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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 6326 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 18 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 35 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 5 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 26 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 13 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 1 ms]
        (22) YES


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

(0)
Obligation:
Rules:
l0(__const_12299HAT0, __const_15137HAT0, __const_16069HAT0, __const_16819HAT0, __const_20995HAT0, __const_2446HAT0, __const_25172HAT0, __const_3196HAT0, __const_4433HAT0, __const_6270HAT0, __const_7373HAT0, __const_8HAT0, __const_9633HAT0, constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0) -> l1(__const_12299HATpost, __const_15137HATpost, __const_16069HATpost, __const_16819HATpost, __const_20995HATpost, __const_2446HATpost, __const_25172HATpost, __const_3196HATpost, __const_4433HATpost, __const_6270HATpost, __const_7373HATpost, __const_8HATpost, __const_9633HATpost, constant22HATpost, i20HATpost, lx2HATpost, tmp03HATpost, tmp1011HATpost, tmp1112HATpost, tmp1213HATpost, tmp1314HATpost, tmp14HATpost, tmp25HATpost, tmp36HATpost, tmp47HATpost, tmp58HATpost, tmp69HATpost, tmp710HATpost, z115HATpost, z216HATpost, z317HATpost, z418HATpost, z519HATpost) :|: z519HAT0 = z519HATpost && z418HAT0 = z418HATpost && z317HAT0 = z317HATpost && z216HAT0 = z216HATpost && z115HAT0 = z115HATpost && tmp710HAT0 = tmp710HATpost && tmp69HAT0 = tmp69HATpost && tmp58HAT0 = tmp58HATpost && tmp47HAT0 = tmp47HATpost && tmp36HAT0 = tmp36HATpost && tmp25HAT0 = tmp25HATpost && tmp14HAT0 = tmp14HATpost && tmp1314HAT0 = tmp1314HATpost && tmp1213HAT0 = tmp1213HATpost && tmp1112HAT0 = tmp1112HATpost && tmp1011HAT0 = tmp1011HATpost && tmp03HAT0 = tmp03HATpost && lx2HAT0 = lx2HATpost && constant22HAT0 = constant22HATpost && __const_9633HAT0 = __const_9633HATpost && __const_8HAT0 = __const_8HATpost && __const_7373HAT0 = __const_7373HATpost && __const_6270HAT0 = __const_6270HATpost && __const_4433HAT0 = __const_4433HATpost && __const_3196HAT0 = __const_3196HATpost && __const_25172HAT0 = __const_25172HATpost && __const_2446HAT0 = __const_2446HATpost && __const_20995HAT0 = __const_20995HATpost && __const_16819HAT0 = __const_16819HATpost && __const_16069HAT0 = __const_16069HATpost && __const_15137HAT0 = __const_15137HATpost && __const_12299HAT0 = __const_12299HATpost && i20HATpost = 0 && __const_8HAT0 <= i20HAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: 1 + x14 <= x11 && x49 = x49 && x66 = x66 && x54 = x54 && x67 = x67 && x55 = x55 && x68 = x68 && x56 = x56 && x69 = x69 && x50 = x49 + x56 && x53 = x49 - x56 && x51 = x54 + x55 && x52 = x54 - x55 && x70 = x8 && x71 = x71 && x72 = x9 && x73 = -1 * x1 && x74 = x69 + x66 && x75 = x68 + x67 && x76 = x69 + x67 && x77 = x68 + x66 && x78 = x12 && x65 = x65 && x79 = x5 && x57 = x57 && x80 = x3 && x58 = x58 && x81 = x6 && x59 = x59 && x82 = x && x60 = x60 && x83 = -1 * x10 && x61 = x61 && x84 = -1 * x4 && x62 = x62 && x85 = -1 * x2 && x86 = x86 && x46 = -1 * x7 && x87 = x87 && x63 = x86 + x65 && x64 = x87 + x65 && x47 = 1 + x14 && x = x33 && x1 = x34 && x2 = x35 && x3 = x36 && x4 = x37 && x5 = x38 && x6 = x39 && x7 = x40 && x8 = x41 && x9 = x42 && x10 = x43 && x11 = x44 && x12 = x45 && x15 = x48
l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l4(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x120 = x153 && x119 = x152 && x118 = x151 && x117 = x150 && x116 = x149 && x115 = x148 && x114 = x147 && x113 = x146 && x112 = x145 && x111 = x144 && x110 = x143 && x109 = x142 && x108 = x141 && x107 = x140 && x106 = x139 && x105 = x138 && x104 = x137 && x103 = x136 && x102 = x135 && x101 = x134 && x100 = x133 && x99 = x132 && x98 = x131 && x97 = x130 && x96 = x129 && x95 = x128 && x94 = x127 && x93 = x126 && x92 = x125 && x91 = x124 && x90 = x123 && x89 = x122 && x88 = x121 && x99 <= x102
l3(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: 1 + x168 <= x165 && x203 = x203 && x220 = x220 && x208 = x208 && x221 = x221 && x209 = x209 && x222 = x222 && x210 = x210 && x223 = x223 && x204 = x203 + x210 && x207 = x203 - x210 && x205 = x208 + x209 && x206 = x208 - x209 && x224 = x162 && x225 = x225 && x226 = x163 && x227 = -1 * x155 && x228 = x223 + x220 && x229 = x222 + x221 && x230 = x223 + x221 && x231 = x222 + x220 && x232 = x166 && x219 = x219 && x233 = x159 && x211 = x211 && x234 = x157 && x212 = x212 && x235 = x160 && x213 = x213 && x236 = x154 && x214 = x214 && x237 = -1 * x164 && x215 = x215 && x238 = -1 * x158 && x216 = x216 && x239 = -1 * x156 && x240 = x240 && x200 = -1 * x161 && x241 = x241 && x217 = x240 + x219 && x218 = x241 + x219 && x201 = 1 + x168 && x154 = x187 && x155 = x188 && x156 = x189 && x157 = x190 && x158 = x191 && x159 = x192 && x160 = x193 && x161 = x194 && x162 = x195 && x163 = x196 && x164 = x197 && x165 = x198 && x166 = x199 && x169 = x202
l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l0(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x274 = x307 && x273 = x306 && x272 = x305 && x271 = x304 && x270 = x303 && x269 = x302 && x268 = x301 && x267 = x300 && x266 = x299 && x265 = x298 && x264 = x297 && x263 = x296 && x262 = x295 && x261 = x294 && x260 = x293 && x259 = x292 && x258 = x291 && x257 = x290 && x256 = x289 && x255 = x288 && x254 = x287 && x253 = x286 && x252 = x285 && x251 = x284 && x250 = x283 && x249 = x282 && x248 = x281 && x247 = x280 && x246 = x279 && x245 = x278 && x244 = x277 && x243 = x276 && x242 = x275
l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l3(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x340 = x373 && x339 = x372 && x338 = x371 && x337 = x370 && x336 = x369 && x335 = x368 && x334 = x367 && x333 = x366 && x332 = x365 && x331 = x364 && x330 = x363 && x329 = x362 && x328 = x361 && x327 = x360 && x326 = x359 && x325 = x358 && x324 = x357 && x323 = x356 && x322 = x355 && x321 = x354 && x320 = x353 && x319 = x352 && x318 = x351 && x317 = x350 && x316 = x349 && x315 = x348 && x314 = x347 && x313 = x346 && x312 = x345 && x311 = x344 && x310 = x343 && x309 = x342 && x308 = x341
l5(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l2(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x406 = x439 && x405 = x438 && x404 = x437 && x403 = x436 && x402 = x435 && x401 = x434 && x400 = x433 && x399 = x432 && x398 = x431 && x397 = x430 && x396 = x429 && x395 = x428 && x394 = x427 && x393 = x426 && x392 = x425 && x391 = x424 && x390 = x423 && x387 = x420 && x386 = x419 && x385 = x418 && x384 = x417 && x383 = x416 && x382 = x415 && x381 = x414 && x380 = x413 && x379 = x412 && x378 = x411 && x377 = x410 && x376 = x409 && x375 = x408 && x374 = x407 && x421 = 0 && x422 = x385
l6(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472) -> l5(x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505) :|: x472 = x505 && x471 = x504 && x470 = x503 && x469 = x502 && x468 = x501 && x467 = x500 && x466 = x499 && x465 = x498 && x464 = x497 && x463 = x496 && x462 = x495 && x461 = x494 && x460 = x493 && x459 = x492 && x458 = x491 && x457 = x490 && x456 = x489 && x455 = x488 && x454 = x487 && x453 = x486 && x452 = x485 && x451 = x484 && x450 = x483 && x449 = x482 && x448 = x481 && x447 = x480 && x446 = x479 && x445 = x478 && x444 = x477 && x443 = x476 && x442 = x475 && x441 = x474 && x440 = x473
Start term: l6(__const_12299HAT0, __const_15137HAT0, __const_16069HAT0, __const_16819HAT0, __const_20995HAT0, __const_2446HAT0, __const_25172HAT0, __const_3196HAT0, __const_4433HAT0, __const_6270HAT0, __const_7373HAT0, __const_8HAT0, __const_9633HAT0, constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0)

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

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

(2)
Obligation:
Rules:
l0(__const_12299HAT0, __const_15137HAT0, __const_16069HAT0, __const_16819HAT0, __const_20995HAT0, __const_2446HAT0, __const_25172HAT0, __const_3196HAT0, __const_4433HAT0, __const_6270HAT0, __const_7373HAT0, __const_8HAT0, __const_9633HAT0, constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0) -> l1(__const_12299HATpost, __const_15137HATpost, __const_16069HATpost, __const_16819HATpost, __const_20995HATpost, __const_2446HATpost, __const_25172HATpost, __const_3196HATpost, __const_4433HATpost, __const_6270HATpost, __const_7373HATpost, __const_8HATpost, __const_9633HATpost, constant22HATpost, i20HATpost, lx2HATpost, tmp03HATpost, tmp1011HATpost, tmp1112HATpost, tmp1213HATpost, tmp1314HATpost, tmp14HATpost, tmp25HATpost, tmp36HATpost, tmp47HATpost, tmp58HATpost, tmp69HATpost, tmp710HATpost, z115HATpost, z216HATpost, z317HATpost, z418HATpost, z519HATpost) :|: z519HAT0 = z519HATpost && z418HAT0 = z418HATpost && z317HAT0 = z317HATpost && z216HAT0 = z216HATpost && z115HAT0 = z115HATpost && tmp710HAT0 = tmp710HATpost && tmp69HAT0 = tmp69HATpost && tmp58HAT0 = tmp58HATpost && tmp47HAT0 = tmp47HATpost && tmp36HAT0 = tmp36HATpost && tmp25HAT0 = tmp25HATpost && tmp14HAT0 = tmp14HATpost && tmp1314HAT0 = tmp1314HATpost && tmp1213HAT0 = tmp1213HATpost && tmp1112HAT0 = tmp1112HATpost && tmp1011HAT0 = tmp1011HATpost && tmp03HAT0 = tmp03HATpost && lx2HAT0 = lx2HATpost && constant22HAT0 = constant22HATpost && __const_9633HAT0 = __const_9633HATpost && __const_8HAT0 = __const_8HATpost && __const_7373HAT0 = __const_7373HATpost && __const_6270HAT0 = __const_6270HATpost && __const_4433HAT0 = __const_4433HATpost && __const_3196HAT0 = __const_3196HATpost && __const_25172HAT0 = __const_25172HATpost && __const_2446HAT0 = __const_2446HATpost && __const_20995HAT0 = __const_20995HATpost && __const_16819HAT0 = __const_16819HATpost && __const_16069HAT0 = __const_16069HATpost && __const_15137HAT0 = __const_15137HATpost && __const_12299HAT0 = __const_12299HATpost && i20HATpost = 0 && __const_8HAT0 <= i20HAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: 1 + x14 <= x11 && x49 = x49 && x66 = x66 && x54 = x54 && x67 = x67 && x55 = x55 && x68 = x68 && x56 = x56 && x69 = x69 && x50 = x49 + x56 && x53 = x49 - x56 && x51 = x54 + x55 && x52 = x54 - x55 && x70 = x8 && x71 = x71 && x72 = x9 && x73 = -1 * x1 && x74 = x69 + x66 && x75 = x68 + x67 && x76 = x69 + x67 && x77 = x68 + x66 && x78 = x12 && x65 = x65 && x79 = x5 && x57 = x57 && x80 = x3 && x58 = x58 && x81 = x6 && x59 = x59 && x82 = x && x60 = x60 && x83 = -1 * x10 && x61 = x61 && x84 = -1 * x4 && x62 = x62 && x85 = -1 * x2 && x86 = x86 && x46 = -1 * x7 && x87 = x87 && x63 = x86 + x65 && x64 = x87 + x65 && x47 = 1 + x14 && x = x33 && x1 = x34 && x2 = x35 && x3 = x36 && x4 = x37 && x5 = x38 && x6 = x39 && x7 = x40 && x8 = x41 && x9 = x42 && x10 = x43 && x11 = x44 && x12 = x45 && x15 = x48
l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l4(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x120 = x153 && x119 = x152 && x118 = x151 && x117 = x150 && x116 = x149 && x115 = x148 && x114 = x147 && x113 = x146 && x112 = x145 && x111 = x144 && x110 = x143 && x109 = x142 && x108 = x141 && x107 = x140 && x106 = x139 && x105 = x138 && x104 = x137 && x103 = x136 && x102 = x135 && x101 = x134 && x100 = x133 && x99 = x132 && x98 = x131 && x97 = x130 && x96 = x129 && x95 = x128 && x94 = x127 && x93 = x126 && x92 = x125 && x91 = x124 && x90 = x123 && x89 = x122 && x88 = x121 && x99 <= x102
l3(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: 1 + x168 <= x165 && x203 = x203 && x220 = x220 && x208 = x208 && x221 = x221 && x209 = x209 && x222 = x222 && x210 = x210 && x223 = x223 && x204 = x203 + x210 && x207 = x203 - x210 && x205 = x208 + x209 && x206 = x208 - x209 && x224 = x162 && x225 = x225 && x226 = x163 && x227 = -1 * x155 && x228 = x223 + x220 && x229 = x222 + x221 && x230 = x223 + x221 && x231 = x222 + x220 && x232 = x166 && x219 = x219 && x233 = x159 && x211 = x211 && x234 = x157 && x212 = x212 && x235 = x160 && x213 = x213 && x236 = x154 && x214 = x214 && x237 = -1 * x164 && x215 = x215 && x238 = -1 * x158 && x216 = x216 && x239 = -1 * x156 && x240 = x240 && x200 = -1 * x161 && x241 = x241 && x217 = x240 + x219 && x218 = x241 + x219 && x201 = 1 + x168 && x154 = x187 && x155 = x188 && x156 = x189 && x157 = x190 && x158 = x191 && x159 = x192 && x160 = x193 && x161 = x194 && x162 = x195 && x163 = x196 && x164 = x197 && x165 = x198 && x166 = x199 && x169 = x202
l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l0(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x274 = x307 && x273 = x306 && x272 = x305 && x271 = x304 && x270 = x303 && x269 = x302 && x268 = x301 && x267 = x300 && x266 = x299 && x265 = x298 && x264 = x297 && x263 = x296 && x262 = x295 && x261 = x294 && x260 = x293 && x259 = x292 && x258 = x291 && x257 = x290 && x256 = x289 && x255 = x288 && x254 = x287 && x253 = x286 && x252 = x285 && x251 = x284 && x250 = x283 && x249 = x282 && x248 = x281 && x247 = x280 && x246 = x279 && x245 = x278 && x244 = x277 && x243 = x276 && x242 = x275
l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l3(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x340 = x373 && x339 = x372 && x338 = x371 && x337 = x370 && x336 = x369 && x335 = x368 && x334 = x367 && x333 = x366 && x332 = x365 && x331 = x364 && x330 = x363 && x329 = x362 && x328 = x361 && x327 = x360 && x326 = x359 && x325 = x358 && x324 = x357 && x323 = x356 && x322 = x355 && x321 = x354 && x320 = x353 && x319 = x352 && x318 = x351 && x317 = x350 && x316 = x349 && x315 = x348 && x314 = x347 && x313 = x346 && x312 = x345 && x311 = x344 && x310 = x343 && x309 = x342 && x308 = x341
l5(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l2(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x406 = x439 && x405 = x438 && x404 = x437 && x403 = x436 && x402 = x435 && x401 = x434 && x400 = x433 && x399 = x432 && x398 = x431 && x397 = x430 && x396 = x429 && x395 = x428 && x394 = x427 && x393 = x426 && x392 = x425 && x391 = x424 && x390 = x423 && x387 = x420 && x386 = x419 && x385 = x418 && x384 = x417 && x383 = x416 && x382 = x415 && x381 = x414 && x380 = x413 && x379 = x412 && x378 = x411 && x377 = x410 && x376 = x409 && x375 = x408 && x374 = x407 && x421 = 0 && x422 = x385
l6(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472) -> l5(x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505) :|: x472 = x505 && x471 = x504 && x470 = x503 && x469 = x502 && x468 = x501 && x467 = x500 && x466 = x499 && x465 = x498 && x464 = x497 && x463 = x496 && x462 = x495 && x461 = x494 && x460 = x493 && x459 = x492 && x458 = x491 && x457 = x490 && x456 = x489 && x455 = x488 && x454 = x487 && x453 = x486 && x452 = x485 && x451 = x484 && x450 = x483 && x449 = x482 && x448 = x481 && x447 = x480 && x446 = x479 && x445 = x478 && x444 = x477 && x443 = x476 && x442 = x475 && x441 = x474 && x440 = x473
Start term: l6(__const_12299HAT0, __const_15137HAT0, __const_16069HAT0, __const_16819HAT0, __const_20995HAT0, __const_2446HAT0, __const_25172HAT0, __const_3196HAT0, __const_4433HAT0, __const_6270HAT0, __const_7373HAT0, __const_8HAT0, __const_9633HAT0, constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(__const_12299HAT0, __const_15137HAT0, __const_16069HAT0, __const_16819HAT0, __const_20995HAT0, __const_2446HAT0, __const_25172HAT0, __const_3196HAT0, __const_4433HAT0, __const_6270HAT0, __const_7373HAT0, __const_8HAT0, __const_9633HAT0, constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0) -> l1(__const_12299HATpost, __const_15137HATpost, __const_16069HATpost, __const_16819HATpost, __const_20995HATpost, __const_2446HATpost, __const_25172HATpost, __const_3196HATpost, __const_4433HATpost, __const_6270HATpost, __const_7373HATpost, __const_8HATpost, __const_9633HATpost, constant22HATpost, i20HATpost, lx2HATpost, tmp03HATpost, tmp1011HATpost, tmp1112HATpost, tmp1213HATpost, tmp1314HATpost, tmp14HATpost, tmp25HATpost, tmp36HATpost, tmp47HATpost, tmp58HATpost, tmp69HATpost, tmp710HATpost, z115HATpost, z216HATpost, z317HATpost, z418HATpost, z519HATpost) :|: z519HAT0 = z519HATpost && z418HAT0 = z418HATpost && z317HAT0 = z317HATpost && z216HAT0 = z216HATpost && z115HAT0 = z115HATpost && tmp710HAT0 = tmp710HATpost && tmp69HAT0 = tmp69HATpost && tmp58HAT0 = tmp58HATpost && tmp47HAT0 = tmp47HATpost && tmp36HAT0 = tmp36HATpost && tmp25HAT0 = tmp25HATpost && tmp14HAT0 = tmp14HATpost && tmp1314HAT0 = tmp1314HATpost && tmp1213HAT0 = tmp1213HATpost && tmp1112HAT0 = tmp1112HATpost && tmp1011HAT0 = tmp1011HATpost && tmp03HAT0 = tmp03HATpost && lx2HAT0 = lx2HATpost && constant22HAT0 = constant22HATpost && __const_9633HAT0 = __const_9633HATpost && __const_8HAT0 = __const_8HATpost && __const_7373HAT0 = __const_7373HATpost && __const_6270HAT0 = __const_6270HATpost && __const_4433HAT0 = __const_4433HATpost && __const_3196HAT0 = __const_3196HATpost && __const_25172HAT0 = __const_25172HATpost && __const_2446HAT0 = __const_2446HATpost && __const_20995HAT0 = __const_20995HATpost && __const_16819HAT0 = __const_16819HATpost && __const_16069HAT0 = __const_16069HATpost && __const_15137HAT0 = __const_15137HATpost && __const_12299HAT0 = __const_12299HATpost && i20HATpost = 0 && __const_8HAT0 <= i20HAT0
(2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: 1 + x14 <= x11 && x49 = x49 && x66 = x66 && x54 = x54 && x67 = x67 && x55 = x55 && x68 = x68 && x56 = x56 && x69 = x69 && x50 = x49 + x56 && x53 = x49 - x56 && x51 = x54 + x55 && x52 = x54 - x55 && x70 = x8 && x71 = x71 && x72 = x9 && x73 = -1 * x1 && x74 = x69 + x66 && x75 = x68 + x67 && x76 = x69 + x67 && x77 = x68 + x66 && x78 = x12 && x65 = x65 && x79 = x5 && x57 = x57 && x80 = x3 && x58 = x58 && x81 = x6 && x59 = x59 && x82 = x && x60 = x60 && x83 = -1 * x10 && x61 = x61 && x84 = -1 * x4 && x62 = x62 && x85 = -1 * x2 && x86 = x86 && x46 = -1 * x7 && x87 = x87 && x63 = x86 + x65 && x64 = x87 + x65 && x47 = 1 + x14 && x = x33 && x1 = x34 && x2 = x35 && x3 = x36 && x4 = x37 && x5 = x38 && x6 = x39 && x7 = x40 && x8 = x41 && x9 = x42 && x10 = x43 && x11 = x44 && x12 = x45 && x15 = x48
(3) l3(x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120) -> l4(x121, x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150, x151, x152, x153) :|: x120 = x153 && x119 = x152 && x118 = x151 && x117 = x150 && x116 = x149 && x115 = x148 && x114 = x147 && x113 = x146 && x112 = x145 && x111 = x144 && x110 = x143 && x109 = x142 && x108 = x141 && x107 = x140 && x106 = x139 && x105 = x138 && x104 = x137 && x103 = x136 && x102 = x135 && x101 = x134 && x100 = x133 && x99 = x132 && x98 = x131 && x97 = x130 && x96 = x129 && x95 = x128 && x94 = x127 && x93 = x126 && x92 = x125 && x91 = x124 && x90 = x123 && x89 = x122 && x88 = x121 && x99 <= x102
(4) l3(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: 1 + x168 <= x165 && x203 = x203 && x220 = x220 && x208 = x208 && x221 = x221 && x209 = x209 && x222 = x222 && x210 = x210 && x223 = x223 && x204 = x203 + x210 && x207 = x203 - x210 && x205 = x208 + x209 && x206 = x208 - x209 && x224 = x162 && x225 = x225 && x226 = x163 && x227 = -1 * x155 && x228 = x223 + x220 && x229 = x222 + x221 && x230 = x223 + x221 && x231 = x222 + x220 && x232 = x166 && x219 = x219 && x233 = x159 && x211 = x211 && x234 = x157 && x212 = x212 && x235 = x160 && x213 = x213 && x236 = x154 && x214 = x214 && x237 = -1 * x164 && x215 = x215 && x238 = -1 * x158 && x216 = x216 && x239 = -1 * x156 && x240 = x240 && x200 = -1 * x161 && x241 = x241 && x217 = x240 + x219 && x218 = x241 + x219 && x201 = 1 + x168 && x154 = x187 && x155 = x188 && x156 = x189 && x157 = x190 && x158 = x191 && x159 = x192 && x160 = x193 && x161 = x194 && x162 = x195 && x163 = x196 && x164 = x197 && x165 = x198 && x166 = x199 && x169 = x202
(5) l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l0(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x274 = x307 && x273 = x306 && x272 = x305 && x271 = x304 && x270 = x303 && x269 = x302 && x268 = x301 && x267 = x300 && x266 = x299 && x265 = x298 && x264 = x297 && x263 = x296 && x262 = x295 && x261 = x294 && x260 = x293 && x259 = x292 && x258 = x291 && x257 = x290 && x256 = x289 && x255 = x288 && x254 = x287 && x253 = x286 && x252 = x285 && x251 = x284 && x250 = x283 && x249 = x282 && x248 = x281 && x247 = x280 && x246 = x279 && x245 = x278 && x244 = x277 && x243 = x276 && x242 = x275
(6) l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l3(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x340 = x373 && x339 = x372 && x338 = x371 && x337 = x370 && x336 = x369 && x335 = x368 && x334 = x367 && x333 = x366 && x332 = x365 && x331 = x364 && x330 = x363 && x329 = x362 && x328 = x361 && x327 = x360 && x326 = x359 && x325 = x358 && x324 = x357 && x323 = x356 && x322 = x355 && x321 = x354 && x320 = x353 && x319 = x352 && x318 = x351 && x317 = x350 && x316 = x349 && x315 = x348 && x314 = x347 && x313 = x346 && x312 = x345 && x311 = x344 && x310 = x343 && x309 = x342 && x308 = x341
(7) l5(x374, x375, x376, x377, x378, x379, x380, x381, x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401, x402, x403, x404, x405, x406) -> l2(x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421, x422, x423, x424, x425, x426, x427, x428, x429, x430, x431, x432, x433, x434, x435, x436, x437, x438, x439) :|: x406 = x439 && x405 = x438 && x404 = x437 && x403 = x436 && x402 = x435 && x401 = x434 && x400 = x433 && x399 = x432 && x398 = x431 && x397 = x430 && x396 = x429 && x395 = x428 && x394 = x427 && x393 = x426 && x392 = x425 && x391 = x424 && x390 = x423 && x387 = x420 && x386 = x419 && x385 = x418 && x384 = x417 && x383 = x416 && x382 = x415 && x381 = x414 && x380 = x413 && x379 = x412 && x378 = x411 && x377 = x410 && x376 = x409 && x375 = x408 && x374 = x407 && x421 = 0 && x422 = x385
(8) l6(x440, x441, x442, x443, x444, x445, x446, x447, x448, x449, x450, x451, x452, x453, x454, x455, x456, x457, x458, x459, x460, x461, x462, x463, x464, x465, x466, x467, x468, x469, x470, x471, x472) -> l5(x473, x474, x475, x476, x477, x478, x479, x480, x481, x482, x483, x484, x485, x486, x487, x488, x489, x490, x491, x492, x493, x494, x495, x496, x497, x498, x499, x500, x501, x502, x503, x504, x505) :|: x472 = x505 && x471 = x504 && x470 = x503 && x469 = x502 && x468 = x501 && x467 = x500 && x466 = x499 && x465 = x498 && x464 = x497 && x463 = x496 && x462 = x495 && x461 = x494 && x460 = x493 && x459 = x492 && x458 = x491 && x457 = x490 && x456 = x489 && x455 = x488 && x454 = x487 && x453 = x486 && x452 = x485 && x451 = x484 && x450 = x483 && x449 = x482 && x448 = x481 && x447 = x480 && x446 = x479 && x445 = x478 && x444 = x477 && x443 = x476 && x442 = x475 && x441 = x474 && x440 = x473

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32) -> l2(x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59, x60, x61, x62, x63, x64, x65) :|: 1 + x14 <= x11 && x49 = x49 && x66 = x66 && x54 = x54 && x67 = x67 && x55 = x55 && x68 = x68 && x56 = x56 && x69 = x69 && x50 = x49 + x56 && x53 = x49 - x56 && x51 = x54 + x55 && x52 = x54 - x55 && x70 = x8 && x71 = x71 && x72 = x9 && x73 = -1 * x1 && x74 = x69 + x66 && x75 = x68 + x67 && x76 = x69 + x67 && x77 = x68 + x66 && x78 = x12 && x65 = x65 && x79 = x5 && x57 = x57 && x80 = x3 && x58 = x58 && x81 = x6 && x59 = x59 && x82 = x && x60 = x60 && x83 = -1 * x10 && x61 = x61 && x84 = -1 * x4 && x62 = x62 && x85 = -1 * x2 && x86 = x86 && x46 = -1 * x7 && x87 = x87 && x63 = x86 + x65 && x64 = x87 + x65 && x47 = 1 + x14 && x = x33 && x1 = x34 && x2 = x35 && x3 = x36 && x4 = x37 && x5 = x38 && x6 = x39 && x7 = x40 && x8 = x41 && x9 = x42 && x10 = x43 && x11 = x44 && x12 = x45 && x15 = x48
(2) l2(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274) -> l0(x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307) :|: x274 = x307 && x273 = x306 && x272 = x305 && x271 = x304 && x270 = x303 && x269 = x302 && x268 = x301 && x267 = x300 && x266 = x299 && x265 = x298 && x264 = x297 && x263 = x296 && x262 = x295 && x261 = x294 && x260 = x293 && x259 = x292 && x258 = x291 && x257 = x290 && x256 = x289 && x255 = x288 && x254 = x287 && x253 = x286 && x252 = x285 && x251 = x284 && x250 = x283 && x249 = x282 && x248 = x281 && x247 = x280 && x246 = x279 && x245 = x278 && x244 = x277 && x243 = x276 && x242 = x275

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l0(x275:0, x1:0, x277:0, x278:0, x279:0, x280:0, x281:0, x282:0, x283:0, x284:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0, x18:0, x19:0, x20:0, x21:0, x22:0, x23:0, x24:0, x25:0, x26:0, x27:0, x28:0, x29:0, x30:0, x31:0, x32:0) -> l0(x275:0, x1:0, x277:0, x278:0, x279:0, x280:0, x281:0, x282:0, x283:0, x284:0, x10:0, x11:0, x12:0, -1 * x282:0, 1 + x14:0, x15:0, x291:0, x291:0 + x298:0, x296:0 + x297:0, x296:0 - x297:0, x291:0 - x298:0, x296:0, x297:0, x298:0, x299:0, x300:0, x301:0, x302:0, x303:0, x304:0, x86:0 + x307:0, x87:0 + x307:0, x307:0) :|: x11:0 >= 1 + x14:0

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

   l0(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) -> l0(x12, x15)

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(9)
Obligation:
Rules:
l0(x11:0, x14:0) -> l0(x11:0, 1 + x14:0) :|: x11:0 >= 1 + x14:0

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(10) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l0(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(11)
Obligation:
Rules:
l0(x11:0, x14:0) -> l0(x11:0, c) :|: c = 1 + x14:0 && x11:0 >= 1 + x14:0

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

The following rules are decreasing:
l0(x11:0, x14:0) -> l0(x11:0, c) :|: c = 1 + x14:0 && x11:0 >= 1 + x14:0

The following rules are bounded:
l0(x11:0, x14:0) -> l0(x11:0, c) :|: c = 1 + x14:0 && x11:0 >= 1 + x14:0


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(13)
YES

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(14)
Obligation:

Termination digraph:
Nodes:
(1) l1(x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330, x331, x332, x333, x334, x335, x336, x337, x338, x339, x340) -> l3(x341, x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361, x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373) :|: x340 = x373 && x339 = x372 && x338 = x371 && x337 = x370 && x336 = x369 && x335 = x368 && x334 = x367 && x333 = x366 && x332 = x365 && x331 = x364 && x330 = x363 && x329 = x362 && x328 = x361 && x327 = x360 && x326 = x359 && x325 = x358 && x324 = x357 && x323 = x356 && x322 = x355 && x321 = x354 && x320 = x353 && x319 = x352 && x318 = x351 && x317 = x350 && x316 = x349 && x315 = x348 && x314 = x347 && x313 = x346 && x312 = x345 && x311 = x344 && x310 = x343 && x309 = x342 && x308 = x341
(2) l3(x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186) -> l1(x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219) :|: 1 + x168 <= x165 && x203 = x203 && x220 = x220 && x208 = x208 && x221 = x221 && x209 = x209 && x222 = x222 && x210 = x210 && x223 = x223 && x204 = x203 + x210 && x207 = x203 - x210 && x205 = x208 + x209 && x206 = x208 - x209 && x224 = x162 && x225 = x225 && x226 = x163 && x227 = -1 * x155 && x228 = x223 + x220 && x229 = x222 + x221 && x230 = x223 + x221 && x231 = x222 + x220 && x232 = x166 && x219 = x219 && x233 = x159 && x211 = x211 && x234 = x157 && x212 = x212 && x235 = x160 && x213 = x213 && x236 = x154 && x214 = x214 && x237 = -1 * x164 && x215 = x215 && x238 = -1 * x158 && x216 = x216 && x239 = -1 * x156 && x240 = x240 && x200 = -1 * x161 && x241 = x241 && x217 = x240 + x219 && x218 = x241 + x219 && x201 = 1 + x168 && x154 = x187 && x155 = x188 && x156 = x189 && x157 = x190 && x158 = x191 && x159 = x192 && x160 = x193 && x161 = x194 && x162 = x195 && x163 = x196 && x164 = x197 && x165 = x198 && x166 = x199 && x169 = x202

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

This digraph is fully evaluated!

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(15) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(16)
Obligation:
Rules:
l1(x187:0, x188:0, x189:0, x190:0, x191:0, x192:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0, x321:0, x322:0, x202:0, x324:0, x325:0, x326:0, x327:0, x328:0, x329:0, x330:0, x331:0, x332:0, x333:0, x334:0, x335:0, x336:0, x337:0, x338:0, x339:0, x340:0) -> l1(x187:0, x188:0, x189:0, x190:0, x191:0, x192:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0, -1 * x194:0, 1 + x322:0, x202:0, x203:0, x203:0 + x210:0, x208:0 + x209:0, x208:0 - x209:0, x203:0 - x210:0, x208:0, x209:0, x210:0, x211:0, x212:0, x213:0, x214:0, x215:0, x216:0, x240:0 + x219:0, x241:0 + x219:0, x219:0) :|: x198:0 >= 1 + x322:0

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

   l1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33) -> l1(x12, x15)

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(18)
Obligation:
Rules:
l1(x198:0, x322:0) -> l1(x198:0, 1 + x322:0) :|: x198:0 >= 1 + x322:0

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(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l1(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
l1(x198:0, x322:0) -> l1(x198:0, c) :|: c = 1 + x322:0 && x198:0 >= 1 + x322:0

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(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l1 ] = l1_1 + -1*l1_2

The following rules are decreasing:
l1(x198:0, x322:0) -> l1(x198:0, c) :|: c = 1 + x322:0 && x198:0 >= 1 + x322:0

The following rules are bounded:
l1(x198:0, x322:0) -> l1(x198:0, c) :|: c = 1 + x322:0 && x198:0 >= 1 + x322:0


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(22)
YES