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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 31.2 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 13 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 13 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 39 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 18 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES


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

(0)
Obligation:
Rules:
l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost) :|: oldX7HAT0 = oldX7HATpost && oldX6HAT0 = oldX6HATpost && oldX5HAT0 = oldX5HATpost && oldX4HAT0 = oldX4HATpost && x3HATpost = oldX3HATpost && x2HATpost = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && -1 + oldX3HATpost <= 0 && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = -1 + x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= -1 + x15 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8
l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 && x25 = x37 && x24 = x36
l3(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l1(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x71 = x64 && x70 = x62 && x69 = x61 && x68 = x60 && x62 <= 0 && x64 = x64 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56
l3(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l0(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x86 && x94 = x86 && x93 = x85 && x92 = x84 && 1 <= x86 && x87 = x83 && x86 = x82 && x85 = x81 && x84 = x80
l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) -> l5(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x103 = x115 && x102 = x114 && x101 = x113 && x119 = x112 && x118 = -8 + x110 && x117 = x109 && x116 = x108 && x112 = x112 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104
l5(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l3(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x143 = x136 && x142 = x134 && x141 = x133 && x140 = x132 && x134 <= 7 && x136 = x136 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128
l5(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l4(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x167 = x160 && x166 = x158 && x165 = x157 && x164 = x156 && 8 <= x158 && x160 = x160 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152
l6(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l5(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x191 = x184 && x190 = x181 && x189 = x181 && x188 = x180 && x184 = x184 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176
l7(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l8(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x215 = x211 && x214 = x210 && x213 = x209 && x212 = x208 && x211 = x211 && x210 = x210 && x209 = x209 && x208 = x208 && x207 = x203 && x206 = x202 && x205 = x201 && x204 = x200
l9(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l6(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x223 = x235 && x222 = x234 && x239 = x233 && x238 = x232 && x237 = x229 && x236 = x228 && x233 = x233 && x232 = x232 && x231 = x227 && x230 = x226 && x229 = x225 && x228 = x224
l9(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l7(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x247 = x259 && x246 = x258 && x263 = x257 && x262 = x256 && x261 = x253 && x260 = x252 && x257 = x257 && x256 = x256 && x255 = x251 && x254 = x250 && x253 = x249 && x252 = x248
l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275) -> l8(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x287 = x283 && x286 = x282 && x285 = x281 && x284 = x280 && x283 = x283 && x282 = x282 && x281 = x281 && x280 = x280 && x279 = x275 && x278 = x274 && x277 = x273 && x276 = x272
l10(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l9(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x295 = x307 && x294 = x306 && x311 = x305 && x310 = x304 && x309 = x301 && x308 = x300 && x305 = x305 && x304 = x304 && x303 = x299 && x302 = x298 && x301 = x297 && x300 = x296
l10(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l0(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x323 = x335 && x322 = x334 && x321 = x333 && x320 = x332 && x319 = x331 && x318 = x330 && x317 = x329 && x316 = x328 && x315 = x327 && x314 = x326 && x313 = x325 && x312 = x324
l10(x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347) -> l3(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x347 = x359 && x346 = x358 && x345 = x357 && x344 = x356 && x343 = x355 && x342 = x354 && x341 = x353 && x340 = x352 && x339 = x351 && x338 = x350 && x337 = x349 && x336 = x348
l10(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371) -> l4(x372, x373, x374, x375, x376, x377, x378, x379, x380, x381, x382, x383) :|: x371 = x383 && x370 = x382 && x369 = x381 && x368 = x380 && x367 = x379 && x366 = x378 && x365 = x377 && x364 = x376 && x363 = x375 && x362 = x374 && x361 = x373 && x360 = x372
l10(x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) -> l5(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407) :|: x395 = x407 && x394 = x406 && x393 = x405 && x392 = x404 && x391 = x403 && x390 = x402 && x389 = x401 && x388 = x400 && x387 = x399 && x386 = x398 && x385 = x397 && x384 = x396
l10(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l8(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x419 = x431 && x418 = x430 && x417 = x429 && x416 = x428 && x415 = x427 && x414 = x426 && x413 = x425 && x412 = x424 && x411 = x423 && x410 = x422 && x409 = x421 && x408 = x420
l10(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) -> l6(x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455) :|: x443 = x455 && x442 = x454 && x441 = x453 && x440 = x452 && x439 = x451 && x438 = x450 && x437 = x449 && x436 = x448 && x435 = x447 && x434 = x446 && x433 = x445 && x432 = x444
l10(x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) -> l7(x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x467 = x479 && x466 = x478 && x465 = x477 && x464 = x476 && x463 = x475 && x462 = x474 && x461 = x473 && x460 = x472 && x459 = x471 && x458 = x470 && x457 = x469 && x456 = x468
l10(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491) -> l9(x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503) :|: x491 = x503 && x490 = x502 && x489 = x501 && x488 = x500 && x487 = x499 && x486 = x498 && x485 = x497 && x484 = x496 && x483 = x495 && x482 = x494 && x481 = x493 && x480 = x492
l10(x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515) -> l1(x516, x517, x518, x519, x520, x521, x522, x523, x524, x525, x526, x527) :|: x515 = x527 && x514 = x526 && x513 = x525 && x512 = x524 && x511 = x523 && x510 = x522 && x509 = x521 && x508 = x520 && x507 = x519 && x506 = x518 && x505 = x517 && x504 = x516
l11(x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l10(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551) :|: x539 = x551 && x538 = x550 && x537 = x549 && x536 = x548 && x535 = x547 && x534 = x546 && x533 = x545 && x532 = x544 && x531 = x543 && x530 = x542 && x529 = x541 && x528 = x540
Start term: l11(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0)

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

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

(2)
Obligation:
Rules:
l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost) :|: oldX7HAT0 = oldX7HATpost && oldX6HAT0 = oldX6HATpost && oldX5HAT0 = oldX5HATpost && oldX4HAT0 = oldX4HATpost && x3HATpost = oldX3HATpost && x2HATpost = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && -1 + oldX3HATpost <= 0 && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = -1 + x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= -1 + x15 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8
l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 && x25 = x37 && x24 = x36
l3(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l1(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x71 = x64 && x70 = x62 && x69 = x61 && x68 = x60 && x62 <= 0 && x64 = x64 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56
l3(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l0(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x86 && x94 = x86 && x93 = x85 && x92 = x84 && 1 <= x86 && x87 = x83 && x86 = x82 && x85 = x81 && x84 = x80
l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) -> l5(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x103 = x115 && x102 = x114 && x101 = x113 && x119 = x112 && x118 = -8 + x110 && x117 = x109 && x116 = x108 && x112 = x112 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104
l5(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l3(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x143 = x136 && x142 = x134 && x141 = x133 && x140 = x132 && x134 <= 7 && x136 = x136 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128
l5(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l4(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x167 = x160 && x166 = x158 && x165 = x157 && x164 = x156 && 8 <= x158 && x160 = x160 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152
l6(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l5(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x191 = x184 && x190 = x181 && x189 = x181 && x188 = x180 && x184 = x184 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176
l7(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l8(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x215 = x211 && x214 = x210 && x213 = x209 && x212 = x208 && x211 = x211 && x210 = x210 && x209 = x209 && x208 = x208 && x207 = x203 && x206 = x202 && x205 = x201 && x204 = x200
l9(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l6(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x223 = x235 && x222 = x234 && x239 = x233 && x238 = x232 && x237 = x229 && x236 = x228 && x233 = x233 && x232 = x232 && x231 = x227 && x230 = x226 && x229 = x225 && x228 = x224
l9(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l7(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x247 = x259 && x246 = x258 && x263 = x257 && x262 = x256 && x261 = x253 && x260 = x252 && x257 = x257 && x256 = x256 && x255 = x251 && x254 = x250 && x253 = x249 && x252 = x248
l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275) -> l8(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x287 = x283 && x286 = x282 && x285 = x281 && x284 = x280 && x283 = x283 && x282 = x282 && x281 = x281 && x280 = x280 && x279 = x275 && x278 = x274 && x277 = x273 && x276 = x272
l10(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l9(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x295 = x307 && x294 = x306 && x311 = x305 && x310 = x304 && x309 = x301 && x308 = x300 && x305 = x305 && x304 = x304 && x303 = x299 && x302 = x298 && x301 = x297 && x300 = x296
l10(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l0(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x323 = x335 && x322 = x334 && x321 = x333 && x320 = x332 && x319 = x331 && x318 = x330 && x317 = x329 && x316 = x328 && x315 = x327 && x314 = x326 && x313 = x325 && x312 = x324
l10(x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347) -> l3(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x347 = x359 && x346 = x358 && x345 = x357 && x344 = x356 && x343 = x355 && x342 = x354 && x341 = x353 && x340 = x352 && x339 = x351 && x338 = x350 && x337 = x349 && x336 = x348
l10(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371) -> l4(x372, x373, x374, x375, x376, x377, x378, x379, x380, x381, x382, x383) :|: x371 = x383 && x370 = x382 && x369 = x381 && x368 = x380 && x367 = x379 && x366 = x378 && x365 = x377 && x364 = x376 && x363 = x375 && x362 = x374 && x361 = x373 && x360 = x372
l10(x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) -> l5(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407) :|: x395 = x407 && x394 = x406 && x393 = x405 && x392 = x404 && x391 = x403 && x390 = x402 && x389 = x401 && x388 = x400 && x387 = x399 && x386 = x398 && x385 = x397 && x384 = x396
l10(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l8(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x419 = x431 && x418 = x430 && x417 = x429 && x416 = x428 && x415 = x427 && x414 = x426 && x413 = x425 && x412 = x424 && x411 = x423 && x410 = x422 && x409 = x421 && x408 = x420
l10(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) -> l6(x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455) :|: x443 = x455 && x442 = x454 && x441 = x453 && x440 = x452 && x439 = x451 && x438 = x450 && x437 = x449 && x436 = x448 && x435 = x447 && x434 = x446 && x433 = x445 && x432 = x444
l10(x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) -> l7(x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x467 = x479 && x466 = x478 && x465 = x477 && x464 = x476 && x463 = x475 && x462 = x474 && x461 = x473 && x460 = x472 && x459 = x471 && x458 = x470 && x457 = x469 && x456 = x468
l10(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491) -> l9(x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503) :|: x491 = x503 && x490 = x502 && x489 = x501 && x488 = x500 && x487 = x499 && x486 = x498 && x485 = x497 && x484 = x496 && x483 = x495 && x482 = x494 && x481 = x493 && x480 = x492
l10(x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515) -> l1(x516, x517, x518, x519, x520, x521, x522, x523, x524, x525, x526, x527) :|: x515 = x527 && x514 = x526 && x513 = x525 && x512 = x524 && x511 = x523 && x510 = x522 && x509 = x521 && x508 = x520 && x507 = x519 && x506 = x518 && x505 = x517 && x504 = x516
l11(x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l10(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551) :|: x539 = x551 && x538 = x550 && x537 = x549 && x536 = x548 && x535 = x547 && x534 = x546 && x533 = x545 && x532 = x544 && x531 = x543 && x530 = x542 && x529 = x541 && x528 = x540
Start term: l11(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost) :|: oldX7HAT0 = oldX7HATpost && oldX6HAT0 = oldX6HATpost && oldX5HAT0 = oldX5HATpost && oldX4HAT0 = oldX4HATpost && x3HATpost = oldX3HATpost && x2HATpost = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && -1 + oldX3HATpost <= 0 && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
(2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = -1 + x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= -1 + x15 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8
(3) l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 && x25 = x37 && x24 = x36
(4) l3(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l1(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x71 = x64 && x70 = x62 && x69 = x61 && x68 = x60 && x62 <= 0 && x64 = x64 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56
(5) l3(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l0(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x86 && x94 = x86 && x93 = x85 && x92 = x84 && 1 <= x86 && x87 = x83 && x86 = x82 && x85 = x81 && x84 = x80
(6) l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) -> l5(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x103 = x115 && x102 = x114 && x101 = x113 && x119 = x112 && x118 = -8 + x110 && x117 = x109 && x116 = x108 && x112 = x112 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104
(7) l5(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l3(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x143 = x136 && x142 = x134 && x141 = x133 && x140 = x132 && x134 <= 7 && x136 = x136 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128
(8) l5(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l4(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x167 = x160 && x166 = x158 && x165 = x157 && x164 = x156 && 8 <= x158 && x160 = x160 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152
(9) l6(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l5(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x191 = x184 && x190 = x181 && x189 = x181 && x188 = x180 && x184 = x184 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176
(10) l7(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l8(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x215 = x211 && x214 = x210 && x213 = x209 && x212 = x208 && x211 = x211 && x210 = x210 && x209 = x209 && x208 = x208 && x207 = x203 && x206 = x202 && x205 = x201 && x204 = x200
(11) l9(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l6(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x223 = x235 && x222 = x234 && x239 = x233 && x238 = x232 && x237 = x229 && x236 = x228 && x233 = x233 && x232 = x232 && x231 = x227 && x230 = x226 && x229 = x225 && x228 = x224
(12) l9(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l7(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) :|: x247 = x259 && x246 = x258 && x263 = x257 && x262 = x256 && x261 = x253 && x260 = x252 && x257 = x257 && x256 = x256 && x255 = x251 && x254 = x250 && x253 = x249 && x252 = x248
(13) l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275) -> l8(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x287 = x283 && x286 = x282 && x285 = x281 && x284 = x280 && x283 = x283 && x282 = x282 && x281 = x281 && x280 = x280 && x279 = x275 && x278 = x274 && x277 = x273 && x276 = x272
(14) l10(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l9(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x295 = x307 && x294 = x306 && x311 = x305 && x310 = x304 && x309 = x301 && x308 = x300 && x305 = x305 && x304 = x304 && x303 = x299 && x302 = x298 && x301 = x297 && x300 = x296
(15) l10(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l0(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x323 = x335 && x322 = x334 && x321 = x333 && x320 = x332 && x319 = x331 && x318 = x330 && x317 = x329 && x316 = x328 && x315 = x327 && x314 = x326 && x313 = x325 && x312 = x324
(16) l10(x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347) -> l3(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x347 = x359 && x346 = x358 && x345 = x357 && x344 = x356 && x343 = x355 && x342 = x354 && x341 = x353 && x340 = x352 && x339 = x351 && x338 = x350 && x337 = x349 && x336 = x348
(17) l10(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371) -> l4(x372, x373, x374, x375, x376, x377, x378, x379, x380, x381, x382, x383) :|: x371 = x383 && x370 = x382 && x369 = x381 && x368 = x380 && x367 = x379 && x366 = x378 && x365 = x377 && x364 = x376 && x363 = x375 && x362 = x374 && x361 = x373 && x360 = x372
(18) l10(x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) -> l5(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407) :|: x395 = x407 && x394 = x406 && x393 = x405 && x392 = x404 && x391 = x403 && x390 = x402 && x389 = x401 && x388 = x400 && x387 = x399 && x386 = x398 && x385 = x397 && x384 = x396
(19) l10(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l8(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x419 = x431 && x418 = x430 && x417 = x429 && x416 = x428 && x415 = x427 && x414 = x426 && x413 = x425 && x412 = x424 && x411 = x423 && x410 = x422 && x409 = x421 && x408 = x420
(20) l10(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) -> l6(x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455) :|: x443 = x455 && x442 = x454 && x441 = x453 && x440 = x452 && x439 = x451 && x438 = x450 && x437 = x449 && x436 = x448 && x435 = x447 && x434 = x446 && x433 = x445 && x432 = x444
(21) l10(x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) -> l7(x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x467 = x479 && x466 = x478 && x465 = x477 && x464 = x476 && x463 = x475 && x462 = x474 && x461 = x473 && x460 = x472 && x459 = x471 && x458 = x470 && x457 = x469 && x456 = x468
(22) l10(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491) -> l9(x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503) :|: x491 = x503 && x490 = x502 && x489 = x501 && x488 = x500 && x487 = x499 && x486 = x498 && x485 = x497 && x484 = x496 && x483 = x495 && x482 = x494 && x481 = x493 && x480 = x492
(23) l10(x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515) -> l1(x516, x517, x518, x519, x520, x521, x522, x523, x524, x525, x526, x527) :|: x515 = x527 && x514 = x526 && x513 = x525 && x512 = x524 && x511 = x523 && x510 = x522 && x509 = x521 && x508 = x520 && x507 = x519 && x506 = x518 && x505 = x517 && x504 = x516
(24) l11(x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l10(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551) :|: x539 = x551 && x538 = x550 && x537 = x549 && x536 = x548 && x535 = x547 && x534 = x546 && x533 = x545 && x532 = x544 && x531 = x543 && x530 = x542 && x529 = x541 && x528 = x540

Arcs:
(1) -> (13)
(2) -> (3)
(3) -> (1), (2)
(4) -> (13)
(5) -> (1), (2)
(6) -> (7), (8)
(7) -> (4), (5)
(8) -> (6)
(9) -> (7), (8)
(11) -> (9)
(12) -> (10)
(14) -> (11), (12)
(15) -> (1), (2)
(16) -> (4), (5)
(17) -> (6)
(18) -> (7), (8)
(20) -> (9)
(21) -> (10)
(22) -> (11), (12)
(23) -> (13)
(24) -> (14), (15), (16), (17), (18), (19), (20), (21), (22), (23)

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l4(x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) -> l5(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x103 = x115 && x102 = x114 && x101 = x113 && x119 = x112 && x118 = -8 + x110 && x117 = x109 && x116 = x108 && x112 = x112 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104
(2) l5(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l4(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x167 = x160 && x166 = x158 && x165 = x157 && x164 = x156 && 8 <= x158 && x160 = x160 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l4(x96:0, x97:0, x98:0, x99:0, x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0) -> l4(x104:0, x105:0, -8 + x106:0, x112:0, x160:0, x101:0, x102:0, x103:0, x104:0, x105:0, -8 + x106:0, x160:0) :|: x106:0 > 15

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(8) 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) -> l4(x11)

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

(9)
Obligation:
Rules:
l4(x106:0) -> l4(-8 + x106:0) :|: x106:0 > 15

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

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

(11)
Obligation:
Rules:
l4(x106:0) -> l4(c) :|: c = -8 + x106:0 && x106:0 > 15

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(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l4(x)] = x

The following rules are decreasing:
l4(x106:0) -> l4(c) :|: c = -8 + x106:0 && x106:0 > 15
The following rules are bounded:
l4(x106:0) -> l4(c) :|: c = -8 + x106:0 && x106:0 > 15

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l2(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = -1 + x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= -1 + x15 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8
(2) l2(x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) -> l0(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47) :|: x35 = x47 && x34 = x46 && x33 = x45 && x32 = x44 && x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x27 = x39 && x26 = x38 && x25 = x37 && x24 = x36

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
l0(x:0, x1:0, x2:0, x3:0, x16:0, x17:0, x18:0, x19:0, x12:0, x13:0, x10:0, x11:0) -> l0(x12:0, x13:0, x10:0, x11:0, x16:0, x17:0, x18:0, x19:0, x12:0, x13:0, x10:0, -1 + x11:0) :|: x11:0 > 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:

   l0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> l0(x12)

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

(18)
Obligation:
Rules:
l0(x11:0) -> l0(-1 + x11:0) :|: x11:0 > 1

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

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

(20)
Obligation:
Rules:
l0(x11:0) -> l0(c) :|: c = -1 + x11:0 && x11:0 > 1

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

(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l0(x)] = x

The following rules are decreasing:
l0(x11:0) -> l0(c) :|: c = -1 + x11:0 && x11:0 > 1
The following rules are bounded:
l0(x11:0) -> l0(c) :|: c = -1 + x11:0 && x11:0 > 1

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(22)
YES