YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 38.8 s] (4) TRUE ---------------------------------------- (0) Obligation: Rules: l0(a10HAT0, a15HAT0, b11HAT0, b16HAT0, c12HAT0, c17HAT0, m13HAT0, ret_max24HAT0, ret_min14HAT0, tmp620HAT0, tmp923HAT0, tmp9HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0, x_promoted_1HAT0, y_promoted_2HAT0, zHAT0) -> l1(a10HATpost, a15HATpost, b11HATpost, b16HATpost, c12HATpost, c17HATpost, m13HATpost, ret_max24HATpost, ret_min14HATpost, tmp620HATpost, tmp923HATpost, tmp9HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost, x_promoted_1HATpost, y_promoted_2HATpost, zHATpost) :|: zHAT0 = zHATpost && y_promoted_2HAT0 = y_promoted_2HATpost && x_promoted_1HAT0 = x_promoted_1HATpost && tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmp923HAT0 = tmp923HATpost && tmp9HAT0 = tmp9HATpost && tmp620HAT0 = tmp620HATpost && tmpHAT0 = tmpHATpost && ret_min14HAT0 = ret_min14HATpost && ret_max24HAT0 = ret_max24HATpost && m13HAT0 = m13HATpost && c17HAT0 = c17HATpost && c12HAT0 = c12HATpost && b16HAT0 = b16HATpost && b11HAT0 = b11HATpost && a15HAT0 = a15HATpost && a10HAT0 = a10HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x16 = x34 && x15 = x33 && x14 = x32 && x10 = x28 && x11 = x29 && x9 = x27 && x12 = x30 && x8 = x26 && x6 = x24 && x5 = x23 && x4 = x22 && x3 = x21 && x2 = x20 && x1 = x19 && x = x18 && x35 = x35 && x31 = x25 && x25 = x1 l4(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l5(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x53 = x71 && x52 = x70 && x51 = x69 && x50 = x68 && x49 = x67 && x46 = x64 && x47 = x65 && x45 = x63 && x48 = x66 && x44 = x62 && x43 = x61 && x42 = x60 && x41 = x59 && x40 = x58 && x39 = x57 && x38 = x56 && x37 = x55 && x36 = x54 && 1 + x52 <= x51 l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l3(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x89 = x107 && x88 = x106 && x87 = x105 && x86 = x104 && x85 = x103 && x82 = x100 && x81 = x99 && x84 = x102 && x80 = x98 && x79 = x97 && x78 = x96 && x77 = x95 && x76 = x94 && x75 = x93 && x74 = x92 && x73 = x91 && x72 = x90 && x101 = x101 && x87 <= x88 l6(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) -> l2(x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x125 = x143 && x124 = x142 && x123 = x141 && x122 = x140 && x121 = x139 && x118 = x136 && x119 = x137 && x117 = x135 && x120 = x138 && x116 = x134 && x115 = x133 && x114 = x132 && x113 = x131 && x112 = x130 && x111 = x129 && x110 = x128 && x109 = x127 && x108 = x126 && 1 + x113 <= x109 l6(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) -> l2(x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x161 = x179 && x160 = x178 && x159 = x177 && x158 = x176 && x157 = x175 && x155 = x173 && x153 = x171 && x156 = x174 && x152 = x170 && x151 = x169 && x150 = x168 && x149 = x167 && x148 = x166 && x147 = x165 && x146 = x164 && x145 = x163 && x144 = x162 && x172 = x172 && x145 <= x149 l7(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) -> l6(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x197 = x215 && x196 = x214 && x195 = x213 && x194 = x212 && x193 = x211 && x190 = x208 && x191 = x209 && x189 = x207 && x192 = x210 && x188 = x206 && x187 = x205 && x186 = x204 && x185 = x203 && x184 = x202 && x183 = x201 && x182 = x200 && x181 = x199 && x180 = x198 && 1 + x183 <= x181 l7(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233) -> l6(x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x233 = x251 && x232 = x250 && x231 = x249 && x230 = x248 && x229 = x247 && x226 = x244 && x227 = x245 && x228 = x246 && x224 = x242 && x223 = x241 && x222 = x240 && x221 = x239 && x220 = x238 && x219 = x237 && x218 = x236 && x217 = x235 && x216 = x234 && x243 = x243 && x217 <= x219 l8(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l9(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x269 = x287 && x268 = x286 && x267 = x285 && x266 = x284 && x265 = x283 && x262 = x280 && x263 = x281 && x261 = x279 && x264 = x282 && x260 = x278 && x259 = x277 && x257 = x275 && x256 = x274 && x255 = x273 && x254 = x272 && x253 = x271 && x252 = x270 && x276 = x256 && 1 + x256 <= x254 l8(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305) -> l9(x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x305 = x323 && x304 = x322 && x303 = x321 && x302 = x320 && x301 = x319 && x298 = x316 && x299 = x317 && x297 = x315 && x300 = x318 && x296 = x314 && x295 = x313 && x293 = x311 && x292 = x310 && x291 = x309 && x290 = x308 && x289 = x307 && x288 = x306 && x312 = x290 && x290 <= x292 l9(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341) -> l3(x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x341 = x359 && x340 = x358 && x338 = x356 && x337 = x355 && x334 = x352 && x335 = x353 && x333 = x351 && x331 = x349 && x330 = x348 && x329 = x347 && x328 = x346 && x327 = x345 && x326 = x344 && x325 = x343 && x324 = x342 && x357 = x354 + x339 && x354 = x350 && x350 = x330 l10(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377) -> l9(x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x377 = x395 && x376 = x394 && x375 = x393 && x374 = x392 && x373 = x391 && x370 = x388 && x371 = x389 && x369 = x387 && x372 = x390 && x368 = x386 && x367 = x385 && x365 = x383 && x364 = x382 && x363 = x381 && x362 = x380 && x361 = x379 && x360 = x378 && x384 = x364 && 1 + x364 <= x360 l10(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413) -> l9(x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x413 = x431 && x412 = x430 && x411 = x429 && x410 = x428 && x409 = x427 && x406 = x424 && x407 = x425 && x405 = x423 && x408 = x426 && x404 = x422 && x403 = x421 && x401 = x419 && x400 = x418 && x399 = x417 && x398 = x416 && x397 = x415 && x396 = x414 && x420 = x396 && x396 <= x400 l11(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448, x449) -> l8(x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) :|: x449 = x467 && x448 = x466 && x447 = x465 && x446 = x464 && x445 = x463 && x442 = x460 && x443 = x461 && x441 = x459 && x444 = x462 && x440 = x458 && x439 = x457 && x438 = x456 && x437 = x455 && x436 = x454 && x435 = x453 && x434 = x452 && x433 = x451 && x432 = x450 && 1 + x434 <= x432 l11(x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483, x484, x485) -> l10(x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503) :|: x485 = x503 && x484 = x502 && x483 = x501 && x482 = x500 && x481 = x499 && x478 = x496 && x479 = x497 && x477 = x495 && x480 = x498 && x476 = x494 && x475 = x493 && x474 = x492 && x473 = x491 && x472 = x490 && x471 = x489 && x470 = x488 && x469 = x487 && x468 = x486 && x468 <= x470 l5(x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521) -> l7(x522, x523, x524, x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) :|: x521 = x539 && x520 = x538 && x519 = x537 && x518 = x536 && x517 = x535 && x514 = x532 && x515 = x533 && x513 = x531 && x516 = x534 && x512 = x530 && x511 = x529 && x510 = x528 && x508 = x526 && x506 = x524 && x504 = x522 && x527 = x519 && x525 = x520 && x523 = x521 && 1 + x521 <= x519 l5(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554, x555, x556, x557) -> l11(x558, x559, x560, x561, x562, x563, x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575) :|: x557 = x575 && x556 = x574 && x555 = x573 && x554 = x572 && x553 = x571 && x550 = x568 && x551 = x569 && x549 = x567 && x552 = x570 && x548 = x566 && x547 = x565 && x546 = x564 && x545 = x563 && x543 = x561 && x541 = x559 && x562 = x557 && x560 = x556 && x558 = x555 && x555 <= x557 l3(x576, x577, x578, x579, x580, x581, x582, x583, x584, x585, x586, x587, x588, x589, x590, x591, x592, x593) -> l0(x594, x595, x596, x597, x598, x599, x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611) :|: x593 = x611 && x592 = x610 && x591 = x609 && x589 = x607 && x586 = x604 && x587 = x605 && x585 = x603 && x588 = x606 && x584 = x602 && x583 = x601 && x582 = x600 && x581 = x599 && x580 = x598 && x579 = x597 && x578 = x596 && x577 = x595 && x576 = x594 && x608 = x592 - x593 && 1 + x593 <= x592 l3(x612, x613, x614, x615, x616, x617, x618, x619, x620, x621, x622, x623, x624, x625, x626, x627, x628, x629) -> l0(x630, x631, x632, x633, x634, x635, x636, x637, x638, x639, x640, x641, x642, x643, x644, x645, x646, x647) :|: x629 = x647 && x628 = x646 && x627 = x645 && x625 = x643 && x622 = x640 && x623 = x641 && x621 = x639 && x624 = x642 && x620 = x638 && x619 = x637 && x618 = x636 && x617 = x635 && x616 = x634 && x615 = x633 && x614 = x632 && x613 = x631 && x612 = x630 && x644 = x628 + x629 && x628 <= x629 l12(x648, x649, x650, x651, x652, x653, x654, x655, x656, x657, x658, x659, x660, x661, x662, x663, x664, x665) -> l4(x666, x667, x668, x669, x670, x671, x672, x673, x674, x675, x676, x677, x678, x679, x680, x681, x682, x683) :|: x662 = x680 && x661 = x679 && x658 = x676 && x659 = x677 && x657 = x675 && x660 = x678 && x656 = x674 && x655 = x673 && x654 = x672 && x653 = x671 && x652 = x670 && x651 = x669 && x650 = x668 && x649 = x667 && x648 = x666 && x683 = 1 && x682 = 2 && x681 = 10 l13(x684, x685, x686, x687, x688, x689, x690, x691, x692, x693, x694, x695, x696, x697, x698, x699, x700, x701) -> l12(x702, x703, x704, x705, x706, x707, x708, x709, x710, x711, x712, x713, x714, x715, x716, x717, x718, x719) :|: x701 = x719 && x700 = x718 && x699 = x717 && x698 = x716 && x697 = x715 && x694 = x712 && x695 = x713 && x693 = x711 && x696 = x714 && x692 = x710 && x691 = x709 && x690 = x708 && x689 = x707 && x688 = x706 && x687 = x705 && x686 = x704 && x685 = x703 && x684 = x702 Start term: l13(a10HAT0, a15HAT0, b11HAT0, b16HAT0, c12HAT0, c17HAT0, m13HAT0, ret_max24HAT0, ret_min14HAT0, tmp620HAT0, tmp923HAT0, tmp9HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0, x_promoted_1HAT0, y_promoted_2HAT0, zHAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(a10HAT0, a15HAT0, b11HAT0, b16HAT0, c12HAT0, c17HAT0, m13HAT0, ret_max24HAT0, ret_min14HAT0, tmp620HAT0, tmp923HAT0, tmp9HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0, x_promoted_1HAT0, y_promoted_2HAT0, zHAT0) -> l1(a10HATpost, a15HATpost, b11HATpost, b16HATpost, c12HATpost, c17HATpost, m13HATpost, ret_max24HATpost, ret_min14HATpost, tmp620HATpost, tmp923HATpost, tmp9HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost, x_promoted_1HATpost, y_promoted_2HATpost, zHATpost) :|: zHAT0 = zHATpost && y_promoted_2HAT0 = y_promoted_2HATpost && x_promoted_1HAT0 = x_promoted_1HATpost && tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmp923HAT0 = tmp923HATpost && tmp9HAT0 = tmp9HATpost && tmp620HAT0 = tmp620HATpost && tmpHAT0 = tmpHATpost && ret_min14HAT0 = ret_min14HATpost && ret_max24HAT0 = ret_max24HATpost && m13HAT0 = m13HATpost && c17HAT0 = c17HATpost && c12HAT0 = c12HATpost && b16HAT0 = b16HATpost && b11HAT0 = b11HATpost && a15HAT0 = a15HATpost && a10HAT0 = a10HATpost l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x16 = x34 && x15 = x33 && x14 = x32 && x10 = x28 && x11 = x29 && x9 = x27 && x12 = x30 && x8 = x26 && x6 = x24 && x5 = x23 && x4 = x22 && x3 = x21 && x2 = x20 && x1 = x19 && x = x18 && x35 = x35 && x31 = x25 && x25 = x1 l4(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l5(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x53 = x71 && x52 = x70 && x51 = x69 && x50 = x68 && x49 = x67 && x46 = x64 && x47 = x65 && x45 = x63 && x48 = x66 && x44 = x62 && x43 = x61 && x42 = x60 && x41 = x59 && x40 = x58 && x39 = x57 && x38 = x56 && x37 = x55 && x36 = x54 && 1 + x52 <= x51 l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l3(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x89 = x107 && x88 = x106 && x87 = x105 && x86 = x104 && x85 = x103 && x82 = x100 && x81 = x99 && x84 = x102 && x80 = x98 && x79 = x97 && x78 = x96 && x77 = x95 && x76 = x94 && x75 = x93 && x74 = x92 && x73 = x91 && x72 = x90 && x101 = x101 && x87 <= x88 l6(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) -> l2(x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x125 = x143 && x124 = x142 && x123 = x141 && x122 = x140 && x121 = x139 && x118 = x136 && x119 = x137 && x117 = x135 && x120 = x138 && x116 = x134 && x115 = x133 && x114 = x132 && x113 = x131 && x112 = x130 && x111 = x129 && x110 = x128 && x109 = x127 && x108 = x126 && 1 + x113 <= x109 l6(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) -> l2(x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x161 = x179 && x160 = x178 && x159 = x177 && x158 = x176 && x157 = x175 && x155 = x173 && x153 = x171 && x156 = x174 && x152 = x170 && x151 = x169 && x150 = x168 && x149 = x167 && x148 = x166 && x147 = x165 && x146 = x164 && x145 = x163 && x144 = x162 && x172 = x172 && x145 <= x149 l7(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) -> l6(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x197 = x215 && x196 = x214 && x195 = x213 && x194 = x212 && x193 = x211 && x190 = x208 && x191 = x209 && x189 = x207 && x192 = x210 && x188 = x206 && x187 = x205 && x186 = x204 && x185 = x203 && x184 = x202 && x183 = x201 && x182 = x200 && x181 = x199 && x180 = x198 && 1 + x183 <= x181 l7(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233) -> l6(x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x233 = x251 && x232 = x250 && x231 = x249 && x230 = x248 && x229 = x247 && x226 = x244 && x227 = x245 && x228 = x246 && x224 = x242 && x223 = x241 && x222 = x240 && x221 = x239 && x220 = x238 && x219 = x237 && x218 = x236 && x217 = x235 && x216 = x234 && x243 = x243 && x217 <= x219 l8(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l9(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x269 = x287 && x268 = x286 && x267 = x285 && x266 = x284 && x265 = x283 && x262 = x280 && x263 = x281 && x261 = x279 && x264 = x282 && x260 = x278 && x259 = x277 && x257 = x275 && x256 = x274 && x255 = x273 && x254 = x272 && x253 = x271 && x252 = x270 && x276 = x256 && 1 + x256 <= x254 l8(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305) -> l9(x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x305 = x323 && x304 = x322 && x303 = x321 && x302 = x320 && x301 = x319 && x298 = x316 && x299 = x317 && x297 = x315 && x300 = x318 && x296 = x314 && x295 = x313 && x293 = x311 && x292 = x310 && x291 = x309 && x290 = x308 && x289 = x307 && x288 = x306 && x312 = x290 && x290 <= x292 l9(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341) -> l3(x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x341 = x359 && x340 = x358 && x338 = x356 && x337 = x355 && x334 = x352 && x335 = x353 && x333 = x351 && x331 = x349 && x330 = x348 && x329 = x347 && x328 = x346 && x327 = x345 && x326 = x344 && x325 = x343 && x324 = x342 && x357 = x354 + x339 && x354 = x350 && x350 = x330 l10(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377) -> l9(x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x377 = x395 && x376 = x394 && x375 = x393 && x374 = x392 && x373 = x391 && x370 = x388 && x371 = x389 && x369 = x387 && x372 = x390 && x368 = x386 && x367 = x385 && x365 = x383 && x364 = x382 && x363 = x381 && x362 = x380 && x361 = x379 && x360 = x378 && x384 = x364 && 1 + x364 <= x360 l10(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413) -> l9(x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x413 = x431 && x412 = x430 && x411 = x429 && x410 = x428 && x409 = x427 && x406 = x424 && x407 = x425 && x405 = x423 && x408 = x426 && x404 = x422 && x403 = x421 && x401 = x419 && x400 = x418 && x399 = x417 && x398 = x416 && x397 = x415 && x396 = x414 && x420 = x396 && x396 <= x400 l11(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448, x449) -> l8(x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) :|: x449 = x467 && x448 = x466 && x447 = x465 && x446 = x464 && x445 = x463 && x442 = x460 && x443 = x461 && x441 = x459 && x444 = x462 && x440 = x458 && x439 = x457 && x438 = x456 && x437 = x455 && x436 = x454 && x435 = x453 && x434 = x452 && x433 = x451 && x432 = x450 && 1 + x434 <= x432 l11(x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483, x484, x485) -> l10(x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503) :|: x485 = x503 && x484 = x502 && x483 = x501 && x482 = x500 && x481 = x499 && x478 = x496 && x479 = x497 && x477 = x495 && x480 = x498 && x476 = x494 && x475 = x493 && x474 = x492 && x473 = x491 && x472 = x490 && x471 = x489 && x470 = x488 && x469 = x487 && x468 = x486 && x468 <= x470 l5(x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521) -> l7(x522, x523, x524, x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) :|: x521 = x539 && x520 = x538 && x519 = x537 && x518 = x536 && x517 = x535 && x514 = x532 && x515 = x533 && x513 = x531 && x516 = x534 && x512 = x530 && x511 = x529 && x510 = x528 && x508 = x526 && x506 = x524 && x504 = x522 && x527 = x519 && x525 = x520 && x523 = x521 && 1 + x521 <= x519 l5(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554, x555, x556, x557) -> l11(x558, x559, x560, x561, x562, x563, x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575) :|: x557 = x575 && x556 = x574 && x555 = x573 && x554 = x572 && x553 = x571 && x550 = x568 && x551 = x569 && x549 = x567 && x552 = x570 && x548 = x566 && x547 = x565 && x546 = x564 && x545 = x563 && x543 = x561 && x541 = x559 && x562 = x557 && x560 = x556 && x558 = x555 && x555 <= x557 l3(x576, x577, x578, x579, x580, x581, x582, x583, x584, x585, x586, x587, x588, x589, x590, x591, x592, x593) -> l0(x594, x595, x596, x597, x598, x599, x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611) :|: x593 = x611 && x592 = x610 && x591 = x609 && x589 = x607 && x586 = x604 && x587 = x605 && x585 = x603 && x588 = x606 && x584 = x602 && x583 = x601 && x582 = x600 && x581 = x599 && x580 = x598 && x579 = x597 && x578 = x596 && x577 = x595 && x576 = x594 && x608 = x592 - x593 && 1 + x593 <= x592 l3(x612, x613, x614, x615, x616, x617, x618, x619, x620, x621, x622, x623, x624, x625, x626, x627, x628, x629) -> l0(x630, x631, x632, x633, x634, x635, x636, x637, x638, x639, x640, x641, x642, x643, x644, x645, x646, x647) :|: x629 = x647 && x628 = x646 && x627 = x645 && x625 = x643 && x622 = x640 && x623 = x641 && x621 = x639 && x624 = x642 && x620 = x638 && x619 = x637 && x618 = x636 && x617 = x635 && x616 = x634 && x615 = x633 && x614 = x632 && x613 = x631 && x612 = x630 && x644 = x628 + x629 && x628 <= x629 l12(x648, x649, x650, x651, x652, x653, x654, x655, x656, x657, x658, x659, x660, x661, x662, x663, x664, x665) -> l4(x666, x667, x668, x669, x670, x671, x672, x673, x674, x675, x676, x677, x678, x679, x680, x681, x682, x683) :|: x662 = x680 && x661 = x679 && x658 = x676 && x659 = x677 && x657 = x675 && x660 = x678 && x656 = x674 && x655 = x673 && x654 = x672 && x653 = x671 && x652 = x670 && x651 = x669 && x650 = x668 && x649 = x667 && x648 = x666 && x683 = 1 && x682 = 2 && x681 = 10 l13(x684, x685, x686, x687, x688, x689, x690, x691, x692, x693, x694, x695, x696, x697, x698, x699, x700, x701) -> l12(x702, x703, x704, x705, x706, x707, x708, x709, x710, x711, x712, x713, x714, x715, x716, x717, x718, x719) :|: x701 = x719 && x700 = x718 && x699 = x717 && x698 = x716 && x697 = x715 && x694 = x712 && x695 = x713 && x693 = x711 && x696 = x714 && x692 = x710 && x691 = x709 && x690 = x708 && x689 = x707 && x688 = x706 && x687 = x705 && x686 = x704 && x685 = x703 && x684 = x702 Start term: l13(a10HAT0, a15HAT0, b11HAT0, b16HAT0, c12HAT0, c17HAT0, m13HAT0, ret_max24HAT0, ret_min14HAT0, tmp620HAT0, tmp923HAT0, tmp9HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0, x_promoted_1HAT0, y_promoted_2HAT0, zHAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(a10HAT0, a15HAT0, b11HAT0, b16HAT0, c12HAT0, c17HAT0, m13HAT0, ret_max24HAT0, ret_min14HAT0, tmp620HAT0, tmp923HAT0, tmp9HAT0, tmpHAT0, tmp___0HAT0, tmp___1HAT0, x_promoted_1HAT0, y_promoted_2HAT0, zHAT0) -> l1(a10HATpost, a15HATpost, b11HATpost, b16HATpost, c12HATpost, c17HATpost, m13HATpost, ret_max24HATpost, ret_min14HATpost, tmp620HATpost, tmp923HATpost, tmp9HATpost, tmpHATpost, tmp___0HATpost, tmp___1HATpost, x_promoted_1HATpost, y_promoted_2HATpost, zHATpost) :|: zHAT0 = zHATpost && y_promoted_2HAT0 = y_promoted_2HATpost && x_promoted_1HAT0 = x_promoted_1HATpost && tmp___1HAT0 = tmp___1HATpost && tmp___0HAT0 = tmp___0HATpost && tmp923HAT0 = tmp923HATpost && tmp9HAT0 = tmp9HATpost && tmp620HAT0 = tmp620HATpost && tmpHAT0 = tmpHATpost && ret_min14HAT0 = ret_min14HATpost && ret_max24HAT0 = ret_max24HATpost && m13HAT0 = m13HATpost && c17HAT0 = c17HATpost && c12HAT0 = c12HATpost && b16HAT0 = b16HATpost && b11HAT0 = b11HATpost && a15HAT0 = a15HATpost && a10HAT0 = a10HATpost (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17) -> l3(x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x16 = x34 && x15 = x33 && x14 = x32 && x10 = x28 && x11 = x29 && x9 = x27 && x12 = x30 && x8 = x26 && x6 = x24 && x5 = x23 && x4 = x22 && x3 = x21 && x2 = x20 && x1 = x19 && x = x18 && x35 = x35 && x31 = x25 && x25 = x1 (3) l4(x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53) -> l5(x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x53 = x71 && x52 = x70 && x51 = x69 && x50 = x68 && x49 = x67 && x46 = x64 && x47 = x65 && x45 = x63 && x48 = x66 && x44 = x62 && x43 = x61 && x42 = x60 && x41 = x59 && x40 = x58 && x39 = x57 && x38 = x56 && x37 = x55 && x36 = x54 && 1 + x52 <= x51 (4) l4(x72, x73, x74, x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l3(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x89 = x107 && x88 = x106 && x87 = x105 && x86 = x104 && x85 = x103 && x82 = x100 && x81 = x99 && x84 = x102 && x80 = x98 && x79 = x97 && x78 = x96 && x77 = x95 && x76 = x94 && x75 = x93 && x74 = x92 && x73 = x91 && x72 = x90 && x101 = x101 && x87 <= x88 (5) l6(x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121, x122, x123, x124, x125) -> l2(x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x125 = x143 && x124 = x142 && x123 = x141 && x122 = x140 && x121 = x139 && x118 = x136 && x119 = x137 && x117 = x135 && x120 = x138 && x116 = x134 && x115 = x133 && x114 = x132 && x113 = x131 && x112 = x130 && x111 = x129 && x110 = x128 && x109 = x127 && x108 = x126 && 1 + x113 <= x109 (6) l6(x144, x145, x146, x147, x148, x149, x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161) -> l2(x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x161 = x179 && x160 = x178 && x159 = x177 && x158 = x176 && x157 = x175 && x155 = x173 && x153 = x171 && x156 = x174 && x152 = x170 && x151 = x169 && x150 = x168 && x149 = x167 && x148 = x166 && x147 = x165 && x146 = x164 && x145 = x163 && x144 = x162 && x172 = x172 && x145 <= x149 (7) l7(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197) -> l6(x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x197 = x215 && x196 = x214 && x195 = x213 && x194 = x212 && x193 = x211 && x190 = x208 && x191 = x209 && x189 = x207 && x192 = x210 && x188 = x206 && x187 = x205 && x186 = x204 && x185 = x203 && x184 = x202 && x183 = x201 && x182 = x200 && x181 = x199 && x180 = x198 && 1 + x183 <= x181 (8) l7(x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230, x231, x232, x233) -> l6(x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x233 = x251 && x232 = x250 && x231 = x249 && x230 = x248 && x229 = x247 && x226 = x244 && x227 = x245 && x228 = x246 && x224 = x242 && x223 = x241 && x222 = x240 && x221 = x239 && x220 = x238 && x219 = x237 && x218 = x236 && x217 = x235 && x216 = x234 && x243 = x243 && x217 <= x219 (9) l8(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) -> l9(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x269 = x287 && x268 = x286 && x267 = x285 && x266 = x284 && x265 = x283 && x262 = x280 && x263 = x281 && x261 = x279 && x264 = x282 && x260 = x278 && x259 = x277 && x257 = x275 && x256 = x274 && x255 = x273 && x254 = x272 && x253 = x271 && x252 = x270 && x276 = x256 && 1 + x256 <= x254 (10) l8(x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305) -> l9(x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x305 = x323 && x304 = x322 && x303 = x321 && x302 = x320 && x301 = x319 && x298 = x316 && x299 = x317 && x297 = x315 && x300 = x318 && x296 = x314 && x295 = x313 && x293 = x311 && x292 = x310 && x291 = x309 && x290 = x308 && x289 = x307 && x288 = x306 && x312 = x290 && x290 <= x292 (11) l9(x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341) -> l3(x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x341 = x359 && x340 = x358 && x338 = x356 && x337 = x355 && x334 = x352 && x335 = x353 && x333 = x351 && x331 = x349 && x330 = x348 && x329 = x347 && x328 = x346 && x327 = x345 && x326 = x344 && x325 = x343 && x324 = x342 && x357 = x354 + x339 && x354 = x350 && x350 = x330 (12) l10(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377) -> l9(x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x377 = x395 && x376 = x394 && x375 = x393 && x374 = x392 && x373 = x391 && x370 = x388 && x371 = x389 && x369 = x387 && x372 = x390 && x368 = x386 && x367 = x385 && x365 = x383 && x364 = x382 && x363 = x381 && x362 = x380 && x361 = x379 && x360 = x378 && x384 = x364 && 1 + x364 <= x360 (13) l10(x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413) -> l9(x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x413 = x431 && x412 = x430 && x411 = x429 && x410 = x428 && x409 = x427 && x406 = x424 && x407 = x425 && x405 = x423 && x408 = x426 && x404 = x422 && x403 = x421 && x401 = x419 && x400 = x418 && x399 = x417 && x398 = x416 && x397 = x415 && x396 = x414 && x420 = x396 && x396 <= x400 (14) l11(x432, x433, x434, x435, x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448, x449) -> l8(x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467) :|: x449 = x467 && x448 = x466 && x447 = x465 && x446 = x464 && x445 = x463 && x442 = x460 && x443 = x461 && x441 = x459 && x444 = x462 && x440 = x458 && x439 = x457 && x438 = x456 && x437 = x455 && x436 = x454 && x435 = x453 && x434 = x452 && x433 = x451 && x432 = x450 && 1 + x434 <= x432 (15) l11(x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483, x484, x485) -> l10(x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503) :|: x485 = x503 && x484 = x502 && x483 = x501 && x482 = x500 && x481 = x499 && x478 = x496 && x479 = x497 && x477 = x495 && x480 = x498 && x476 = x494 && x475 = x493 && x474 = x492 && x473 = x491 && x472 = x490 && x471 = x489 && x470 = x488 && x469 = x487 && x468 = x486 && x468 <= x470 (16) l5(x504, x505, x506, x507, x508, x509, x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521) -> l7(x522, x523, x524, x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) :|: x521 = x539 && x520 = x538 && x519 = x537 && x518 = x536 && x517 = x535 && x514 = x532 && x515 = x533 && x513 = x531 && x516 = x534 && x512 = x530 && x511 = x529 && x510 = x528 && x508 = x526 && x506 = x524 && x504 = x522 && x527 = x519 && x525 = x520 && x523 = x521 && 1 + x521 <= x519 (17) l5(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554, x555, x556, x557) -> l11(x558, x559, x560, x561, x562, x563, x564, x565, x566, x567, x568, x569, x570, x571, x572, x573, x574, x575) :|: x557 = x575 && x556 = x574 && x555 = x573 && x554 = x572 && x553 = x571 && x550 = x568 && x551 = x569 && x549 = x567 && x552 = x570 && x548 = x566 && x547 = x565 && x546 = x564 && x545 = x563 && x543 = x561 && x541 = x559 && x562 = x557 && x560 = x556 && x558 = x555 && x555 <= x557 (18) l3(x576, x577, x578, x579, x580, x581, x582, x583, x584, x585, x586, x587, x588, x589, x590, x591, x592, x593) -> l0(x594, x595, x596, x597, x598, x599, x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611) :|: x593 = x611 && x592 = x610 && x591 = x609 && x589 = x607 && x586 = x604 && x587 = x605 && x585 = x603 && x588 = x606 && x584 = x602 && x583 = x601 && x582 = x600 && x581 = x599 && x580 = x598 && x579 = x597 && x578 = x596 && x577 = x595 && x576 = x594 && x608 = x592 - x593 && 1 + x593 <= x592 (19) l3(x612, x613, x614, x615, x616, x617, x618, x619, x620, x621, x622, x623, x624, x625, x626, x627, x628, x629) -> l0(x630, x631, x632, x633, x634, x635, x636, x637, x638, x639, x640, x641, x642, x643, x644, x645, x646, x647) :|: x629 = x647 && x628 = x646 && x627 = x645 && x625 = x643 && x622 = x640 && x623 = x641 && x621 = x639 && x624 = x642 && x620 = x638 && x619 = x637 && x618 = x636 && x617 = x635 && x616 = x634 && x615 = x633 && x614 = x632 && x613 = x631 && x612 = x630 && x644 = x628 + x629 && x628 <= x629 (20) l12(x648, x649, x650, x651, x652, x653, x654, x655, x656, x657, x658, x659, x660, x661, x662, x663, x664, x665) -> l4(x666, x667, x668, x669, x670, x671, x672, x673, x674, x675, x676, x677, x678, x679, x680, x681, x682, x683) :|: x662 = x680 && x661 = x679 && x658 = x676 && x659 = x677 && x657 = x675 && x660 = x678 && x656 = x674 && x655 = x673 && x654 = x672 && x653 = x671 && x652 = x670 && x651 = x669 && x650 = x668 && x649 = x667 && x648 = x666 && x683 = 1 && x682 = 2 && x681 = 10 (21) l13(x684, x685, x686, x687, x688, x689, x690, x691, x692, x693, x694, x695, x696, x697, x698, x699, x700, x701) -> l12(x702, x703, x704, x705, x706, x707, x708, x709, x710, x711, x712, x713, x714, x715, x716, x717, x718, x719) :|: x701 = x719 && x700 = x718 && x699 = x717 && x698 = x716 && x697 = x715 && x694 = x712 && x695 = x713 && x693 = x711 && x696 = x714 && x692 = x710 && x691 = x709 && x690 = x708 && x689 = x707 && x688 = x706 && x687 = x705 && x686 = x704 && x685 = x703 && x684 = x702 Arcs: (2) -> (18), (19) (3) -> (16), (17) (4) -> (18), (19) (5) -> (2) (6) -> (2) (7) -> (5), (6) (8) -> (5), (6) (9) -> (11) (10) -> (11) (11) -> (18), (19) (12) -> (11) (13) -> (11) (14) -> (9), (10) (15) -> (12), (13) (16) -> (7), (8) (17) -> (14), (15) (18) -> (1) (19) -> (1) (20) -> (3) (21) -> (20) This digraph is fully evaluated! ---------------------------------------- (4) TRUE