YES proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could be proven: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof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, 44.5 s] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 0 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 585 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 4 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (17) IRSwT (18) TempFilterProof [SOUND, 3 ms] (19) IntTRS (20) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (21) YES (22) IRSwT (23) IntTRSCompressionProof [EQUIVALENT, 0 ms] (24) IRSwT (25) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (26) IRSwT (27) TempFilterProof [SOUND, 6 ms] (28) IntTRS (29) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (30) YES ---------------------------------------- (0) Obligation: Rules: l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, oldX8HAT0, oldX9HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0, x4HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, oldX8HATpost, oldX9HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost, x4HATpost) :|: oldX9HAT0 = oldX9HATpost && oldX8HAT0 = oldX8HATpost && oldX7HAT0 = oldX7HATpost && oldX6HAT0 = oldX6HATpost && oldX5HAT0 = oldX5HATpost && x4HATpost = 1 + oldX4HATpost && x3HATpost = 1 + oldX3HATpost && x2HATpost = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX4HATpost = x4HAT0 && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l1(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) :|: x9 = x24 && x8 = x23 && x7 = x22 && x6 = x21 && x5 = x20 && x29 = -1 + x19 && x28 = -1 + x18 && x27 = x17 && x26 = x16 && x25 = x15 && x19 = x14 && x18 = x13 && x17 = x12 && x16 = x11 && x15 = x10 l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x39 = x54 && x38 = x53 && x37 = x52 && x59 = x51 && x58 = x50 && x57 = x49 && x56 = x46 && x55 = x45 && x51 = x51 && x50 = x50 && x49 = x44 && x48 = x43 && x47 = x42 && x46 = x41 && x45 = x40 l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l0(x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x69 = x84 && x68 = x83 && x67 = x82 && x66 = x81 && x65 = x80 && x89 = x79 && x88 = x78 && x87 = x77 && x86 = x76 && x85 = x75 && x78 <= 0 && x79 = x74 && x78 = x73 && x77 = x72 && x76 = x71 && x75 = x70 l5(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l2(x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x114 && x98 = x113 && x97 = x112 && x96 = x111 && x95 = x110 && x119 = x109 && x118 = x108 && x117 = x107 && x116 = x106 && x115 = x105 && 1 <= x108 && x109 = x104 && x108 = x103 && x107 = x102 && x106 = x101 && x105 = x100 l6(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l7(x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) :|: x149 = x144 && x148 = x143 && x147 = x142 && x146 = x141 && x145 = x140 && x144 = x144 && x143 = x143 && x142 = x142 && x141 = x141 && x140 = x140 && x139 = x134 && x138 = x133 && x137 = x132 && x136 = x131 && x135 = x130 l1(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x159 = x174 && x158 = x173 && x157 = x172 && x156 = x171 && x155 = x170 && x179 = x169 && x178 = x168 && x177 = x167 && x176 = x166 && x175 = x165 && 0 <= x168 && x168 <= 0 && x169 = x164 && x168 = x163 && x167 = x162 && x166 = x161 && x165 = x160 l1(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194) -> l5(x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) :|: x189 = x204 && x188 = x203 && x187 = x202 && x186 = x201 && x185 = x200 && x209 = x199 && x208 = x198 && x207 = x197 && x206 = x196 && x205 = x195 && 1 <= x198 && x199 = x194 && x198 = x193 && x197 = x192 && x196 = x191 && x195 = x190 l1(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l5(x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x234 && x218 = x233 && x217 = x232 && x216 = x231 && x215 = x230 && x239 = x229 && x238 = x228 && x237 = x227 && x236 = x226 && x235 = x225 && 1 + x228 <= 0 && x229 = x224 && x228 = x223 && x227 = x222 && x226 = x221 && x225 = x220 l4(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254) -> l6(x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x249 = x264 && x248 = x263 && x247 = x262 && x269 = x261 && x268 = x260 && x267 = x257 && x266 = x256 && x265 = x255 && x256 <= 0 && x261 = x261 && x260 = x260 && x259 = x254 && x258 = x253 && x257 = x252 && x256 = x251 && x255 = x250 l4(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284) -> l6(x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x279 = x294 && x278 = x293 && x277 = x292 && x299 = x291 && x298 = x290 && x297 = x287 && x296 = x286 && x295 = x285 && 1 + x287 <= x286 && x291 = x291 && x290 = x290 && x289 = x284 && x288 = x283 && x287 = x282 && x286 = x281 && x285 = x280 l4(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l1(x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x309 = x324 && x308 = x323 && x307 = x322 && x306 = x321 && x305 = x320 && x329 = x317 && x328 = x316 && x327 = x317 && x326 = x316 && x325 = x315 && 1 <= x316 && x316 <= x317 && x319 = x314 && x318 = x313 && x317 = x312 && x316 = x311 && x315 = x310 l8(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344) -> l4(x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x339 = x354 && x338 = x353 && x337 = x352 && x359 = x351 && x358 = x350 && x357 = x345 && x356 = x346 && x355 = x345 && x351 = x351 && x350 = x350 && x349 = x344 && x348 = x343 && x347 = x342 && x346 = x341 && x345 = x340 l9(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374) -> l8(x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389) :|: x369 = x384 && x368 = x383 && x389 = x382 && x388 = x381 && x387 = x380 && x386 = x376 && x385 = x375 && x382 = x382 && x381 = x381 && x380 = x380 && x379 = x374 && x378 = x373 && x377 = x372 && x376 = x371 && x375 = x370 l9(x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l0(x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) :|: x404 = x419 && x403 = x418 && x402 = x417 && x401 = x416 && x400 = x415 && x399 = x414 && x398 = x413 && x397 = x412 && x396 = x411 && x395 = x410 && x394 = x409 && x393 = x408 && x392 = x407 && x391 = x406 && x390 = x405 l9(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434) -> l2(x435, x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448, x449) :|: x434 = x449 && x433 = x448 && x432 = x447 && x431 = x446 && x430 = x445 && x429 = x444 && x428 = x443 && x427 = x442 && x426 = x441 && x425 = x440 && x424 = x439 && x423 = x438 && x422 = x437 && x421 = x436 && x420 = x435 l9(x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464) -> l3(x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x464 = x479 && x463 = x478 && x462 = x477 && x461 = x476 && x460 = x475 && x459 = x474 && x458 = x473 && x457 = x472 && x456 = x471 && x455 = x470 && x454 = x469 && x453 = x468 && x452 = x467 && x451 = x466 && x450 = x465 l9(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494) -> l5(x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505, x506, x507, x508, x509) :|: x494 = x509 && x493 = x508 && x492 = x507 && x491 = x506 && x490 = x505 && x489 = x504 && x488 = x503 && x487 = x502 && x486 = x501 && x485 = x500 && x484 = x499 && x483 = x498 && x482 = x497 && x481 = x496 && x480 = x495 l9(x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521, x522, x523, x524) -> l6(x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) :|: x524 = x539 && x523 = x538 && x522 = x537 && x521 = x536 && x520 = x535 && x519 = x534 && x518 = x533 && x517 = x532 && x516 = x531 && x515 = x530 && x514 = x529 && x513 = x528 && x512 = x527 && x511 = x526 && x510 = x525 l9(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554) -> l1(x555, x556, x557, x558, x559, x560, x561, x562, x563, x564, x565, x566, x567, x568, x569) :|: x554 = x569 && x553 = x568 && x552 = x567 && x551 = x566 && x550 = x565 && x549 = x564 && x548 = x563 && x547 = x562 && x546 = x561 && x545 = x560 && x544 = x559 && x543 = x558 && x542 = x557 && x541 = x556 && x540 = x555 l9(x570, x571, x572, x573, x574, x575, x576, x577, x578, x579, x580, x581, x582, x583, x584) -> l4(x585, x586, x587, x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x584 = x599 && x583 = x598 && x582 = x597 && x581 = x596 && x580 = x595 && x579 = x594 && x578 = x593 && x577 = x592 && x576 = x591 && x575 = x590 && x574 = x589 && x573 = x588 && x572 = x587 && x571 = x586 && x570 = x585 l9(x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611, x612, x613, x614) -> l8(x615, x616, x617, x618, x619, x620, x621, x622, x623, x624, x625, x626, x627, x628, x629) :|: x614 = x629 && x613 = x628 && x612 = x627 && x611 = x626 && x610 = x625 && x609 = x624 && x608 = x623 && x607 = x622 && x606 = x621 && x605 = x620 && x604 = x619 && x603 = x618 && x602 = x617 && x601 = x616 && x600 = x615 l9(x630, x631, x632, x633, x634, x635, x636, x637, x638, x639, x640, x641, x642, x643, x644) -> l7(x645, x646, x647, x648, x649, x650, x651, x652, x653, x654, x655, x656, x657, x658, x659) :|: x644 = x659 && x643 = x658 && x642 = x657 && x641 = x656 && x640 = x655 && x639 = x654 && x638 = x653 && x637 = x652 && x636 = x651 && x635 = x650 && x634 = x649 && x633 = x648 && x632 = x647 && x631 = x646 && x630 = x645 l10(x660, x661, x662, x663, x664, x665, x666, x667, x668, x669, x670, x671, x672, x673, x674) -> l9(x675, x676, x677, x678, x679, x680, x681, x682, x683, x684, x685, x686, x687, x688, x689) :|: x674 = x689 && x673 = x688 && x672 = x687 && x671 = x686 && x670 = x685 && x669 = x684 && x668 = x683 && x667 = x682 && x666 = x681 && x665 = x680 && x664 = x679 && x663 = x678 && x662 = x677 && x661 = x676 && x660 = x675 Start term: l10(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, oldX8HAT0, oldX9HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0, x4HAT0) ---------------------------------------- (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, oldX8HAT0, oldX9HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0, x4HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, oldX8HATpost, oldX9HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost, x4HATpost) :|: oldX9HAT0 = oldX9HATpost && oldX8HAT0 = oldX8HATpost && oldX7HAT0 = oldX7HATpost && oldX6HAT0 = oldX6HATpost && oldX5HAT0 = oldX5HATpost && x4HATpost = 1 + oldX4HATpost && x3HATpost = 1 + oldX3HATpost && x2HATpost = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX4HATpost = x4HAT0 && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l1(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) :|: x9 = x24 && x8 = x23 && x7 = x22 && x6 = x21 && x5 = x20 && x29 = -1 + x19 && x28 = -1 + x18 && x27 = x17 && x26 = x16 && x25 = x15 && x19 = x14 && x18 = x13 && x17 = x12 && x16 = x11 && x15 = x10 l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x39 = x54 && x38 = x53 && x37 = x52 && x59 = x51 && x58 = x50 && x57 = x49 && x56 = x46 && x55 = x45 && x51 = x51 && x50 = x50 && x49 = x44 && x48 = x43 && x47 = x42 && x46 = x41 && x45 = x40 l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l0(x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x69 = x84 && x68 = x83 && x67 = x82 && x66 = x81 && x65 = x80 && x89 = x79 && x88 = x78 && x87 = x77 && x86 = x76 && x85 = x75 && x78 <= 0 && x79 = x74 && x78 = x73 && x77 = x72 && x76 = x71 && x75 = x70 l5(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l2(x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x114 && x98 = x113 && x97 = x112 && x96 = x111 && x95 = x110 && x119 = x109 && x118 = x108 && x117 = x107 && x116 = x106 && x115 = x105 && 1 <= x108 && x109 = x104 && x108 = x103 && x107 = x102 && x106 = x101 && x105 = x100 l6(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l7(x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) :|: x149 = x144 && x148 = x143 && x147 = x142 && x146 = x141 && x145 = x140 && x144 = x144 && x143 = x143 && x142 = x142 && x141 = x141 && x140 = x140 && x139 = x134 && x138 = x133 && x137 = x132 && x136 = x131 && x135 = x130 l1(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x159 = x174 && x158 = x173 && x157 = x172 && x156 = x171 && x155 = x170 && x179 = x169 && x178 = x168 && x177 = x167 && x176 = x166 && x175 = x165 && 0 <= x168 && x168 <= 0 && x169 = x164 && x168 = x163 && x167 = x162 && x166 = x161 && x165 = x160 l1(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194) -> l5(x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) :|: x189 = x204 && x188 = x203 && x187 = x202 && x186 = x201 && x185 = x200 && x209 = x199 && x208 = x198 && x207 = x197 && x206 = x196 && x205 = x195 && 1 <= x198 && x199 = x194 && x198 = x193 && x197 = x192 && x196 = x191 && x195 = x190 l1(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l5(x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x234 && x218 = x233 && x217 = x232 && x216 = x231 && x215 = x230 && x239 = x229 && x238 = x228 && x237 = x227 && x236 = x226 && x235 = x225 && 1 + x228 <= 0 && x229 = x224 && x228 = x223 && x227 = x222 && x226 = x221 && x225 = x220 l4(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254) -> l6(x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x249 = x264 && x248 = x263 && x247 = x262 && x269 = x261 && x268 = x260 && x267 = x257 && x266 = x256 && x265 = x255 && x256 <= 0 && x261 = x261 && x260 = x260 && x259 = x254 && x258 = x253 && x257 = x252 && x256 = x251 && x255 = x250 l4(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284) -> l6(x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x279 = x294 && x278 = x293 && x277 = x292 && x299 = x291 && x298 = x290 && x297 = x287 && x296 = x286 && x295 = x285 && 1 + x287 <= x286 && x291 = x291 && x290 = x290 && x289 = x284 && x288 = x283 && x287 = x282 && x286 = x281 && x285 = x280 l4(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l1(x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x309 = x324 && x308 = x323 && x307 = x322 && x306 = x321 && x305 = x320 && x329 = x317 && x328 = x316 && x327 = x317 && x326 = x316 && x325 = x315 && 1 <= x316 && x316 <= x317 && x319 = x314 && x318 = x313 && x317 = x312 && x316 = x311 && x315 = x310 l8(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344) -> l4(x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x339 = x354 && x338 = x353 && x337 = x352 && x359 = x351 && x358 = x350 && x357 = x345 && x356 = x346 && x355 = x345 && x351 = x351 && x350 = x350 && x349 = x344 && x348 = x343 && x347 = x342 && x346 = x341 && x345 = x340 l9(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374) -> l8(x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389) :|: x369 = x384 && x368 = x383 && x389 = x382 && x388 = x381 && x387 = x380 && x386 = x376 && x385 = x375 && x382 = x382 && x381 = x381 && x380 = x380 && x379 = x374 && x378 = x373 && x377 = x372 && x376 = x371 && x375 = x370 l9(x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l0(x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) :|: x404 = x419 && x403 = x418 && x402 = x417 && x401 = x416 && x400 = x415 && x399 = x414 && x398 = x413 && x397 = x412 && x396 = x411 && x395 = x410 && x394 = x409 && x393 = x408 && x392 = x407 && x391 = x406 && x390 = x405 l9(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434) -> l2(x435, x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448, x449) :|: x434 = x449 && x433 = x448 && x432 = x447 && x431 = x446 && x430 = x445 && x429 = x444 && x428 = x443 && x427 = x442 && x426 = x441 && x425 = x440 && x424 = x439 && x423 = x438 && x422 = x437 && x421 = x436 && x420 = x435 l9(x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464) -> l3(x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x464 = x479 && x463 = x478 && x462 = x477 && x461 = x476 && x460 = x475 && x459 = x474 && x458 = x473 && x457 = x472 && x456 = x471 && x455 = x470 && x454 = x469 && x453 = x468 && x452 = x467 && x451 = x466 && x450 = x465 l9(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494) -> l5(x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505, x506, x507, x508, x509) :|: x494 = x509 && x493 = x508 && x492 = x507 && x491 = x506 && x490 = x505 && x489 = x504 && x488 = x503 && x487 = x502 && x486 = x501 && x485 = x500 && x484 = x499 && x483 = x498 && x482 = x497 && x481 = x496 && x480 = x495 l9(x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521, x522, x523, x524) -> l6(x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) :|: x524 = x539 && x523 = x538 && x522 = x537 && x521 = x536 && x520 = x535 && x519 = x534 && x518 = x533 && x517 = x532 && x516 = x531 && x515 = x530 && x514 = x529 && x513 = x528 && x512 = x527 && x511 = x526 && x510 = x525 l9(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554) -> l1(x555, x556, x557, x558, x559, x560, x561, x562, x563, x564, x565, x566, x567, x568, x569) :|: x554 = x569 && x553 = x568 && x552 = x567 && x551 = x566 && x550 = x565 && x549 = x564 && x548 = x563 && x547 = x562 && x546 = x561 && x545 = x560 && x544 = x559 && x543 = x558 && x542 = x557 && x541 = x556 && x540 = x555 l9(x570, x571, x572, x573, x574, x575, x576, x577, x578, x579, x580, x581, x582, x583, x584) -> l4(x585, x586, x587, x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x584 = x599 && x583 = x598 && x582 = x597 && x581 = x596 && x580 = x595 && x579 = x594 && x578 = x593 && x577 = x592 && x576 = x591 && x575 = x590 && x574 = x589 && x573 = x588 && x572 = x587 && x571 = x586 && x570 = x585 l9(x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611, x612, x613, x614) -> l8(x615, x616, x617, x618, x619, x620, x621, x622, x623, x624, x625, x626, x627, x628, x629) :|: x614 = x629 && x613 = x628 && x612 = x627 && x611 = x626 && x610 = x625 && x609 = x624 && x608 = x623 && x607 = x622 && x606 = x621 && x605 = x620 && x604 = x619 && x603 = x618 && x602 = x617 && x601 = x616 && x600 = x615 l9(x630, x631, x632, x633, x634, x635, x636, x637, x638, x639, x640, x641, x642, x643, x644) -> l7(x645, x646, x647, x648, x649, x650, x651, x652, x653, x654, x655, x656, x657, x658, x659) :|: x644 = x659 && x643 = x658 && x642 = x657 && x641 = x656 && x640 = x655 && x639 = x654 && x638 = x653 && x637 = x652 && x636 = x651 && x635 = x650 && x634 = x649 && x633 = x648 && x632 = x647 && x631 = x646 && x630 = x645 l10(x660, x661, x662, x663, x664, x665, x666, x667, x668, x669, x670, x671, x672, x673, x674) -> l9(x675, x676, x677, x678, x679, x680, x681, x682, x683, x684, x685, x686, x687, x688, x689) :|: x674 = x689 && x673 = x688 && x672 = x687 && x671 = x686 && x670 = x685 && x669 = x684 && x668 = x683 && x667 = x682 && x666 = x681 && x665 = x680 && x664 = x679 && x663 = x678 && x662 = x677 && x661 = x676 && x660 = x675 Start term: l10(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, oldX8HAT0, oldX9HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0, x4HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, oldX8HAT0, oldX9HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0, x4HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, oldX8HATpost, oldX9HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost, x4HATpost) :|: oldX9HAT0 = oldX9HATpost && oldX8HAT0 = oldX8HATpost && oldX7HAT0 = oldX7HATpost && oldX6HAT0 = oldX6HATpost && oldX5HAT0 = oldX5HATpost && x4HATpost = 1 + oldX4HATpost && x3HATpost = 1 + oldX3HATpost && x2HATpost = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX4HATpost = x4HAT0 && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l1(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) :|: x9 = x24 && x8 = x23 && x7 = x22 && x6 = x21 && x5 = x20 && x29 = -1 + x19 && x28 = -1 + x18 && x27 = x17 && x26 = x16 && x25 = x15 && x19 = x14 && x18 = x13 && x17 = x12 && x16 = x11 && x15 = x10 (3) l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x39 = x54 && x38 = x53 && x37 = x52 && x59 = x51 && x58 = x50 && x57 = x49 && x56 = x46 && x55 = x45 && x51 = x51 && x50 = x50 && x49 = x44 && x48 = x43 && x47 = x42 && x46 = x41 && x45 = x40 (4) l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l0(x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x69 = x84 && x68 = x83 && x67 = x82 && x66 = x81 && x65 = x80 && x89 = x79 && x88 = x78 && x87 = x77 && x86 = x76 && x85 = x75 && x78 <= 0 && x79 = x74 && x78 = x73 && x77 = x72 && x76 = x71 && x75 = x70 (5) l5(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l2(x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x114 && x98 = x113 && x97 = x112 && x96 = x111 && x95 = x110 && x119 = x109 && x118 = x108 && x117 = x107 && x116 = x106 && x115 = x105 && 1 <= x108 && x109 = x104 && x108 = x103 && x107 = x102 && x106 = x101 && x105 = x100 (6) l6(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l7(x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149) :|: x149 = x144 && x148 = x143 && x147 = x142 && x146 = x141 && x145 = x140 && x144 = x144 && x143 = x143 && x142 = x142 && x141 = x141 && x140 = x140 && x139 = x134 && x138 = x133 && x137 = x132 && x136 = x131 && x135 = x130 (7) l1(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x159 = x174 && x158 = x173 && x157 = x172 && x156 = x171 && x155 = x170 && x179 = x169 && x178 = x168 && x177 = x167 && x176 = x166 && x175 = x165 && 0 <= x168 && x168 <= 0 && x169 = x164 && x168 = x163 && x167 = x162 && x166 = x161 && x165 = x160 (8) l1(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194) -> l5(x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) :|: x189 = x204 && x188 = x203 && x187 = x202 && x186 = x201 && x185 = x200 && x209 = x199 && x208 = x198 && x207 = x197 && x206 = x196 && x205 = x195 && 1 <= x198 && x199 = x194 && x198 = x193 && x197 = x192 && x196 = x191 && x195 = x190 (9) l1(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l5(x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x234 && x218 = x233 && x217 = x232 && x216 = x231 && x215 = x230 && x239 = x229 && x238 = x228 && x237 = x227 && x236 = x226 && x235 = x225 && 1 + x228 <= 0 && x229 = x224 && x228 = x223 && x227 = x222 && x226 = x221 && x225 = x220 (10) l4(x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254) -> l6(x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x249 = x264 && x248 = x263 && x247 = x262 && x269 = x261 && x268 = x260 && x267 = x257 && x266 = x256 && x265 = x255 && x256 <= 0 && x261 = x261 && x260 = x260 && x259 = x254 && x258 = x253 && x257 = x252 && x256 = x251 && x255 = x250 (11) l4(x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284) -> l6(x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299) :|: x279 = x294 && x278 = x293 && x277 = x292 && x299 = x291 && x298 = x290 && x297 = x287 && x296 = x286 && x295 = x285 && 1 + x287 <= x286 && x291 = x291 && x290 = x290 && x289 = x284 && x288 = x283 && x287 = x282 && x286 = x281 && x285 = x280 (12) l4(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l1(x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x309 = x324 && x308 = x323 && x307 = x322 && x306 = x321 && x305 = x320 && x329 = x317 && x328 = x316 && x327 = x317 && x326 = x316 && x325 = x315 && 1 <= x316 && x316 <= x317 && x319 = x314 && x318 = x313 && x317 = x312 && x316 = x311 && x315 = x310 (13) l8(x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340, x341, x342, x343, x344) -> l4(x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x339 = x354 && x338 = x353 && x337 = x352 && x359 = x351 && x358 = x350 && x357 = x345 && x356 = x346 && x355 = x345 && x351 = x351 && x350 = x350 && x349 = x344 && x348 = x343 && x347 = x342 && x346 = x341 && x345 = x340 (14) l9(x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374) -> l8(x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389) :|: x369 = x384 && x368 = x383 && x389 = x382 && x388 = x381 && x387 = x380 && x386 = x376 && x385 = x375 && x382 = x382 && x381 = x381 && x380 = x380 && x379 = x374 && x378 = x373 && x377 = x372 && x376 = x371 && x375 = x370 (15) l9(x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l0(x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419) :|: x404 = x419 && x403 = x418 && x402 = x417 && x401 = x416 && x400 = x415 && x399 = x414 && x398 = x413 && x397 = x412 && x396 = x411 && x395 = x410 && x394 = x409 && x393 = x408 && x392 = x407 && x391 = x406 && x390 = x405 (16) l9(x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434) -> l2(x435, x436, x437, x438, x439, x440, x441, x442, x443, x444, x445, x446, x447, x448, x449) :|: x434 = x449 && x433 = x448 && x432 = x447 && x431 = x446 && x430 = x445 && x429 = x444 && x428 = x443 && x427 = x442 && x426 = x441 && x425 = x440 && x424 = x439 && x423 = x438 && x422 = x437 && x421 = x436 && x420 = x435 (17) l9(x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464) -> l3(x465, x466, x467, x468, x469, x470, x471, x472, x473, x474, x475, x476, x477, x478, x479) :|: x464 = x479 && x463 = x478 && x462 = x477 && x461 = x476 && x460 = x475 && x459 = x474 && x458 = x473 && x457 = x472 && x456 = x471 && x455 = x470 && x454 = x469 && x453 = x468 && x452 = x467 && x451 = x466 && x450 = x465 (18) l9(x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494) -> l5(x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505, x506, x507, x508, x509) :|: x494 = x509 && x493 = x508 && x492 = x507 && x491 = x506 && x490 = x505 && x489 = x504 && x488 = x503 && x487 = x502 && x486 = x501 && x485 = x500 && x484 = x499 && x483 = x498 && x482 = x497 && x481 = x496 && x480 = x495 (19) l9(x510, x511, x512, x513, x514, x515, x516, x517, x518, x519, x520, x521, x522, x523, x524) -> l6(x525, x526, x527, x528, x529, x530, x531, x532, x533, x534, x535, x536, x537, x538, x539) :|: x524 = x539 && x523 = x538 && x522 = x537 && x521 = x536 && x520 = x535 && x519 = x534 && x518 = x533 && x517 = x532 && x516 = x531 && x515 = x530 && x514 = x529 && x513 = x528 && x512 = x527 && x511 = x526 && x510 = x525 (20) l9(x540, x541, x542, x543, x544, x545, x546, x547, x548, x549, x550, x551, x552, x553, x554) -> l1(x555, x556, x557, x558, x559, x560, x561, x562, x563, x564, x565, x566, x567, x568, x569) :|: x554 = x569 && x553 = x568 && x552 = x567 && x551 = x566 && x550 = x565 && x549 = x564 && x548 = x563 && x547 = x562 && x546 = x561 && x545 = x560 && x544 = x559 && x543 = x558 && x542 = x557 && x541 = x556 && x540 = x555 (21) l9(x570, x571, x572, x573, x574, x575, x576, x577, x578, x579, x580, x581, x582, x583, x584) -> l4(x585, x586, x587, x588, x589, x590, x591, x592, x593, x594, x595, x596, x597, x598, x599) :|: x584 = x599 && x583 = x598 && x582 = x597 && x581 = x596 && x580 = x595 && x579 = x594 && x578 = x593 && x577 = x592 && x576 = x591 && x575 = x590 && x574 = x589 && x573 = x588 && x572 = x587 && x571 = x586 && x570 = x585 (22) l9(x600, x601, x602, x603, x604, x605, x606, x607, x608, x609, x610, x611, x612, x613, x614) -> l8(x615, x616, x617, x618, x619, x620, x621, x622, x623, x624, x625, x626, x627, x628, x629) :|: x614 = x629 && x613 = x628 && x612 = x627 && x611 = x626 && x610 = x625 && x609 = x624 && x608 = x623 && x607 = x622 && x606 = x621 && x605 = x620 && x604 = x619 && x603 = x618 && x602 = x617 && x601 = x616 && x600 = x615 (23) l9(x630, x631, x632, x633, x634, x635, x636, x637, x638, x639, x640, x641, x642, x643, x644) -> l7(x645, x646, x647, x648, x649, x650, x651, x652, x653, x654, x655, x656, x657, x658, x659) :|: x644 = x659 && x643 = x658 && x642 = x657 && x641 = x656 && x640 = x655 && x639 = x654 && x638 = x653 && x637 = x652 && x636 = x651 && x635 = x650 && x634 = x649 && x633 = x648 && x632 = x647 && x631 = x646 && x630 = x645 (24) l10(x660, x661, x662, x663, x664, x665, x666, x667, x668, x669, x670, x671, x672, x673, x674) -> l9(x675, x676, x677, x678, x679, x680, x681, x682, x683, x684, x685, x686, x687, x688, x689) :|: x674 = x689 && x673 = x688 && x672 = x687 && x671 = x686 && x670 = x685 && x669 = x684 && x668 = x683 && x667 = x682 && x666 = x681 && x665 = x680 && x664 = x679 && x663 = x678 && x662 = x677 && x661 = x676 && x660 = x675 Arcs: (1) -> (7), (8), (9) (2) -> (7), (8), (9) (3) -> (10), (11), (12) (4) -> (1) (5) -> (2) (7) -> (3) (8) -> (5) (9) -> (4) (10) -> (6) (11) -> (6) (12) -> (8) (13) -> (10), (11), (12) (14) -> (13) (15) -> (1) (16) -> (2) (17) -> (3) (18) -> (4), (5) (19) -> (6) (20) -> (7), (8), (9) (21) -> (10), (11), (12) (22) -> (13) (24) -> (14), (15), (16), (17), (18), (19), (20), (21), (22), (23) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, oldX6HAT0, oldX7HAT0, oldX8HAT0, oldX9HAT0, x0HAT0, x1HAT0, x2HAT0, x3HAT0, x4HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, oldX6HATpost, oldX7HATpost, oldX8HATpost, oldX9HATpost, x0HATpost, x1HATpost, x2HATpost, x3HATpost, x4HATpost) :|: oldX9HAT0 = oldX9HATpost && oldX8HAT0 = oldX8HATpost && oldX7HAT0 = oldX7HATpost && oldX6HAT0 = oldX6HATpost && oldX5HAT0 = oldX5HATpost && x4HATpost = 1 + oldX4HATpost && x3HATpost = 1 + oldX3HATpost && x2HATpost = oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX4HATpost = x4HAT0 && oldX3HATpost = x3HAT0 && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0 (2) l5(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74) -> l0(x75, x76, x77, x78, x79, x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x69 = x84 && x68 = x83 && x67 = x82 && x66 = x81 && x65 = x80 && x89 = x79 && x88 = x78 && x87 = x77 && x86 = x76 && x85 = x75 && x78 <= 0 && x79 = x74 && x78 = x73 && x77 = x72 && x76 = x71 && x75 = x70 (3) l1(x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l5(x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239) :|: x219 = x234 && x218 = x233 && x217 = x232 && x216 = x231 && x215 = x230 && x239 = x229 && x238 = x228 && x237 = x227 && x236 = x226 && x235 = x225 && 1 + x228 <= 0 && x229 = x224 && x228 = x223 && x227 = x222 && x226 = x221 && x225 = x220 (4) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> l1(x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) :|: x9 = x24 && x8 = x23 && x7 = x22 && x6 = x21 && x5 = x20 && x29 = -1 + x19 && x28 = -1 + x18 && x27 = x17 && x26 = x16 && x25 = x15 && x19 = x14 && x18 = x13 && x17 = x12 && x16 = x11 && x15 = x10 (5) l5(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104) -> l2(x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x99 = x114 && x98 = x113 && x97 = x112 && x96 = x111 && x95 = x110 && x119 = x109 && x118 = x108 && x117 = x107 && x116 = x106 && x115 = x105 && 1 <= x108 && x109 = x104 && x108 = x103 && x107 = x102 && x106 = x101 && x105 = x100 (6) l1(x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194) -> l5(x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209) :|: x189 = x204 && x188 = x203 && x187 = x202 && x186 = x201 && x185 = x200 && x209 = x199 && x208 = x198 && x207 = x197 && x206 = x196 && x205 = x195 && 1 <= x198 && x199 = x194 && x198 = x193 && x197 = x192 && x196 = x191 && x195 = x190 (7) l4(x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l1(x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329) :|: x309 = x324 && x308 = x323 && x307 = x322 && x306 = x321 && x305 = x320 && x329 = x317 && x328 = x316 && x327 = x317 && x326 = x316 && x325 = x315 && 1 <= x316 && x316 <= x317 && x319 = x314 && x318 = x313 && x317 = x312 && x316 = x311 && x315 = x310 (8) l3(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l4(x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x39 = x54 && x38 = x53 && x37 = x52 && x59 = x51 && x58 = x50 && x57 = x49 && x56 = x46 && x55 = x45 && x51 = x51 && x50 = x50 && x49 = x44 && x48 = x43 && x47 = x42 && x46 = x41 && x45 = x40 (9) l1(x150, x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164) -> l3(x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x159 = x174 && x158 = x173 && x157 = x172 && x156 = x171 && x155 = x170 && x179 = x169 && x178 = x168 && x177 = x167 && x176 = x166 && x175 = x165 && 0 <= x168 && x168 <= 0 && x169 = x164 && x168 = x163 && x167 = x162 && x166 = x161 && x165 = x160 Arcs: (1) -> (3), (6), (9) (2) -> (1) (3) -> (2) (4) -> (3), (6), (9) (5) -> (4) (6) -> (5) (7) -> (6) (8) -> (7) (9) -> (8) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x210:0, x211:0, x212:0, x213:0, x214:0, x215:0, x216:0, x217:0, x218:0, x219:0, x220:0, x221:0, x222:0, x223:0, x224:0) -> l5(x220:0, x221:0, x222:0, x223:0, x224:0, x215:0, x216:0, x217:0, x218:0, x219:0, x220:0, x221:0, x222:0, x223:0, x224:0) :|: x223:0 < 0 l1(x180:0, x181:0, x182:0, x183:0, x184:0, x185:0, x186:0, x187:0, x188:0, x189:0, x190:0, x191:0, x192:0, x193:0, x194:0) -> l5(x190:0, x191:0, x192:0, x193:0, x194:0, x185:0, x186:0, x187:0, x188:0, x189:0, x190:0, x191:0, x192:0, x193:0, x194:0) :|: x193:0 > 0 l5(x90:0, x91:0, x92:0, x93:0, x94:0, x110:0, x111:0, x112:0, x113:0, x114:0, x100:0, x101:0, x102:0, x103:0, x104:0) -> l1(x100:0, x101:0, x102:0, x103:0, x104:0, x110:0, x111:0, x112:0, x113:0, x114:0, x100:0, x101:0, x102:0, -1 + x103:0, -1 + x104:0) :|: x103:0 > 0 l5(x60:0, x61:0, x62:0, x63:0, x64:0, oldX5HATpost:0, oldX6HATpost:0, oldX7HATpost:0, oldX8HATpost:0, oldX9HATpost:0, oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0, oldX3HATpost:0, oldX4HATpost:0) -> l1(oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0, oldX3HATpost:0, oldX4HATpost:0, oldX5HATpost:0, oldX6HATpost:0, oldX7HATpost:0, oldX8HATpost:0, oldX9HATpost:0, oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0, 1 + oldX3HATpost:0, 1 + oldX4HATpost:0) :|: oldX3HATpost:0 < 1 l1(x150:0, x151:0, x152:0, x153:0, x154:0, x155:0, x156:0, x157:0, x158:0, x159:0, x160:0, x161:0, x162:0, x163:0, x164:0) -> l1(x160:0, x161:0, x164:0, x318:0, x319:0, x318:0, x319:0, x157:0, x158:0, x159:0, x160:0, x161:0, x164:0, x161:0, x164:0) :|: x163:0 > -1 && x163:0 < 1 && x161:0 > 0 && x164:0 >= x161:0 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> l1(x12, x14, x15) l5(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> l5(x12, x14, x15) ---------------------------------------- (8) Obligation: Rules: l1(x221:0, x223:0, x224:0) -> l5(x221:0, x223:0, x224:0) :|: x223:0 < 0 l1(x191:0, x193:0, x194:0) -> l5(x191:0, x193:0, x194:0) :|: x193:0 > 0 l5(x101:0, x103:0, x104:0) -> l1(x101:0, -1 + x103:0, -1 + x104:0) :|: x103:0 > 0 l5(oldX1HATpost:0, oldX3HATpost:0, oldX4HATpost:0) -> l1(oldX1HATpost:0, 1 + oldX3HATpost:0, 1 + oldX4HATpost:0) :|: oldX3HATpost:0 < 1 l1(x161:0, x163:0, x164:0) -> l1(x161:0, x161:0, x164:0) :|: x163:0 > -1 && x163:0 < 1 && x161:0 > 0 && x164:0 >= x161:0 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(VARIABLE, INTEGER, VARIABLE) l5(VARIABLE, INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: l1(x221:0, x223:0, x224:0) -> l5(x221:0, x223:0, x224:0) :|: x223:0 < 0 l1(x191:0, x193:0, x194:0) -> l5(x191:0, x193:0, x194:0) :|: x193:0 > 0 l5(x101:0, x103:0, x104:0) -> l1(x101:0, c, c1) :|: c1 = -1 + x104:0 && c = -1 + x103:0 && x103:0 > 0 l5(oldX1HATpost:0, oldX3HATpost:0, oldX4HATpost:0) -> l1(oldX1HATpost:0, c2, c3) :|: c3 = 1 + oldX4HATpost:0 && c2 = 1 + oldX3HATpost:0 && oldX3HATpost:0 < 1 l1(x161:0, x163:0, x164:0) -> l1(x161:0, x161:0, x164:0) :|: x163:0 > -1 && x163:0 < 1 && x161:0 > 0 && x164:0 >= x161:0 Found the following polynomial interpretation: [l1(x, x1, x2)] = -2 + x - x1 + x2 [l5(x3, x4, x5)] = -2 + x3 - x4 + x5 The following rules are decreasing: l1(x161:0, x163:0, x164:0) -> l1(x161:0, x161:0, x164:0) :|: x163:0 > -1 && x163:0 < 1 && x161:0 > 0 && x164:0 >= x161:0 The following rules are bounded: l1(x161:0, x163:0, x164:0) -> l1(x161:0, x161:0, x164:0) :|: x163:0 > -1 && x163:0 < 1 && x161:0 > 0 && x164:0 >= x161:0 - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l1(x221:0, x223:0, x224:0) -> l5(x221:0, x223:0, x224:0) :|: x223:0 < 0 l1(x191:0, x193:0, x194:0) -> l5(x191:0, x193:0, x194:0) :|: x193:0 > 0 l5(x101:0, x103:0, x104:0) -> l1(x101:0, c, c1) :|: c1 = -1 + x104:0 && c = -1 + x103:0 && x103:0 > 0 l5(oldX1HATpost:0, oldX3HATpost:0, oldX4HATpost:0) -> l1(oldX1HATpost:0, c2, c3) :|: c3 = 1 + oldX4HATpost:0 && c2 = 1 + oldX3HATpost:0 && oldX3HATpost:0 < 1 ---------------------------------------- (10) Obligation: Rules: l1(x221:0, x223:0, x224:0) -> l5(x221:0, x223:0, x224:0) :|: x223:0 < 0 l1(x191:0, x193:0, x194:0) -> l5(x191:0, x193:0, x194:0) :|: x193:0 > 0 l5(x101:0, x103:0, x104:0) -> l1(x101:0, -1 + x103:0, -1 + x104:0) :|: x103:0 > 0 l5(oldX1HATpost:0, oldX3HATpost:0, oldX4HATpost:0) -> l1(oldX1HATpost:0, 1 + oldX3HATpost:0, 1 + oldX4HATpost:0) :|: oldX3HATpost:0 < 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l1(x221:0, x223:0, x224:0) -> l5(x221:0, x223:0, x224:0) :|: x223:0 < 0 (2) l1(x191:0, x193:0, x194:0) -> l5(x191:0, x193:0, x194:0) :|: x193:0 > 0 (3) l5(x101:0, x103:0, x104:0) -> l1(x101:0, -1 + x103:0, -1 + x104:0) :|: x103:0 > 0 (4) l5(oldX1HATpost:0, oldX3HATpost:0, oldX4HATpost:0) -> l1(oldX1HATpost:0, 1 + oldX3HATpost:0, 1 + oldX4HATpost:0) :|: oldX3HATpost:0 < 1 Arcs: (1) -> (4) (2) -> (3) (3) -> (2) (4) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) l1(x221:0, x223:0, x224:0) -> l5(x221:0, x223:0, x224:0) :|: x223:0 < 0 (2) l5(oldX1HATpost:0, oldX3HATpost:0, oldX4HATpost:0) -> l1(oldX1HATpost:0, 1 + oldX3HATpost:0, 1 + oldX4HATpost:0) :|: oldX3HATpost:0 < 1 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: l1(x221:0:0, x223:0:0, x224:0:0) -> l1(x221:0:0, 1 + x223:0:0, 1 + x224:0:0) :|: x223:0:0 < 0 && x223:0:0 < 1 ---------------------------------------- (16) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3) -> l1(x2) ---------------------------------------- (17) Obligation: Rules: l1(x223:0:0) -> l1(1 + x223:0:0) :|: x223:0:0 < 0 && x223:0:0 < 1 ---------------------------------------- (18) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (19) Obligation: Rules: l1(x223:0:0) -> l1(c) :|: c = 1 + x223:0:0 && (x223:0:0 < 0 && x223:0:0 < 1) ---------------------------------------- (20) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l1(x)] = -x The following rules are decreasing: l1(x223:0:0) -> l1(c) :|: c = 1 + x223:0:0 && (x223:0:0 < 0 && x223:0:0 < 1) The following rules are bounded: l1(x223:0:0) -> l1(c) :|: c = 1 + x223:0:0 && (x223:0:0 < 0 && x223:0:0 < 1) ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Termination digraph: Nodes: (1) l1(x191:0, x193:0, x194:0) -> l5(x191:0, x193:0, x194:0) :|: x193:0 > 0 (2) l5(x101:0, x103:0, x104:0) -> l1(x101:0, -1 + x103:0, -1 + x104:0) :|: x103:0 > 0 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (23) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (24) Obligation: Rules: l1(x191:0:0, x193:0:0, x194:0:0) -> l1(x191:0:0, -1 + x193:0:0, -1 + x194:0:0) :|: x193:0:0 > 0 ---------------------------------------- (25) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3) -> l1(x2) ---------------------------------------- (26) Obligation: Rules: l1(x193:0:0) -> l1(-1 + x193:0:0) :|: x193:0:0 > 0 ---------------------------------------- (27) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (28) Obligation: Rules: l1(x193:0:0) -> l1(c) :|: c = -1 + x193:0:0 && x193:0:0 > 0 ---------------------------------------- (29) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [l1(x)] = x The following rules are decreasing: l1(x193:0:0) -> l1(c) :|: c = -1 + x193:0:0 && x193:0:0 > 0 The following rules are bounded: l1(x193:0:0) -> l1(c) :|: c = -1 + x193:0:0 && x193:0:0 > 0 ---------------------------------------- (30) YES