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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 6288 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 4 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 21 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 1 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 10 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 3 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) TempFilterProof [SOUND, 23 ms]
        (29) IntTRS
        (30) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (31) YES


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

(0)
Obligation:
Rules:
l0(nNHAT0, nPow___010HAT0, nPow___015HAT0, nPow___020HAT0, naHAT0, nbHAT0, ncHAT0, ni11HAT0, ni16HAT0, ni21HAT0, np14HAT0, np19HAT0, np9HAT0, nx13HAT0, nx18HAT0, nx8HAT0, ret_nPow12HAT0, ret_nPow17HAT0, ret_nPow22HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nNHATpost, nPow___010HATpost, nPow___015HATpost, nPow___020HATpost, naHATpost, nbHATpost, ncHATpost, ni11HATpost, ni16HATpost, ni21HATpost, np14HATpost, np19HATpost, np9HATpost, nx13HATpost, nx18HATpost, nx8HATpost, ret_nPow12HATpost, ret_nPow17HATpost, ret_nPow22HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && ret_nPow22HAT0 = ret_nPow22HATpost && ret_nPow17HAT0 = ret_nPow17HATpost && ret_nPow12HAT0 = ret_nPow12HATpost && nx8HAT0 = nx8HATpost && nx18HAT0 = nx18HATpost && nx13HAT0 = nx13HATpost && np9HAT0 = np9HATpost && np19HAT0 = np19HATpost && np14HAT0 = np14HATpost && ni21HAT0 = ni21HATpost && ni16HAT0 = ni16HATpost && ni11HAT0 = ni11HATpost && ncHAT0 = ncHATpost && nbHAT0 = nbHATpost && naHAT0 = naHATpost && nPow___020HAT0 = nPow___020HATpost && nPow___015HAT0 = nPow___015HATpost && nPow___010HAT0 = nPow___010HATpost && nNHAT0 = nNHATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> l3(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x20 = x42 && x19 = x41 && 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 && x4 = x26 && x3 = x25 && x2 = x24 && x1 = x23 && x = x22 && x43 = x40 && x40 = x3 && x11 <= x9
l2(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 && x52 = x74 && x51 = x73 && x50 = x72 && x49 = x71 && x48 = x70 && x46 = x68 && x45 = x67 && x44 = x66 && x75 = 1 + x53 && x69 = x69 && 1 + x53 <= x55
l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l6(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x109 = x131 && x108 = x130 && x107 = x129 && x106 = x128 && x105 = x127 && x104 = x126 && x103 = x125 && x102 = x124 && x101 = x123 && x100 = x122 && x99 = x121 && x98 = x120 && x97 = x119 && x96 = x118 && x95 = x117 && x94 = x116 && x93 = x115 && x92 = x114 && x91 = x113 && x90 = x112 && x89 = x111 && x88 = x110
l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) -> l4(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x153 = x175 && x151 = x173 && x150 = x172 && x148 = x170 && x147 = x169 && x145 = x167 && x144 = x166 && x142 = x164 && x140 = x162 && x139 = x161 && x138 = x160 && x137 = x159 && x136 = x158 && x134 = x156 && x133 = x155 && x132 = x154 && x163 = 0 && x157 = 1 && x165 = x132 && x168 = x138 && x174 = x171 && x171 = x134 && x142 <= x140
l6(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) -> l5(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209 && x186 = x208 && x185 = x207 && x183 = x205 && x182 = x204 && x181 = x203 && x180 = x202 && x179 = x201 && x177 = x199 && x176 = x198 && x206 = 1 + x184 && x200 = x200 && 1 + x184 <= x186
l4(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) -> l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253 && x230 = x252 && x229 = x251 && x228 = x250 && x227 = x249 && x226 = x248 && x225 = x247 && x224 = x246 && x223 = x245 && x222 = x244 && x221 = x243 && x220 = x242
l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) -> l5(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x285 = x307 && x284 = x306 && x282 = x304 && x281 = x303 && x279 = x301 && x278 = x300 && x276 = x298 && x275 = x297 && x273 = x295 && x271 = x293 && x270 = x292 && x269 = x291 && x268 = x290 && x267 = x289 && x265 = x287 && x264 = x286 && x294 = 0 && x288 = 1 && x296 = x264 && x299 = x269 && x305 = x302 && x302 = x265 && x276 <= x271
l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l0(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x329 = x351 && x328 = x350 && x327 = x349 && x326 = x348 && x325 = x347 && x324 = x346 && x323 = x345 && x322 = x344 && x321 = x343 && x320 = x342 && x319 = x341 && x318 = x340 && x317 = x339 && x316 = x338 && x314 = x336 && x313 = x335 && x312 = x334 && x311 = x333 && x310 = x332 && x308 = x330 && x337 = 1 + x315 && x331 = x331 && 1 + x315 <= x320
l7(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) -> l0(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x373 = x395 && x372 = x394 && x371 = x393 && x370 = x392 && x369 = x391 && x368 = x390 && x366 = x388 && x365 = x387 && x363 = x385 && x362 = x384 && x361 = x383 && x360 = x382 && x358 = x380 && x357 = x379 && x356 = x378 && x355 = x377 && x354 = x376 && x381 = 0 && x375 = 1 && x386 = x374 && x389 = x356 && x374 = 3
l8(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) -> l7(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x417 = x439 && x416 = x438 && x415 = x437 && x414 = x436 && x413 = x435 && x412 = x434 && x411 = x433 && x410 = x432 && x409 = x431 && x408 = x430 && x407 = x429 && x406 = x428 && x405 = x427 && x404 = x426 && x403 = x425 && x402 = x424 && x401 = x423 && x400 = x422 && x399 = x421 && x398 = x420 && x397 = x419 && x396 = x418
Start term: l8(nNHAT0, nPow___010HAT0, nPow___015HAT0, nPow___020HAT0, naHAT0, nbHAT0, ncHAT0, ni11HAT0, ni16HAT0, ni21HAT0, np14HAT0, np19HAT0, np9HAT0, nx13HAT0, nx18HAT0, nx8HAT0, ret_nPow12HAT0, ret_nPow17HAT0, ret_nPow22HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0)

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

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

(2)
Obligation:
Rules:
l0(nNHAT0, nPow___010HAT0, nPow___015HAT0, nPow___020HAT0, naHAT0, nbHAT0, ncHAT0, ni11HAT0, ni16HAT0, ni21HAT0, np14HAT0, np19HAT0, np9HAT0, nx13HAT0, nx18HAT0, nx8HAT0, ret_nPow12HAT0, ret_nPow17HAT0, ret_nPow22HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nNHATpost, nPow___010HATpost, nPow___015HATpost, nPow___020HATpost, naHATpost, nbHATpost, ncHATpost, ni11HATpost, ni16HATpost, ni21HATpost, np14HATpost, np19HATpost, np9HATpost, nx13HATpost, nx18HATpost, nx8HATpost, ret_nPow12HATpost, ret_nPow17HATpost, ret_nPow22HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && ret_nPow22HAT0 = ret_nPow22HATpost && ret_nPow17HAT0 = ret_nPow17HATpost && ret_nPow12HAT0 = ret_nPow12HATpost && nx8HAT0 = nx8HATpost && nx18HAT0 = nx18HATpost && nx13HAT0 = nx13HATpost && np9HAT0 = np9HATpost && np19HAT0 = np19HATpost && np14HAT0 = np14HATpost && ni21HAT0 = ni21HATpost && ni16HAT0 = ni16HATpost && ni11HAT0 = ni11HATpost && ncHAT0 = ncHATpost && nbHAT0 = nbHATpost && naHAT0 = naHATpost && nPow___020HAT0 = nPow___020HATpost && nPow___015HAT0 = nPow___015HATpost && nPow___010HAT0 = nPow___010HATpost && nNHAT0 = nNHATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> l3(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x20 = x42 && x19 = x41 && 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 && x4 = x26 && x3 = x25 && x2 = x24 && x1 = x23 && x = x22 && x43 = x40 && x40 = x3 && x11 <= x9
l2(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 && x52 = x74 && x51 = x73 && x50 = x72 && x49 = x71 && x48 = x70 && x46 = x68 && x45 = x67 && x44 = x66 && x75 = 1 + x53 && x69 = x69 && 1 + x53 <= x55
l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l6(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x109 = x131 && x108 = x130 && x107 = x129 && x106 = x128 && x105 = x127 && x104 = x126 && x103 = x125 && x102 = x124 && x101 = x123 && x100 = x122 && x99 = x121 && x98 = x120 && x97 = x119 && x96 = x118 && x95 = x117 && x94 = x116 && x93 = x115 && x92 = x114 && x91 = x113 && x90 = x112 && x89 = x111 && x88 = x110
l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) -> l4(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x153 = x175 && x151 = x173 && x150 = x172 && x148 = x170 && x147 = x169 && x145 = x167 && x144 = x166 && x142 = x164 && x140 = x162 && x139 = x161 && x138 = x160 && x137 = x159 && x136 = x158 && x134 = x156 && x133 = x155 && x132 = x154 && x163 = 0 && x157 = 1 && x165 = x132 && x168 = x138 && x174 = x171 && x171 = x134 && x142 <= x140
l6(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) -> l5(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209 && x186 = x208 && x185 = x207 && x183 = x205 && x182 = x204 && x181 = x203 && x180 = x202 && x179 = x201 && x177 = x199 && x176 = x198 && x206 = 1 + x184 && x200 = x200 && 1 + x184 <= x186
l4(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) -> l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253 && x230 = x252 && x229 = x251 && x228 = x250 && x227 = x249 && x226 = x248 && x225 = x247 && x224 = x246 && x223 = x245 && x222 = x244 && x221 = x243 && x220 = x242
l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) -> l5(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x285 = x307 && x284 = x306 && x282 = x304 && x281 = x303 && x279 = x301 && x278 = x300 && x276 = x298 && x275 = x297 && x273 = x295 && x271 = x293 && x270 = x292 && x269 = x291 && x268 = x290 && x267 = x289 && x265 = x287 && x264 = x286 && x294 = 0 && x288 = 1 && x296 = x264 && x299 = x269 && x305 = x302 && x302 = x265 && x276 <= x271
l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l0(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x329 = x351 && x328 = x350 && x327 = x349 && x326 = x348 && x325 = x347 && x324 = x346 && x323 = x345 && x322 = x344 && x321 = x343 && x320 = x342 && x319 = x341 && x318 = x340 && x317 = x339 && x316 = x338 && x314 = x336 && x313 = x335 && x312 = x334 && x311 = x333 && x310 = x332 && x308 = x330 && x337 = 1 + x315 && x331 = x331 && 1 + x315 <= x320
l7(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) -> l0(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x373 = x395 && x372 = x394 && x371 = x393 && x370 = x392 && x369 = x391 && x368 = x390 && x366 = x388 && x365 = x387 && x363 = x385 && x362 = x384 && x361 = x383 && x360 = x382 && x358 = x380 && x357 = x379 && x356 = x378 && x355 = x377 && x354 = x376 && x381 = 0 && x375 = 1 && x386 = x374 && x389 = x356 && x374 = 3
l8(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) -> l7(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x417 = x439 && x416 = x438 && x415 = x437 && x414 = x436 && x413 = x435 && x412 = x434 && x411 = x433 && x410 = x432 && x409 = x431 && x408 = x430 && x407 = x429 && x406 = x428 && x405 = x427 && x404 = x426 && x403 = x425 && x402 = x424 && x401 = x423 && x400 = x422 && x399 = x421 && x398 = x420 && x397 = x419 && x396 = x418
Start term: l8(nNHAT0, nPow___010HAT0, nPow___015HAT0, nPow___020HAT0, naHAT0, nbHAT0, ncHAT0, ni11HAT0, ni16HAT0, ni21HAT0, np14HAT0, np19HAT0, np9HAT0, nx13HAT0, nx18HAT0, nx8HAT0, ret_nPow12HAT0, ret_nPow17HAT0, ret_nPow22HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(nNHAT0, nPow___010HAT0, nPow___015HAT0, nPow___020HAT0, naHAT0, nbHAT0, ncHAT0, ni11HAT0, ni16HAT0, ni21HAT0, np14HAT0, np19HAT0, np9HAT0, nx13HAT0, nx18HAT0, nx8HAT0, ret_nPow12HAT0, ret_nPow17HAT0, ret_nPow22HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nNHATpost, nPow___010HATpost, nPow___015HATpost, nPow___020HATpost, naHATpost, nbHATpost, ncHATpost, ni11HATpost, ni16HATpost, ni21HATpost, np14HATpost, np19HATpost, np9HATpost, nx13HATpost, nx18HATpost, nx8HATpost, ret_nPow12HATpost, ret_nPow17HATpost, ret_nPow22HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && ret_nPow22HAT0 = ret_nPow22HATpost && ret_nPow17HAT0 = ret_nPow17HATpost && ret_nPow12HAT0 = ret_nPow12HATpost && nx8HAT0 = nx8HATpost && nx18HAT0 = nx18HATpost && nx13HAT0 = nx13HATpost && np9HAT0 = np9HATpost && np19HAT0 = np19HATpost && np14HAT0 = np14HATpost && ni21HAT0 = ni21HATpost && ni16HAT0 = ni16HATpost && ni11HAT0 = ni11HATpost && ncHAT0 = ncHATpost && nbHAT0 = nbHATpost && naHAT0 = naHATpost && nPow___020HAT0 = nPow___020HATpost && nPow___015HAT0 = nPow___015HATpost && nPow___010HAT0 = nPow___010HATpost && nNHAT0 = nNHATpost
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21) -> l3(x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43) :|: x20 = x42 && x19 = x41 && 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 && x4 = x26 && x3 = x25 && x2 = x24 && x1 = x23 && x = x22 && x43 = x40 && x40 = x3 && x11 <= x9
(3) l2(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 && x52 = x74 && x51 = x73 && x50 = x72 && x49 = x71 && x48 = x70 && x46 = x68 && x45 = x67 && x44 = x66 && x75 = 1 + x53 && x69 = x69 && 1 + x53 <= x55
(4) l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l6(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x109 = x131 && x108 = x130 && x107 = x129 && x106 = x128 && x105 = x127 && x104 = x126 && x103 = x125 && x102 = x124 && x101 = x123 && x100 = x122 && x99 = x121 && x98 = x120 && x97 = x119 && x96 = x118 && x95 = x117 && x94 = x116 && x93 = x115 && x92 = x114 && x91 = x113 && x90 = x112 && x89 = x111 && x88 = x110
(5) l6(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) -> l4(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175) :|: x153 = x175 && x151 = x173 && x150 = x172 && x148 = x170 && x147 = x169 && x145 = x167 && x144 = x166 && x142 = x164 && x140 = x162 && x139 = x161 && x138 = x160 && x137 = x159 && x136 = x158 && x134 = x156 && x133 = x155 && x132 = x154 && x163 = 0 && x157 = 1 && x165 = x132 && x168 = x138 && x174 = x171 && x171 = x134 && x142 <= x140
(6) l6(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) -> l5(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209 && x186 = x208 && x185 = x207 && x183 = x205 && x182 = x204 && x181 = x203 && x180 = x202 && x179 = x201 && x177 = x199 && x176 = x198 && x206 = 1 + x184 && x200 = x200 && 1 + x184 <= x186
(7) l4(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) -> l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253 && x230 = x252 && x229 = x251 && x228 = x250 && x227 = x249 && x226 = x248 && x225 = x247 && x224 = x246 && x223 = x245 && x222 = x244 && x221 = x243 && x220 = x242
(8) l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285) -> l5(x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x285 = x307 && x284 = x306 && x282 = x304 && x281 = x303 && x279 = x301 && x278 = x300 && x276 = x298 && x275 = x297 && x273 = x295 && x271 = x293 && x270 = x292 && x269 = x291 && x268 = x290 && x267 = x289 && x265 = x287 && x264 = x286 && x294 = 0 && x288 = 1 && x296 = x264 && x299 = x269 && x305 = x302 && x302 = x265 && x276 <= x271
(9) l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l0(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x329 = x351 && x328 = x350 && x327 = x349 && x326 = x348 && x325 = x347 && x324 = x346 && x323 = x345 && x322 = x344 && x321 = x343 && x320 = x342 && x319 = x341 && x318 = x340 && x317 = x339 && x316 = x338 && x314 = x336 && x313 = x335 && x312 = x334 && x311 = x333 && x310 = x332 && x308 = x330 && x337 = 1 + x315 && x331 = x331 && 1 + x315 <= x320
(10) l7(x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) -> l0(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x373 = x395 && x372 = x394 && x371 = x393 && x370 = x392 && x369 = x391 && x368 = x390 && x366 = x388 && x365 = x387 && x363 = x385 && x362 = x384 && x361 = x383 && x360 = x382 && x358 = x380 && x357 = x379 && x356 = x378 && x355 = x377 && x354 = x376 && x381 = 0 && x375 = 1 && x386 = x374 && x389 = x356 && x374 = 3
(11) l8(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417) -> l7(x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x417 = x439 && x416 = x438 && x415 = x437 && x414 = x436 && x413 = x435 && x412 = x434 && x411 = x433 && x410 = x432 && x409 = x431 && x408 = x430 && x407 = x429 && x406 = x428 && x405 = x427 && x404 = x426 && x403 = x425 && x402 = x424 && x401 = x423 && x400 = x422 && x399 = x421 && x398 = x420 && x397 = x419 && x396 = x418

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

This digraph is fully evaluated!
----------------------------------------

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(nNHAT0, nPow___010HAT0, nPow___015HAT0, nPow___020HAT0, naHAT0, nbHAT0, ncHAT0, ni11HAT0, ni16HAT0, ni21HAT0, np14HAT0, np19HAT0, np9HAT0, nx13HAT0, nx18HAT0, nx8HAT0, ret_nPow12HAT0, ret_nPow17HAT0, ret_nPow22HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0) -> l1(nNHATpost, nPow___010HATpost, nPow___015HATpost, nPow___020HATpost, naHATpost, nbHATpost, ncHATpost, ni11HATpost, ni16HATpost, ni21HATpost, np14HATpost, np19HATpost, np9HATpost, nx13HATpost, nx18HATpost, nx8HATpost, ret_nPow12HATpost, ret_nPow17HATpost, ret_nPow22HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost) :|: tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && ret_nPow22HAT0 = ret_nPow22HATpost && ret_nPow17HAT0 = ret_nPow17HATpost && ret_nPow12HAT0 = ret_nPow12HATpost && nx8HAT0 = nx8HATpost && nx18HAT0 = nx18HATpost && nx13HAT0 = nx13HATpost && np9HAT0 = np9HATpost && np19HAT0 = np19HATpost && np14HAT0 = np14HATpost && ni21HAT0 = ni21HATpost && ni16HAT0 = ni16HATpost && ni11HAT0 = ni11HATpost && ncHAT0 = ncHATpost && nbHAT0 = nbHATpost && naHAT0 = naHATpost && nPow___020HAT0 = nPow___020HATpost && nPow___015HAT0 = nPow___015HATpost && nPow___010HAT0 = nPow___010HATpost && nNHAT0 = nNHATpost
(2) l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) -> l0(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351) :|: x329 = x351 && x328 = x350 && x327 = x349 && x326 = x348 && x325 = x347 && x324 = x346 && x323 = x345 && x322 = x344 && x321 = x343 && x320 = x342 && x319 = x341 && x318 = x340 && x317 = x339 && x316 = x338 && x314 = x336 && x313 = x335 && x312 = x334 && x311 = x333 && x310 = x332 && x308 = x330 && x337 = 1 + x315 && x331 = x331 && 1 + x315 <= x320

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

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
l0(nNHAT0:0, nPow___010HAT0:0, nPow___015HAT0:0, nPow___020HAT0:0, naHAT0:0, nbHAT0:0, ncHAT0:0, ni11HAT0:0, ni16HAT0:0, ni21HAT0:0, np14HAT0:0, np19HAT0:0, np9HAT0:0, nx13HAT0:0, nx18HAT0:0, nx8HAT0:0, ret_nPow12HAT0:0, ret_nPow17HAT0:0, ret_nPow22HAT0:0, tmpHAT0:0, tmp___0HAT0:0, tmp___1HAT0:0) -> l0(nNHAT0:0, x331:0, nPow___015HAT0:0, nPow___020HAT0:0, naHAT0:0, nbHAT0:0, ncHAT0:0, 1 + ni11HAT0:0, ni16HAT0:0, ni21HAT0:0, np14HAT0:0, np19HAT0:0, np9HAT0:0, nx13HAT0:0, nx18HAT0:0, nx8HAT0:0, ret_nPow12HAT0:0, ret_nPow17HAT0:0, ret_nPow22HAT0:0, tmpHAT0:0, tmp___0HAT0:0, tmp___1HAT0:0) :|: np9HAT0:0 >= 1 + ni11HAT0:0

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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(x8, x13)

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(9)
Obligation:
Rules:
l0(ni11HAT0:0, np9HAT0:0) -> l0(1 + ni11HAT0:0, np9HAT0:0) :|: np9HAT0:0 >= 1 + ni11HAT0:0

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(11)
Obligation:
Rules:
l0(ni11HAT0:0, np9HAT0:0) -> l0(c, np9HAT0:0) :|: c = 1 + ni11HAT0:0 && np9HAT0:0 >= 1 + ni11HAT0:0

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(12) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l0 ] = l0_2 + -1*l0_1

The following rules are decreasing:
l0(ni11HAT0:0, np9HAT0:0) -> l0(c, np9HAT0:0) :|: c = 1 + ni11HAT0:0 && np9HAT0:0 >= 1 + ni11HAT0:0

The following rules are bounded:
l0(ni11HAT0:0, np9HAT0:0) -> l0(c, np9HAT0:0) :|: c = 1 + ni11HAT0:0 && np9HAT0:0 >= 1 + ni11HAT0:0


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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) l5(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l6(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) :|: x109 = x131 && x108 = x130 && x107 = x129 && x106 = x128 && x105 = x127 && x104 = x126 && x103 = x125 && x102 = x124 && x101 = x123 && x100 = x122 && x99 = x121 && x98 = x120 && x97 = x119 && x96 = x118 && x95 = x117 && x94 = x116 && x93 = x115 && x92 = x114 && x91 = x113 && x90 = x112 && x89 = x111 && x88 = x110
(2) l6(x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) -> l5(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: x197 = x219 && x196 = x218 && x195 = x217 && x194 = x216 && x193 = x215 && x192 = x214 && x191 = x213 && x190 = x212 && x189 = x211 && x188 = x210 && x187 = x209 && x186 = x208 && x185 = x207 && x183 = x205 && x182 = x204 && x181 = x203 && x180 = x202 && x179 = x201 && x177 = x199 && x176 = x198 && x206 = 1 + x184 && x200 = x200 && 1 + x184 <= x186

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

This digraph is fully evaluated!

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

(16)
Obligation:
Rules:
l5(x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0, x117:0, x118:0, x119:0, x120:0, x121:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0) -> l5(x110:0, x111:0, x200:0, x113:0, x114:0, x115:0, x116:0, x117:0, 1 + x118:0, x119:0, x120:0, x121:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0) :|: x120:0 >= 1 + x118:0

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(17) 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(x9, x11)

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(18)
Obligation:
Rules:
l5(x118:0, x120:0) -> l5(1 + x118:0, x120:0) :|: x120:0 >= 1 + x118:0

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

(20)
Obligation:
Rules:
l5(x118:0, x120:0) -> l5(c, x120:0) :|: c = 1 + x118:0 && x120:0 >= 1 + x118:0

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(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l5(x, x1)] = -x + x1

The following rules are decreasing:
l5(x118:0, x120:0) -> l5(c, x120:0) :|: c = 1 + x118:0 && x120:0 >= 1 + x118:0
The following rules are bounded:
l5(x118:0, x120:0) -> l5(c, x120:0) :|: c = 1 + x118:0 && x120:0 >= 1 + x118:0

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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) l4(x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) -> l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x241 = x263 && x240 = x262 && x239 = x261 && x238 = x260 && x237 = x259 && x236 = x258 && x235 = x257 && x234 = x256 && x233 = x255 && x232 = x254 && x231 = x253 && x230 = x252 && x229 = x251 && x228 = x250 && x227 = x249 && x226 = x248 && x225 = x247 && x224 = x246 && x223 = x245 && x222 = x244 && x221 = x243 && x220 = x242
(2) l2(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 && x52 = x74 && x51 = x73 && x50 = x72 && x49 = x71 && x48 = x70 && x46 = x68 && x45 = x67 && x44 = x66 && x75 = 1 + x53 && x69 = x69 && 1 + x53 <= x55

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

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
l4(x220:0, x221:0, x222:0, x223:0, x224:0, x225:0, x226:0, x227:0, x228:0, x229:0, x230:0, x231:0, x232:0, x233:0, x234:0, x235:0, x236:0, x237:0, x238:0, x239:0, x240:0, x241:0) -> l4(x220:0, x221:0, x222:0, x69:0, x224:0, x225:0, x226:0, x227:0, x228:0, 1 + x229:0, x230:0, x231:0, x232:0, x233:0, x234:0, x235:0, x236:0, x237:0, x238:0, x239:0, x240:0, x241:0) :|: x231:0 >= 1 + x229:0

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

   l4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22) -> l4(x10, x12)

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(27)
Obligation:
Rules:
l4(x229:0, x231:0) -> l4(1 + x229:0, x231:0) :|: x231:0 >= 1 + x229:0

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(28) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l4(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
l4(x229:0, x231:0) -> l4(c, x231:0) :|: c = 1 + x229:0 && x231:0 >= 1 + x229:0

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(30) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l4 ] = l4_2 + -1*l4_1

The following rules are decreasing:
l4(x229:0, x231:0) -> l4(c, x231:0) :|: c = 1 + x229:0 && x231:0 >= 1 + x229:0

The following rules are bounded:
l4(x229:0, x231:0) -> l4(c, x231:0) :|: c = 1 + x229:0 && x231:0 >= 1 + x229:0


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(31)
YES