x120 = x120 && x133 = x133 && x121 = x121 && x134 = x134 && x122 = x122 && x135 = x135 && x116 = x115 + x122 && x119 = x115 - x122 && x117 = x120 + x121 && x118 = x120 - x121 && x136 = x136 && x137 = x135 + x132 && x138 = x134 + x133 && x139 = x135 + x133 && x140 = x134 + x132 && x131 = x131 && x123 = x123 && x124 = x124 && x125 = x125 && x126 = x126 && x127 = x127 && x128 = x128 && x141 = x141 && x142 = x142 && x129 = x141 + x131 && x130 = x142 + x131 && x112 = -1 + x90 && x88 = x110 && x89 = x111 && x91 = x113 && x92 = x114
(5) l2(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l0(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) :|: x164 = x186 && x163 = x185 && x162 = x184 && x161 = x183 && x160 = x182 && x159 = x181 && x158 = x180 && x157 = x179 && x156 = x178 && x155 = x177 && x154 = x176 && x153 = x175 && x152 = x174 && x151 = x173 && x150 = x172 && x149 = x171 && x148 = x170 && x147 = x169 && x146 = x168 && x145 = x167 && x144 = x166 && x143 = x165
(6) l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) :|: x208 = x230 && x207 = x229 && x206 = x228 && x205 = x227 && x204 = x226 && x203 = x225 && x202 = x224 && x201 = x223 && x200 = x222 && x199 = x221 && x198 = x220 && x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209
(7) l5(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l3(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) :|: x252 = x274 && x251 = x273 && x250 = x272 && x249 = x271 && x248 = x270 && x247 = x269 && x246 = x268 && x245 = x267 && x244 = x266 && x243 = x265 && x242 = x264 && x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253
(8) l6(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l5(x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318) :|: x296 = x318 && x295 = x317 && x294 = x316 && x293 = x315 && x292 = x314 && x291 = x313 && x290 = x312 && x289 = x311 && x288 = x310 && x287 = x309 && x286 = x308 && x285 = x307 && x284 = x306 && x283 = x305 && x282 = x304 && x281 = x303 && x280 = x302 && x279 = x301 && x278 = x300 && x276 = x298 && x275 = x297 && x299 = x276 && 1 + x277 <= 0
(9) l6(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l1(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: 0 <= x321 && x346 = x346 && x363 = x363 && x351 = x351 && x364 = x364 && x352 = x352 && x365 = x365 && x353 = x353 && x366 = x366 && x347 = x346 + x353 && x350 = x346 - x353 && x348 = x351 + x352 && x349 = x351 - x352 && x367 = x367 && x368 = x366 + x363 && x369 = x365 + x364 && x370 = x366 + x364 && x371 = x365 + x363 && x362 = x362 && x354 = x354 && x355 = x355 && x356 = x356 && x357 = x357 && x358 = x358 && x359 = x359 && x372 = x372 && x373 = x373 && x360 = x372 + x362 && x361 = x373 + x362 && x343 = -1 + x321 && x319 = x341 && x320 = x342 && x322 = x344 && x323 = x345
(10) l7(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) -> l2(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) :|: x395 = x417 && x394 = x416 && x393 = x415 && x392 = x414 && x391 = x413 && x390 = x412 && x389 = x411 && x388 = x410 && x387 = x409 && x386 = x408 && x385 = x407 && x384 = x406 && x383 = x405 && x382 = x404 && x381 = x403 && x380 = x402 && x379 = x401 && x376 = x398 && x375 = x397 && x374 = x396 && x399 = 0 && x400 = 0
(11) l8(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) -> l7(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461) :|: x439 = x461 && x438 = x460 && x437 = x459 && x436 = x458 && x435 = x457 && x434 = x456 && x433 = x455 && x432 = x454 && x431 = x453 && x430 = x452 && x429 = x451 && x428 = x450 && x427 = x449 && x426 = x448 && x425 = x447 && x424 = x446 && x423 = x445 && x422 = x444 && x421 = x443 && x420 = x442 && x419 = x441 && x418 = x440

Arcs:
(1) -> (6)
(2) -> (5)
(4) -> (7)
(5) -> (1), (2)
(6) -> (8), (9)
(7) -> (3), (4)
(8) -> (7)
(9) -> (6)
(10) -> (5)
(11) -> (10)

This digraph is fully evaluated!
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(4)
Complex Obligation (AND)

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(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> l2(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x21 = x43 && x20 = x42 && x19 = x41 && x18 = x40 && x17 = x39 && x16 = x38 && x15 = x37 && x14 = x36 && x13 = x35 && x12 = x34 && x11 = x33 && x10 = x32 && x9 = x31 && x8 = x30 && x7 = x29 && x6 = x28 && x5 = x27 && x2 = x24 && x1 = x23 && x = x22 && x25 = 1 + x3 && x26 = x26 && 1 + x3 <= x
(2) l2(x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l0(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) :|: x164 = x186 && x163 = x185 && x162 = x184 && x161 = x183 && x160 = x182 && x159 = x181 && x158 = x180 && x157 = x179 && x156 = x178 && x155 = x177 && x154 = x176 && x153 = x175 && x152 = x174 && x151 = x173 && x150 = x172 && x149 = x171 && x148 = x170 && x147 = x169 && x146 = x168 && x145 = x167 && x144 = x166 && x143 = x165

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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(6) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(7)
Obligation:
Rules:
l0(x165:0, x166:0, x167:0, x3:0, x4:0, x170:0, x171:0, x172:0, x173:0, x174:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0, x183:0, x184:0, x185:0, x186:0) -> l0(x165:0, x166:0, x167:0, 1 + x3:0, x169:0, x170:0, x171:0, x172:0, x173:0, x174:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0, x183:0, x184:0, x185:0, x186:0) :|: x165:0 >= 1 + x3:0

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(8) 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, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> l0(x1, x4)

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(9)
Obligation:
Rules:
l0(x165:0, x3:0) -> l0(x165:0, 1 + x3:0) :|: x165:0 >= 1 + x3:0

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
l0(x165:0, x3:0) -> l0(x165:0, c) :|: c = 1 + x3:0 && x165:0 >= 1 + x3:0

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l0(x, x1)] = x - x1

The following rules are decreasing:
l0(x165:0, x3:0) -> l0(x165:0, c) :|: c = 1 + x3:0 && x165:0 >= 1 + x3:0
The following rules are bounded:
l0(x165:0, x3:0) -> l0(x165:0, c) :|: c = 1 + x3:0 && x165:0 >= 1 + x3:0

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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208) -> l6(x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) :|: x208 = x230 && x207 = x229 && x206 = x228 && x205 = x227 && x204 = x226 && x203 = x225 && x202 = x224 && x201 = x223 && x200 = x222 && x199 = x221 && x198 = x220 && x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209
(2) l6(x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l1(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: 0 <= x321 && x346 = x346 && x363 = x363 && x351 = x351 && x364 = x364 && x352 = x352 && x365 = x365 && x353 = x353 && x366 = x366 && x347 = x346 + x353 && x350 = x346 - x353 && x348 = x351 + x352 && x349 = x351 - x352 && x367 = x367 && x368 = x366 + x363 && x369 = x365 + x364 && x370 = x366 + x364 && x371 = x365 + x363 && x362 = x362 && x354 = x354 && x355 = x355 && x356 = x356 && x357 = x357 && x358 = x358 && x359 = x359 && x372 = x372 && x373 = x373 && x360 = x372 + x362 && x361 = x373 + x362 && x343 = -1 + x321 && x319 = x341 && x320 = x342 && x322 = x344 && x323 = x345

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
l1(x187:0, x188:0, x189:0, x190:0, x191:0, x192:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0, x200:0, x201:0, x202:0, x203:0, x204:0, x205:0, x206:0, x207:0, x208:0) -> l1(x187:0, x188:0, -1 + x189:0, x190:0, x191:0, x346:0, x346:0 + x353:0, x351:0 + x352:0, x351:0 - x352:0, x346:0 - x353:0, x351:0, x352:0, x353:0, x354:0, x355:0, x356:0, x357:0, x358:0, x359:0, x372:0 + x362:0, x373:0 + x362:0, x362:0) :|: x189:0 > -1

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(17) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   l1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> l1(x3)

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(18)
Obligation:
Rules:
l1(x189:0) -> l1(-1 + x189:0) :|: x189:0 > -1

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l1(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(20)
Obligation:
Rules:
l1(x189:0) -> l1(c) :|: c = -1 + x189:0 && x189:0 > -1

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l1(x)] = x

The following rules are decreasing:
l1(x189:0) -> l1(c) :|: c = -1 + x189:0 && x189:0 > -1
The following rules are bounded:
l1(x189:0) -> l1(c) :|: c = -1 + x189:0 && x189:0 > -1

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(22)
YES

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(23)
Obligation:

Termination digraph:
Nodes:
(1) l5(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252) -> l3(x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) :|: x252 = x274 && x251 = x273 && x250 = x272 && x249 = x271 && x248 = x270 && x247 = x269 && x246 = x268 && x245 = x267 && x244 = x266 && x243 = x265 && x242 = x264 && x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253
(2) l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l5(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: 0 <= x90 && x115 = x115 && x132 = x132 && x120 = x120 && x133 = x133 && x121 = x121 && x134 = x134 && x122 = x122 && x135 = x135 && x116 = x115 + x122 && x119 = x115 - x122 && x117 = x120 + x121 && x118 = x120 - x121 && x136 = x136 && x137 = x135 + x132 && x138 = x134 + x133 && x139 = x135 + x133 && x140 = x134 + x132 && x131 = x131 && x123 = x123 && x124 = x124 && x125 = x125 && x126 = x126 && x127 = x127 && x128 = x128 && x141 = x141 && x142 = x142 && x129 = x141 + x131 && x130 = x142 + x131 && x112 = -1 + x90 && x88 = x110 && x89 = x111 && x91 = x113 && x92 = x114

Arcs:
(1) -> (2)
(2) -> (1)

This digraph is fully evaluated!

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(24) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(25)
Obligation:
Rules:
l5(x110:0, x111:0, x233:0, x113:0, x114:0, x236:0, x237:0, x238:0, x239:0, x240:0, x241:0, x242:0, x243:0, x244:0, x245:0, x246:0, x247:0, x248:0, x249:0, x250:0, x251:0, x252:0) -> l5(x110:0, x111:0, -1 + x233:0, x113:0, x114:0, x115:0, x115:0 + x122:0, x120:0 + x121:0, x120:0 - x121:0, x115:0 - x122:0, x120:0, x121:0, x122:0, x123:0, x124:0, x125:0, x126:0, x127:0, x128:0, x141:0 + x131:0, x142:0 + x131:0, x131:0) :|: x233:0 > -1

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(26) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:

   l5(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> l5(x3)

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(27)
Obligation:
Rules:
l5(x233:0) -> l5(-1 + x233:0) :|: x233:0 > -1

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(28) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l5(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
l5(x233:0) -> l5(c) :|: c = -1 + x233:0 && x233:0 > -1

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(30) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l5 ] = l5_1

The following rules are decreasing:
l5(x233:0) -> l5(c) :|: c = -1 + x233:0 && x233:0 > -1

The following rules are bounded:
l5(x233:0) -> l5(c) :|: c = -1 + x233:0 && x233:0 > -1


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(31)
YES