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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 42.7 s]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 88 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 42 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) IntTRS
(13) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(14) 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 = -1 + oldX3HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= x14 && 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) :|: x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x47 = x39 && x46 = x38 && x45 = x37 && x44 = x36 && 1 + x38 <= 0 && x39 = x35 && x38 = x34 && x37 = x33 && x36 = x32
l2(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l3(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x52 = x64 && x71 = x63 && x70 = x62 && x69 = x61 && x68 = x60 && 0 <= x62 && x62 <= 0 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56
l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l5(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x87 && x94 = x86 && x93 = x85 && x92 = x84 && x87 <= 0 && 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 && x100 = x112 && x119 = x111 && x118 = x110 && x117 = x109 && x116 = x108 && x110 <= 0 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104
l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 1 <= x135 && 1 <= x134 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128
l3(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l1(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x148 = x160 && x167 = x159 && x166 = x156 && x165 = 1 + x157 && x164 = x156 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152
l6(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && 1 <= x182 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176
l6(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l4(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x199 = x211 && x198 = x210 && x197 = x209 && x196 = x208 && x215 = x207 && x214 = x206 && x213 = x205 && x212 = x204 && 1 + x206 <= 0 && x207 = x203 && x206 = x202 && x205 = x201 && x204 = x200
l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l3(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x223 = x235 && x222 = x234 && x221 = x233 && x220 = x232 && x239 = x231 && x238 = x230 && x237 = x229 && x236 = x228 && 0 <= x230 && x230 <= 0 && x231 = x227 && x230 = x226 && x229 = x225 && x228 = x224
l5(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) :|: x263 = x259 && x262 = x258 && x261 = x257 && x260 = x256 && x259 = x259 && x258 = x258 && 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) -> l6(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x271 = x283 && x270 = x282 && x269 = x281 && x268 = x280 && x287 = x279 && x286 = x278 && x285 = x277 && x284 = x276 && 1 <= x276 && x279 = x275 && x278 = x274 && x277 = x273 && x276 = x272
l1(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l5(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x295 = x307 && x294 = x306 && x293 = x305 && x292 = x304 && x311 = x303 && x310 = x302 && x309 = x301 && x308 = x300 && x300 <= 0 && x303 = x299 && x302 = x298 && x301 = x297 && x300 = x296
l8(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l1(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x319 = x331 && x318 = x330 && x335 = x329 && x334 = x328 && x333 = 0 && x332 = x328 && x329 = x329 && x328 = x328 && x327 = x323 && x326 = x322 && x325 = x321 && x324 = x320
l9(x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347) -> l8(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x359 = x355 && x358 = x354 && x357 = x353 && x356 = x352 && x355 = x355 && x354 = x354 && x353 = x353 && x352 = x352 && x351 = x347 && x350 = x346 && x349 = x345 && x348 = x344
l9(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371) -> l0(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
l9(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) :|: x395 = x407 && x394 = x406 && x393 = x405 && x392 = x404 && x391 = x403 && x390 = x402 && x389 = x401 && x388 = x400 && x387 = x399 && x386 = x398 && x385 = x397 && x384 = x396
l9(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l4(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
l9(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) -> l3(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
l9(x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) -> l6(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
l9(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491) -> l5(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
l9(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
l9(x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l8(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
l9(x552, x553, x554, x555, x556, x557, x558, x559, x560, x561, x562, x563) -> l7(x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575) :|: x563 = x575 && x562 = x574 && x561 = x573 && x560 = x572 && x559 = x571 && x558 = x570 && x557 = x569 && x556 = x568 && x555 = x567 && x554 = x566 && x553 = x565 && x552 = x564
l10(x576, x577, x578, x579, x580, x581, x582, x583, x584, x585, x586, x587) -> l9(x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x587 = x599 && x586 = x598 && x585 = x597 && x584 = x596 && x583 = x595 && x582 = x594 && x581 = x593 && x580 = x592 && x579 = x591 && x578 = x590 && x577 = x589 && x576 = x588
Start term: l10(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 = -1 + oldX3HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= x14 && 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) :|: x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x47 = x39 && x46 = x38 && x45 = x37 && x44 = x36 && 1 + x38 <= 0 && x39 = x35 && x38 = x34 && x37 = x33 && x36 = x32
l2(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l3(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x52 = x64 && x71 = x63 && x70 = x62 && x69 = x61 && x68 = x60 && 0 <= x62 && x62 <= 0 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56
l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l5(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x87 && x94 = x86 && x93 = x85 && x92 = x84 && x87 <= 0 && 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 && x100 = x112 && x119 = x111 && x118 = x110 && x117 = x109 && x116 = x108 && x110 <= 0 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104
l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 1 <= x135 && 1 <= x134 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128
l3(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l1(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x148 = x160 && x167 = x159 && x166 = x156 && x165 = 1 + x157 && x164 = x156 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152
l6(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && 1 <= x182 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176
l6(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l4(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x199 = x211 && x198 = x210 && x197 = x209 && x196 = x208 && x215 = x207 && x214 = x206 && x213 = x205 && x212 = x204 && 1 + x206 <= 0 && x207 = x203 && x206 = x202 && x205 = x201 && x204 = x200
l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l3(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x223 = x235 && x222 = x234 && x221 = x233 && x220 = x232 && x239 = x231 && x238 = x230 && x237 = x229 && x236 = x228 && 0 <= x230 && x230 <= 0 && x231 = x227 && x230 = x226 && x229 = x225 && x228 = x224
l5(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) :|: x263 = x259 && x262 = x258 && x261 = x257 && x260 = x256 && x259 = x259 && x258 = x258 && 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) -> l6(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x271 = x283 && x270 = x282 && x269 = x281 && x268 = x280 && x287 = x279 && x286 = x278 && x285 = x277 && x284 = x276 && 1 <= x276 && x279 = x275 && x278 = x274 && x277 = x273 && x276 = x272
l1(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l5(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x295 = x307 && x294 = x306 && x293 = x305 && x292 = x304 && x311 = x303 && x310 = x302 && x309 = x301 && x308 = x300 && x300 <= 0 && x303 = x299 && x302 = x298 && x301 = x297 && x300 = x296
l8(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l1(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x319 = x331 && x318 = x330 && x335 = x329 && x334 = x328 && x333 = 0 && x332 = x328 && x329 = x329 && x328 = x328 && x327 = x323 && x326 = x322 && x325 = x321 && x324 = x320
l9(x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347) -> l8(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x359 = x355 && x358 = x354 && x357 = x353 && x356 = x352 && x355 = x355 && x354 = x354 && x353 = x353 && x352 = x352 && x351 = x347 && x350 = x346 && x349 = x345 && x348 = x344
l9(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371) -> l0(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
l9(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) :|: x395 = x407 && x394 = x406 && x393 = x405 && x392 = x404 && x391 = x403 && x390 = x402 && x389 = x401 && x388 = x400 && x387 = x399 && x386 = x398 && x385 = x397 && x384 = x396
l9(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l4(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
l9(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) -> l3(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
l9(x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) -> l6(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
l9(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491) -> l5(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
l9(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
l9(x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l8(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
l9(x552, x553, x554, x555, x556, x557, x558, x559, x560, x561, x562, x563) -> l7(x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575) :|: x563 = x575 && x562 = x574 && x561 = x573 && x560 = x572 && x559 = x571 && x558 = x570 && x557 = x569 && x556 = x568 && x555 = x567 && x554 = x566 && x553 = x565 && x552 = x564
l10(x576, x577, x578, x579, x580, x581, x582, x583, x584, x585, x586, x587) -> l9(x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x587 = x599 && x586 = x598 && x585 = x597 && x584 = x596 && x583 = x595 && x582 = x594 && x581 = x593 && x580 = x592 && x579 = x591 && x578 = x590 && x577 = x589 && x576 = x588
Start term: l10(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 = -1 + oldX3HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= x14 && 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) :|: x31 = x43 && x30 = x42 && x29 = x41 && x28 = x40 && x47 = x39 && x46 = x38 && x45 = x37 && x44 = x36 && 1 + x38 <= 0 && x39 = x35 && x38 = x34 && x37 = x33 && x36 = x32
(4) l2(x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l3(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x55 = x67 && x54 = x66 && x53 = x65 && x52 = x64 && x71 = x63 && x70 = x62 && x69 = x61 && x68 = x60 && 0 <= x62 && x62 <= 0 && x63 = x59 && x62 = x58 && x61 = x57 && x60 = x56
(5) l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83) -> l5(x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95) :|: x79 = x91 && x78 = x90 && x77 = x89 && x76 = x88 && x95 = x87 && x94 = x86 && x93 = x85 && x92 = x84 && x87 <= 0 && 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 && x100 = x112 && x119 = x111 && x118 = x110 && x117 = x109 && x116 = x108 && x110 <= 0 && x111 = x107 && x110 = x106 && x109 = x105 && x108 = x104
(7) l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 1 <= x135 && 1 <= x134 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128
(8) l3(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l1(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x148 = x160 && x167 = x159 && x166 = x156 && x165 = 1 + x157 && x164 = x156 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152
(9) l6(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && 1 <= x182 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176
(10) l6(x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) -> l4(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x199 = x211 && x198 = x210 && x197 = x209 && x196 = x208 && x215 = x207 && x214 = x206 && x213 = x205 && x212 = x204 && 1 + x206 <= 0 && x207 = x203 && x206 = x202 && x205 = x201 && x204 = x200
(11) l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l3(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x223 = x235 && x222 = x234 && x221 = x233 && x220 = x232 && x239 = x231 && x238 = x230 && x237 = x229 && x236 = x228 && 0 <= x230 && x230 <= 0 && x231 = x227 && x230 = x226 && x229 = x225 && x228 = x224
(12) l5(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) :|: x263 = x259 && x262 = x258 && x261 = x257 && x260 = x256 && x259 = x259 && x258 = x258 && 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) -> l6(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x271 = x283 && x270 = x282 && x269 = x281 && x268 = x280 && x287 = x279 && x286 = x278 && x285 = x277 && x284 = x276 && 1 <= x276 && x279 = x275 && x278 = x274 && x277 = x273 && x276 = x272
(14) l1(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) -> l5(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311) :|: x295 = x307 && x294 = x306 && x293 = x305 && x292 = x304 && x311 = x303 && x310 = x302 && x309 = x301 && x308 = x300 && x300 <= 0 && x303 = x299 && x302 = x298 && x301 = x297 && x300 = x296
(15) l8(x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) -> l1(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335) :|: x319 = x331 && x318 = x330 && x335 = x329 && x334 = x328 && x333 = 0 && x332 = x328 && x329 = x329 && x328 = x328 && x327 = x323 && x326 = x322 && x325 = x321 && x324 = x320
(16) l9(x336, x337, x338, x339, x340, x341, x342, x343, x344, x345, x346, x347) -> l8(x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x359 = x355 && x358 = x354 && x357 = x353 && x356 = x352 && x355 = x355 && x354 = x354 && x353 = x353 && x352 = x352 && x351 = x347 && x350 = x346 && x349 = x345 && x348 = x344
(17) l9(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371) -> l0(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) l9(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) :|: 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) l9(x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) -> l4(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) l9(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) -> l3(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) l9(x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) -> l6(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) l9(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491) -> l5(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) l9(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) l9(x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) -> l8(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
(25) l9(x552, x553, x554, x555, x556, x557, x558, x559, x560, x561, x562, x563) -> l7(x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575) :|: x563 = x575 && x562 = x574 && x561 = x573 && x560 = x572 && x559 = x571 && x558 = x570 && x557 = x569 && x556 = x568 && x555 = x567 && x554 = x566 && x553 = x565 && x552 = x564
(26) l10(x576, x577, x578, x579, x580, x581, x582, x583, x584, x585, x586, x587) -> l9(x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x587 = x599 && x586 = x598 && x585 = x597 && x584 = x596 && x583 = x595 && x582 = x594 && x581 = x593 && x580 = x592 && x579 = x591 && x578 = x590 && x577 = x589 && x576 = x588

Arcs:
(1) -> (13), (14)
(2) -> (1)
(3) -> (1)
(4) -> (8)
(5) -> (12)
(6) -> (12)
(7) -> (2)
(8) -> (13), (14)
(9) -> (5), (7)
(10) -> (5), (6)
(11) -> (8)
(13) -> (9), (10), (11)
(14) -> (12)
(15) -> (13), (14)
(16) -> (15)
(17) -> (1)
(18) -> (2), (3), (4)
(19) -> (5), (6), (7)
(20) -> (8)
(21) -> (9), (10), (11)
(22) -> (12)
(23) -> (13), (14)
(24) -> (15)
(26) -> (16), (17), (18), (19), (20), (21), (22), (23), (24), (25)

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

(4)
Obligation:

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 = -1 + oldX3HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> l0(x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23) :|: x7 = x19 && x6 = x18 && x5 = x17 && x4 = x16 && x23 = x15 && x22 = x14 && x21 = x13 && x20 = x12 && 1 <= x14 && x15 = x11 && x14 = x10 && x13 = x9 && x12 = x8
(3) l4(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131) -> l2(x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x127 = x139 && x126 = x138 && x125 = x137 && x124 = x136 && x143 = x135 && x142 = x134 && x141 = x133 && x140 = x132 && 1 <= x135 && 1 <= x134 && x135 = x131 && x134 = x130 && x133 = x129 && x132 = x128
(4) l6(x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) -> l4(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191) :|: x175 = x187 && x174 = x186 && x173 = x185 && x172 = x184 && x191 = x183 && x190 = x182 && x189 = x181 && x188 = x180 && 1 <= x182 && x183 = x179 && x182 = x178 && x181 = x177 && x180 = x176
(5) l1(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275) -> l6(x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x271 = x283 && x270 = x282 && x269 = x281 && x268 = x280 && x287 = x279 && x286 = x278 && x285 = x277 && x284 = x276 && 1 <= x276 && x279 = x275 && x278 = x274 && x277 = x273 && x276 = x272
(6) l3(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155) -> l1(x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167) :|: x151 = x163 && x150 = x162 && x149 = x161 && x148 = x160 && x167 = x159 && x166 = x156 && x165 = 1 + x157 && x164 = x156 && x159 = x155 && x158 = x154 && x157 = x153 && x156 = x152
(7) l6(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227) -> l3(x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x223 = x235 && x222 = x234 && x221 = x233 && x220 = x232 && x239 = x231 && x238 = x230 && x237 = x229 && x236 = x228 && 0 <= x230 && x230 <= 0 && x231 = x227 && x230 = x226 && x229 = x225 && x228 = x224

Arcs:
(1) -> (5)
(2) -> (1)
(3) -> (2)
(4) -> (3)
(5) -> (4), (7)
(6) -> (5)
(7) -> (6)

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
l6(x216:0, x217:0, x218:0, x219:0, x160:0, x161:0, x162:0, x163:0, x156:0, x157:0, x158:0, x159:0) -> l6(x156:0, 1 + x157:0, x156:0, x159:0, x160:0, x161:0, x162:0, x163:0, x156:0, 1 + x157:0, x156:0, x159:0) :|: x158:0 > -1 && x156:0 > 0 && x158:0 < 1
l6(x168:0, x169:0, x170:0, x171:0, oldX4HATpost:0, oldX5HATpost:0, oldX6HATpost:0, oldX7HATpost:0, oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0, oldX3HATpost:0) -> l6(oldX0HATpost:0, oldX1HATpost:0, -1 + oldX2HATpost:0, -1 + oldX3HATpost:0, oldX4HATpost:0, oldX5HATpost:0, oldX6HATpost:0, oldX7HATpost:0, oldX0HATpost:0, oldX1HATpost:0, -1 + oldX2HATpost:0, -1 + oldX3HATpost:0) :|: oldX3HATpost:0 > 0 && oldX0HATpost:0 > 0 && oldX2HATpost:0 > 0

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

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

   l6(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> l6(x9, x11, x12)

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

(8)
Obligation:
Rules:
l6(x156:0, x158:0, x159:0) -> l6(x156:0, x156:0, x159:0) :|: x158:0 > -1 && x156:0 > 0 && x158:0 < 1
l6(oldX0HATpost:0, oldX2HATpost:0, oldX3HATpost:0) -> l6(oldX0HATpost:0, -1 + oldX2HATpost:0, -1 + oldX3HATpost:0) :|: oldX3HATpost:0 > 0 && oldX0HATpost:0 > 0 && oldX2HATpost:0 > 0

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

(9) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l6(INTEGER, INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(10)
Obligation:
Rules:
l6(x156:0, x158:0, x159:0) -> l6(x156:0, x156:0, x159:0) :|: x158:0 > -1 && x156:0 > 0 && x158:0 < 1
l6(oldX0HATpost:0, oldX2HATpost:0, oldX3HATpost:0) -> l6(oldX0HATpost:0, c, c1) :|: c1 = -1 + oldX3HATpost:0 && c = -1 + oldX2HATpost:0 && (oldX3HATpost:0 > 0 && oldX0HATpost:0 > 0 && oldX2HATpost:0 > 0)

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

(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l6(x, x1, x2)] = -1 + x2

The following rules are decreasing:
l6(oldX0HATpost:0, oldX2HATpost:0, oldX3HATpost:0) -> l6(oldX0HATpost:0, c, c1) :|: c1 = -1 + oldX3HATpost:0 && c = -1 + oldX2HATpost:0 && (oldX3HATpost:0 > 0 && oldX0HATpost:0 > 0 && oldX2HATpost:0 > 0)
The following rules are bounded:
l6(oldX0HATpost:0, oldX2HATpost:0, oldX3HATpost:0) -> l6(oldX0HATpost:0, c, c1) :|: c1 = -1 + oldX3HATpost:0 && c = -1 + oldX2HATpost:0 && (oldX3HATpost:0 > 0 && oldX0HATpost:0 > 0 && oldX2HATpost:0 > 0)

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

(12)
Obligation:
Rules:
l6(x156:0, x158:0, x159:0) -> l6(x156:0, x156:0, x159:0) :|: x158:0 > -1 && x156:0 > 0 && x158:0 < 1

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

(13) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l6(x, x1, x2)] = -x1

The following rules are decreasing:
l6(x156:0, x158:0, x159:0) -> l6(x156:0, x156:0, x159:0) :|: x158:0 > -1 && x156:0 > 0 && x158:0 < 1
The following rules are bounded:
l6(x156:0, x158:0, x159:0) -> l6(x156:0, x156:0, x159:0) :|: x158:0 > -1 && x156:0 > 0 && x158:0 < 1

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

(14)
YES