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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 30.3 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 5 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 6 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 4 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 34 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 3 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) TempFilterProof [SOUND, 7 ms]
        (29) IntTRS
        (30) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) IRSwT
        (33) IntTRSCompressionProof [EQUIVALENT, 2 ms]
        (34) IRSwT
        (35) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (36) IRSwT
        (37) TempFilterProof [SOUND, 8 ms]
        (38) IntTRS
        (39) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (40) YES
    (41) IRSwT
        (42) IntTRSCompressionProof [EQUIVALENT, 22 ms]
        (43) IRSwT
        (44) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (45) IRSwT
        (46) TempFilterProof [SOUND, 6 ms]
        (47) IntTRS
        (48) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (49) YES
    (50) IRSwT
        (51) IntTRSCompressionProof [EQUIVALENT, 3 ms]
        (52) IRSwT
        (53) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (54) IRSwT
        (55) TempFilterProof [SOUND, 9 ms]
        (56) IntTRS
        (57) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (58) YES
    (59) IRSwT
        (60) IntTRSCompressionProof [EQUIVALENT, 3 ms]
        (61) IRSwT
        (62) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (63) IRSwT
        (64) TempFilterProof [SOUND, 8 ms]
        (65) IntTRS
        (66) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (67) YES
    (68) IRSwT
        (69) IntTRSCompressionProof [EQUIVALENT, 3 ms]
        (70) IRSwT
        (71) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (72) IRSwT
        (73) TempFilterProof [SOUND, 9 ms]
        (74) IntTRS
        (75) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (76) YES


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

(0)
Obligation:
Rules:
l0(__const_50HAT0, i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l3(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x7 = x17 && x = x10 && x <= x7
l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x37 = 1 + x27 && 1 + x27 <= x20
l5(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l6(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x47 = x57 && x40 = x50
l7(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l4(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x68 = x78 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72 && x61 = x71 && x60 = x70 && x77 = 0 && x60 <= x64
l7(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x86 = x96 && x85 = x95 && x83 = x93 && x82 = x92 && x81 = x91 && x87 = x97 && x80 = x90 && x94 = 1 + x84 && 1 + x84 <= x80
l9(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l10(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x107 = x117 && x100 = x110
l11(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l8(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x120 <= x123 && x140 = 0 && x134 = 0 && x120 = x130 && x127 = x137 && x121 = x131 && x122 = x132 && x123 = x133 && x125 = x135 && x126 = x136 && x128 = x138 && x129 = x139
l11(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l12(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160) :|: x150 = x160 && x149 = x159 && x147 = x157 && x146 = x156 && x145 = x155 && x143 = x153 && x142 = x152 && x148 = x158 && x141 = x151 && x154 = 1 + x144 && 1 + x144 <= x141
l13(x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l14(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180) :|: x170 = x180 && x169 = x179 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x168 = x178 && x161 = x171
l15(x181, x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l12(x191, x192, x193, x194, x195, x196, x197, x198, x199, x200) :|: x181 <= x183 && x201 = 0 && x194 = 0 && x181 = x191 && x188 = x198 && x182 = x192 && x183 = x193 && x185 = x195 && x186 = x196 && x187 = x197 && x189 = x199 && x190 = x200
l15(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211) -> l16(x212, x213, x214, x215, x216, x217, x218, x219, x220, x221) :|: x211 = x221 && x210 = x220 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x203 = x213 && x209 = x219 && x202 = x212 && x214 = 1 + x204 && 1 + x204 <= x202
l16(x222, x223, x224, x225, x226, x227, x228, x229, x230, x231) -> l15(x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x231 = x241 && x230 = x240 && x228 = x238 && x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x229 = x239 && x222 = x232
l14(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l16(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261) :|: x242 <= x249 && x262 = 0 && x254 = 0 && x242 = x252 && x249 = x259 && x243 = x253 && x245 = x255 && x246 = x256 && x247 = x257 && x248 = x258 && x250 = x260 && x251 = x261
l14(x263, x264, x265, x266, x267, x268, x269, x270, x271, x272) -> l13(x273, x274, x275, x276, x277, x278, x279, x280, x281, x282) :|: x272 = x282 && x271 = x281 && x269 = x279 && x268 = x278 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x280 = 1 + x270 && 1 + x270 <= x263
l12(x283, x284, x285, x286, x287, x288, x289, x290, x291, x292) -> l11(x293, x294, x295, x296, x297, x298, x299, x300, x301, x302) :|: x292 = x302 && x291 = x301 && x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x290 = x300 && x283 = x293
l10(x303, x304, x305, x306, x307, x308, x309, x310, x311, x312) -> l13(x313, x314, x315, x316, x317, x318, x319, x320, x321, x322) :|: x312 = x322 && x311 = x321 && x309 = x319 && x308 = x318 && x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x320 = 0 && x303 <= x304
l10(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l9(x333, x334, x335, x336, x337, x338, x339, x340, x341, x342) :|: x332 = x342 && x331 = x341 && x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x330 = x340 && x323 = x333 && x334 = 1 + x324 && 1 + x324 <= x323
l8(x343, x344, x345, x346, x347, x348, x349, x350, x351, x352) -> l7(x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: x352 = x362 && x351 = x361 && x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x350 = x360 && x343 = x353
l6(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372) -> l9(x373, x374, x375, x376, x377, x378, x379, x380, x381, x382) :|: x363 <= x369 && x383 = 0 && x374 = 0 && x363 = x373 && x370 = x380 && x365 = x375 && x366 = x376 && x367 = x377 && x368 = x378 && x369 = x379 && x371 = x381 && x372 = x382
l6(x384, x385, x386, x387, x388, x389, x390, x391, x392, x393) -> l5(x394, x395, x396, x397, x398, x399, x400, x401, x402, x403) :|: x393 = x403 && x392 = x402 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x391 = x401 && x384 = x394 && x400 = 1 + x390 && 1 + x390 <= x384
l4(x404, x405, x406, x407, x408, x409, x410, x411, x412, x413) -> l2(x414, x415, x416, x417, x418, x419, x420, x421, x422, x423) :|: x413 = x423 && x412 = x422 && x410 = x420 && x409 = x419 && x408 = x418 && x407 = x417 && x406 = x416 && x405 = x415 && x411 = x421 && x404 = x414
l1(x424, x425, x426, x427, x428, x429, x430, x431, x432, x433) -> l5(x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) :|: x424 <= x429 && x444 = 0 && x440 = 0 && x424 = x434 && x431 = x441 && x425 = x435 && x426 = x436 && x427 = x437 && x428 = x438 && x429 = x439 && x432 = x442 && x433 = x443
l1(x445, x446, x447, x448, x449, x450, x451, x452, x453, x454) -> l0(x455, x456, x457, x458, x459, x460, x461, x462, x463, x464) :|: x454 = x464 && x453 = x463 && x451 = x461 && x449 = x459 && x448 = x458 && x447 = x457 && x446 = x456 && x452 = x462 && x445 = x455 && x460 = 1 + x450 && 1 + x450 <= x445
l17(x465, x466, x467, x468, x469, x470, x471, x472, x473, x474) -> l0(x475, x476, x477, x478, x479, x480, x481, x482, x483, x484) :|: x482 = 0 && x483 = x483 && x484 = x484 && x485 = 0 && x480 = 0 && x465 = x475 && x466 = x476 && x467 = x477 && x468 = x478 && x469 = x479 && x471 = x481
l18(x486, x487, x488, x489, x490, x491, x492, x493, x494, x495) -> l17(x496, x497, x498, x499, x500, x501, x502, x503, x504, x505) :|: x495 = x505 && x494 = x504 && x492 = x502 && x491 = x501 && x490 = x500 && x489 = x499 && x488 = x498 && x487 = x497 && x493 = x503 && x486 = x496
Start term: l18(__const_50HAT0, i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0)

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

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

(2)
Obligation:
Rules:
l0(__const_50HAT0, i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l3(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x7 = x17 && x = x10 && x <= x7
l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x37 = 1 + x27 && 1 + x27 <= x20
l5(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l6(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x47 = x57 && x40 = x50
l7(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l4(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x68 = x78 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72 && x61 = x71 && x60 = x70 && x77 = 0 && x60 <= x64
l7(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x86 = x96 && x85 = x95 && x83 = x93 && x82 = x92 && x81 = x91 && x87 = x97 && x80 = x90 && x94 = 1 + x84 && 1 + x84 <= x80
l9(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l10(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x107 = x117 && x100 = x110
l11(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l8(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x120 <= x123 && x140 = 0 && x134 = 0 && x120 = x130 && x127 = x137 && x121 = x131 && x122 = x132 && x123 = x133 && x125 = x135 && x126 = x136 && x128 = x138 && x129 = x139
l11(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l12(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160) :|: x150 = x160 && x149 = x159 && x147 = x157 && x146 = x156 && x145 = x155 && x143 = x153 && x142 = x152 && x148 = x158 && x141 = x151 && x154 = 1 + x144 && 1 + x144 <= x141
l13(x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l14(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180) :|: x170 = x180 && x169 = x179 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x168 = x178 && x161 = x171
l15(x181, x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l12(x191, x192, x193, x194, x195, x196, x197, x198, x199, x200) :|: x181 <= x183 && x201 = 0 && x194 = 0 && x181 = x191 && x188 = x198 && x182 = x192 && x183 = x193 && x185 = x195 && x186 = x196 && x187 = x197 && x189 = x199 && x190 = x200
l15(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211) -> l16(x212, x213, x214, x215, x216, x217, x218, x219, x220, x221) :|: x211 = x221 && x210 = x220 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x203 = x213 && x209 = x219 && x202 = x212 && x214 = 1 + x204 && 1 + x204 <= x202
l16(x222, x223, x224, x225, x226, x227, x228, x229, x230, x231) -> l15(x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x231 = x241 && x230 = x240 && x228 = x238 && x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x229 = x239 && x222 = x232
l14(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l16(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261) :|: x242 <= x249 && x262 = 0 && x254 = 0 && x242 = x252 && x249 = x259 && x243 = x253 && x245 = x255 && x246 = x256 && x247 = x257 && x248 = x258 && x250 = x260 && x251 = x261
l14(x263, x264, x265, x266, x267, x268, x269, x270, x271, x272) -> l13(x273, x274, x275, x276, x277, x278, x279, x280, x281, x282) :|: x272 = x282 && x271 = x281 && x269 = x279 && x268 = x278 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x280 = 1 + x270 && 1 + x270 <= x263
l12(x283, x284, x285, x286, x287, x288, x289, x290, x291, x292) -> l11(x293, x294, x295, x296, x297, x298, x299, x300, x301, x302) :|: x292 = x302 && x291 = x301 && x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x290 = x300 && x283 = x293
l10(x303, x304, x305, x306, x307, x308, x309, x310, x311, x312) -> l13(x313, x314, x315, x316, x317, x318, x319, x320, x321, x322) :|: x312 = x322 && x311 = x321 && x309 = x319 && x308 = x318 && x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x320 = 0 && x303 <= x304
l10(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l9(x333, x334, x335, x336, x337, x338, x339, x340, x341, x342) :|: x332 = x342 && x331 = x341 && x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x330 = x340 && x323 = x333 && x334 = 1 + x324 && 1 + x324 <= x323
l8(x343, x344, x345, x346, x347, x348, x349, x350, x351, x352) -> l7(x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: x352 = x362 && x351 = x361 && x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x350 = x360 && x343 = x353
l6(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372) -> l9(x373, x374, x375, x376, x377, x378, x379, x380, x381, x382) :|: x363 <= x369 && x383 = 0 && x374 = 0 && x363 = x373 && x370 = x380 && x365 = x375 && x366 = x376 && x367 = x377 && x368 = x378 && x369 = x379 && x371 = x381 && x372 = x382
l6(x384, x385, x386, x387, x388, x389, x390, x391, x392, x393) -> l5(x394, x395, x396, x397, x398, x399, x400, x401, x402, x403) :|: x393 = x403 && x392 = x402 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x391 = x401 && x384 = x394 && x400 = 1 + x390 && 1 + x390 <= x384
l4(x404, x405, x406, x407, x408, x409, x410, x411, x412, x413) -> l2(x414, x415, x416, x417, x418, x419, x420, x421, x422, x423) :|: x413 = x423 && x412 = x422 && x410 = x420 && x409 = x419 && x408 = x418 && x407 = x417 && x406 = x416 && x405 = x415 && x411 = x421 && x404 = x414
l1(x424, x425, x426, x427, x428, x429, x430, x431, x432, x433) -> l5(x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) :|: x424 <= x429 && x444 = 0 && x440 = 0 && x424 = x434 && x431 = x441 && x425 = x435 && x426 = x436 && x427 = x437 && x428 = x438 && x429 = x439 && x432 = x442 && x433 = x443
l1(x445, x446, x447, x448, x449, x450, x451, x452, x453, x454) -> l0(x455, x456, x457, x458, x459, x460, x461, x462, x463, x464) :|: x454 = x464 && x453 = x463 && x451 = x461 && x449 = x459 && x448 = x458 && x447 = x457 && x446 = x456 && x452 = x462 && x445 = x455 && x460 = 1 + x450 && 1 + x450 <= x445
l17(x465, x466, x467, x468, x469, x470, x471, x472, x473, x474) -> l0(x475, x476, x477, x478, x479, x480, x481, x482, x483, x484) :|: x482 = 0 && x483 = x483 && x484 = x484 && x485 = 0 && x480 = 0 && x465 = x475 && x466 = x476 && x467 = x477 && x468 = x478 && x469 = x479 && x471 = x481
l18(x486, x487, x488, x489, x490, x491, x492, x493, x494, x495) -> l17(x496, x497, x498, x499, x500, x501, x502, x503, x504, x505) :|: x495 = x505 && x494 = x504 && x492 = x502 && x491 = x501 && x490 = x500 && x489 = x499 && x488 = x498 && x487 = x497 && x493 = x503 && x486 = x496
Start term: l18(__const_50HAT0, i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(__const_50HAT0, i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l3(x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) :|: x9 = x19 && x8 = x18 && x6 = x16 && x5 = x15 && x4 = x14 && x3 = x13 && x2 = x12 && x1 = x11 && x7 = x17 && x = x10 && x <= x7
(3) l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x37 = 1 + x27 && 1 + x27 <= x20
(4) l5(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l6(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x47 = x57 && x40 = x50
(5) l7(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69) -> l4(x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x69 = x79 && x68 = x78 && x66 = x76 && x65 = x75 && x64 = x74 && x63 = x73 && x62 = x72 && x61 = x71 && x60 = x70 && x77 = 0 && x60 <= x64
(6) l7(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x86 = x96 && x85 = x95 && x83 = x93 && x82 = x92 && x81 = x91 && x87 = x97 && x80 = x90 && x94 = 1 + x84 && 1 + x84 <= x80
(7) l9(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l10(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x107 = x117 && x100 = x110
(8) l11(x120, x121, x122, x123, x124, x125, x126, x127, x128, x129) -> l8(x130, x131, x132, x133, x134, x135, x136, x137, x138, x139) :|: x120 <= x123 && x140 = 0 && x134 = 0 && x120 = x130 && x127 = x137 && x121 = x131 && x122 = x132 && x123 = x133 && x125 = x135 && x126 = x136 && x128 = x138 && x129 = x139
(9) l11(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l12(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160) :|: x150 = x160 && x149 = x159 && x147 = x157 && x146 = x156 && x145 = x155 && x143 = x153 && x142 = x152 && x148 = x158 && x141 = x151 && x154 = 1 + x144 && 1 + x144 <= x141
(10) l13(x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l14(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180) :|: x170 = x180 && x169 = x179 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x168 = x178 && x161 = x171
(11) l15(x181, x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l12(x191, x192, x193, x194, x195, x196, x197, x198, x199, x200) :|: x181 <= x183 && x201 = 0 && x194 = 0 && x181 = x191 && x188 = x198 && x182 = x192 && x183 = x193 && x185 = x195 && x186 = x196 && x187 = x197 && x189 = x199 && x190 = x200
(12) l15(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211) -> l16(x212, x213, x214, x215, x216, x217, x218, x219, x220, x221) :|: x211 = x221 && x210 = x220 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x203 = x213 && x209 = x219 && x202 = x212 && x214 = 1 + x204 && 1 + x204 <= x202
(13) l16(x222, x223, x224, x225, x226, x227, x228, x229, x230, x231) -> l15(x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x231 = x241 && x230 = x240 && x228 = x238 && x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x229 = x239 && x222 = x232
(14) l14(x242, x243, x244, x245, x246, x247, x248, x249, x250, x251) -> l16(x252, x253, x254, x255, x256, x257, x258, x259, x260, x261) :|: x242 <= x249 && x262 = 0 && x254 = 0 && x242 = x252 && x249 = x259 && x243 = x253 && x245 = x255 && x246 = x256 && x247 = x257 && x248 = x258 && x250 = x260 && x251 = x261
(15) l14(x263, x264, x265, x266, x267, x268, x269, x270, x271, x272) -> l13(x273, x274, x275, x276, x277, x278, x279, x280, x281, x282) :|: x272 = x282 && x271 = x281 && x269 = x279 && x268 = x278 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x280 = 1 + x270 && 1 + x270 <= x263
(16) l12(x283, x284, x285, x286, x287, x288, x289, x290, x291, x292) -> l11(x293, x294, x295, x296, x297, x298, x299, x300, x301, x302) :|: x292 = x302 && x291 = x301 && x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x290 = x300 && x283 = x293
(17) l10(x303, x304, x305, x306, x307, x308, x309, x310, x311, x312) -> l13(x313, x314, x315, x316, x317, x318, x319, x320, x321, x322) :|: x312 = x322 && x311 = x321 && x309 = x319 && x308 = x318 && x307 = x317 && x306 = x316 && x305 = x315 && x304 = x314 && x303 = x313 && x320 = 0 && x303 <= x304
(18) l10(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l9(x333, x334, x335, x336, x337, x338, x339, x340, x341, x342) :|: x332 = x342 && x331 = x341 && x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x330 = x340 && x323 = x333 && x334 = 1 + x324 && 1 + x324 <= x323
(19) l8(x343, x344, x345, x346, x347, x348, x349, x350, x351, x352) -> l7(x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: x352 = x362 && x351 = x361 && x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x350 = x360 && x343 = x353
(20) l6(x363, x364, x365, x366, x367, x368, x369, x370, x371, x372) -> l9(x373, x374, x375, x376, x377, x378, x379, x380, x381, x382) :|: x363 <= x369 && x383 = 0 && x374 = 0 && x363 = x373 && x370 = x380 && x365 = x375 && x366 = x376 && x367 = x377 && x368 = x378 && x369 = x379 && x371 = x381 && x372 = x382
(21) l6(x384, x385, x386, x387, x388, x389, x390, x391, x392, x393) -> l5(x394, x395, x396, x397, x398, x399, x400, x401, x402, x403) :|: x393 = x403 && x392 = x402 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x391 = x401 && x384 = x394 && x400 = 1 + x390 && 1 + x390 <= x384
(22) l4(x404, x405, x406, x407, x408, x409, x410, x411, x412, x413) -> l2(x414, x415, x416, x417, x418, x419, x420, x421, x422, x423) :|: x413 = x423 && x412 = x422 && x410 = x420 && x409 = x419 && x408 = x418 && x407 = x417 && x406 = x416 && x405 = x415 && x411 = x421 && x404 = x414
(23) l1(x424, x425, x426, x427, x428, x429, x430, x431, x432, x433) -> l5(x434, x435, x436, x437, x438, x439, x440, x441, x442, x443) :|: x424 <= x429 && x444 = 0 && x440 = 0 && x424 = x434 && x431 = x441 && x425 = x435 && x426 = x436 && x427 = x437 && x428 = x438 && x429 = x439 && x432 = x442 && x433 = x443
(24) l1(x445, x446, x447, x448, x449, x450, x451, x452, x453, x454) -> l0(x455, x456, x457, x458, x459, x460, x461, x462, x463, x464) :|: x454 = x464 && x453 = x463 && x451 = x461 && x449 = x459 && x448 = x458 && x447 = x457 && x446 = x456 && x452 = x462 && x445 = x455 && x460 = 1 + x450 && 1 + x450 <= x445
(25) l17(x465, x466, x467, x468, x469, x470, x471, x472, x473, x474) -> l0(x475, x476, x477, x478, x479, x480, x481, x482, x483, x484) :|: x482 = 0 && x483 = x483 && x484 = x484 && x485 = 0 && x480 = 0 && x465 = x475 && x466 = x476 && x467 = x477 && x468 = x478 && x469 = x479 && x471 = x481
(26) l18(x486, x487, x488, x489, x490, x491, x492, x493, x494, x495) -> l17(x496, x497, x498, x499, x500, x501, x502, x503, x504, x505) :|: x495 = x505 && x494 = x504 && x492 = x502 && x491 = x501 && x490 = x500 && x489 = x499 && x488 = x498 && x487 = x497 && x493 = x503 && x486 = x496

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(__const_50HAT0, i11HAT0, i13HAT0, i15HAT0, i17HAT0, i7HAT0, i9HAT0, iHAT0, tmpHAT0, tmp___0HAT0) -> l1(__const_50HATpost, i11HATpost, i13HATpost, i15HATpost, i17HATpost, i7HATpost, i9HATpost, iHATpost, tmpHATpost, tmp___0HATpost) :|: tmp___0HAT0 = tmp___0HATpost && tmpHAT0 = tmpHATpost && i9HAT0 = i9HATpost && i7HAT0 = i7HATpost && i17HAT0 = i17HATpost && i15HAT0 = i15HATpost && i13HAT0 = i13HATpost && i11HAT0 = i11HATpost && iHAT0 = iHATpost && __const_50HAT0 = __const_50HATpost
(2) l1(x445, x446, x447, x448, x449, x450, x451, x452, x453, x454) -> l0(x455, x456, x457, x458, x459, x460, x461, x462, x463, x464) :|: x454 = x464 && x453 = x463 && x451 = x461 && x449 = x459 && x448 = x458 && x447 = x457 && x446 = x456 && x452 = x462 && x445 = x455 && x460 = 1 + x450 && 1 + x450 <= x445

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

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l0(__const_50HAT0:0, i11HAT0:0, i13HAT0:0, i15HAT0:0, i17HAT0:0, i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) -> l0(__const_50HAT0:0, i11HAT0:0, i13HAT0:0, i15HAT0:0, i17HAT0:0, 1 + i7HAT0:0, i9HAT0:0, iHAT0:0, tmpHAT0:0, tmp___0HAT0:0) :|: __const_50HAT0:0 >= 1 + i7HAT0:0

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

(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) -> l0(x1, x6)

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

(9)
Obligation:
Rules:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, 1 + i7HAT0:0) :|: __const_50HAT0:0 >= 1 + i7HAT0:0

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

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

(11)
Obligation:
Rules:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, c) :|: c = 1 + i7HAT0:0 && __const_50HAT0:0 >= 1 + i7HAT0:0

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

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

The following rules are decreasing:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, c) :|: c = 1 + i7HAT0:0 && __const_50HAT0:0 >= 1 + i7HAT0:0

The following rules are bounded:
l0(__const_50HAT0:0, i7HAT0:0) -> l0(__const_50HAT0:0, c) :|: c = 1 + i7HAT0:0 && __const_50HAT0:0 >= 1 + i7HAT0:0


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) l5(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49) -> l6(x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) :|: x49 = x59 && x48 = x58 && x46 = x56 && x45 = x55 && x44 = x54 && x43 = x53 && x42 = x52 && x41 = x51 && x47 = x57 && x40 = x50
(2) l6(x384, x385, x386, x387, x388, x389, x390, x391, x392, x393) -> l5(x394, x395, x396, x397, x398, x399, x400, x401, x402, x403) :|: x393 = x403 && x392 = x402 && x389 = x399 && x388 = x398 && x387 = x397 && x386 = x396 && x385 = x395 && x391 = x401 && x384 = x394 && x400 = 1 + x390 && 1 + x390 <= x384

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
l5(x394:0, x395:0, x396:0, x397:0, x398:0, x399:0, x46:0, x401:0, x402:0, x403:0) -> l5(x394:0, x395:0, x396:0, x397:0, x398:0, x399:0, 1 + x46:0, x401:0, x402:0, x403:0) :|: x394:0 >= 1 + x46:0

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

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

   l5(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l5(x1, x7)

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

(18)
Obligation:
Rules:
l5(x394:0, x46:0) -> l5(x394:0, 1 + x46:0) :|: x394:0 >= 1 + x46:0

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

(19) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l5(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(20)
Obligation:
Rules:
l5(x394:0, x46:0) -> l5(x394:0, c) :|: c = 1 + x46:0 && x394:0 >= 1 + x46:0

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l5 ] = l5_1 + -1*l5_2

The following rules are decreasing:
l5(x394:0, x46:0) -> l5(x394:0, c) :|: c = 1 + x46:0 && x394:0 >= 1 + x46:0

The following rules are bounded:
l5(x394:0, x46:0) -> l5(x394:0, c) :|: c = 1 + x46:0 && x394:0 >= 1 + x46:0


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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) l9(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109) -> l10(x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: x109 = x119 && x108 = x118 && x106 = x116 && x105 = x115 && x104 = x114 && x103 = x113 && x102 = x112 && x101 = x111 && x107 = x117 && x100 = x110
(2) l10(x323, x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l9(x333, x334, x335, x336, x337, x338, x339, x340, x341, x342) :|: x332 = x342 && x331 = x341 && x329 = x339 && x328 = x338 && x327 = x337 && x326 = x336 && x325 = x335 && x330 = x340 && x323 = x333 && x334 = 1 + x324 && 1 + x324 <= x323

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

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
l9(x100:0, x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0) -> l9(x100:0, 1 + x101:0, x102:0, x103:0, x104:0, x105:0, x106:0, x107:0, x108:0, x109:0) :|: x100:0 >= 1 + x101:0

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

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

   l9(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l9(x1, x2)

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

(27)
Obligation:
Rules:
l9(x100:0, x101:0) -> l9(x100:0, 1 + x101:0) :|: x100:0 >= 1 + x101:0

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

(28) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l9(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(29)
Obligation:
Rules:
l9(x100:0, x101:0) -> l9(x100:0, c) :|: c = 1 + x101:0 && x100:0 >= 1 + x101:0

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

(30) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l9 ] = l9_1 + -1*l9_2

The following rules are decreasing:
l9(x100:0, x101:0) -> l9(x100:0, c) :|: c = 1 + x101:0 && x100:0 >= 1 + x101:0

The following rules are bounded:
l9(x100:0, x101:0) -> l9(x100:0, c) :|: c = 1 + x101:0 && x100:0 >= 1 + x101:0


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

(31)
YES

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

(32)
Obligation:

Termination digraph:
Nodes:
(1) l13(x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l14(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180) :|: x170 = x180 && x169 = x179 && x167 = x177 && x166 = x176 && x165 = x175 && x164 = x174 && x163 = x173 && x162 = x172 && x168 = x178 && x161 = x171
(2) l14(x263, x264, x265, x266, x267, x268, x269, x270, x271, x272) -> l13(x273, x274, x275, x276, x277, x278, x279, x280, x281, x282) :|: x272 = x282 && x271 = x281 && x269 = x279 && x268 = x278 && x267 = x277 && x266 = x276 && x265 = x275 && x264 = x274 && x263 = x273 && x280 = 1 + x270 && 1 + x270 <= x263

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

This digraph is fully evaluated!

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

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

(34)
Obligation:
Rules:
l13(x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, x168:0, x169:0, x170:0) -> l13(x161:0, x162:0, x163:0, x164:0, x165:0, x166:0, x167:0, 1 + x168:0, x169:0, x170:0) :|: x161:0 >= 1 + x168:0

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

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

   l13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l13(x1, x8)

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

(36)
Obligation:
Rules:
l13(x161:0, x168:0) -> l13(x161:0, 1 + x168:0) :|: x161:0 >= 1 + x168:0

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

(37) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l13(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(38)
Obligation:
Rules:
l13(x161:0, x168:0) -> l13(x161:0, c) :|: c = 1 + x168:0 && x161:0 >= 1 + x168:0

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

(39) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l13 ] = l13_1 + -1*l13_2

The following rules are decreasing:
l13(x161:0, x168:0) -> l13(x161:0, c) :|: c = 1 + x168:0 && x161:0 >= 1 + x168:0

The following rules are bounded:
l13(x161:0, x168:0) -> l13(x161:0, c) :|: c = 1 + x168:0 && x161:0 >= 1 + x168:0


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

(40)
YES

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

(41)
Obligation:

Termination digraph:
Nodes:
(1) l16(x222, x223, x224, x225, x226, x227, x228, x229, x230, x231) -> l15(x232, x233, x234, x235, x236, x237, x238, x239, x240, x241) :|: x231 = x241 && x230 = x240 && x228 = x238 && x227 = x237 && x226 = x236 && x225 = x235 && x224 = x234 && x223 = x233 && x229 = x239 && x222 = x232
(2) l15(x202, x203, x204, x205, x206, x207, x208, x209, x210, x211) -> l16(x212, x213, x214, x215, x216, x217, x218, x219, x220, x221) :|: x211 = x221 && x210 = x220 && x208 = x218 && x207 = x217 && x206 = x216 && x205 = x215 && x203 = x213 && x209 = x219 && x202 = x212 && x214 = 1 + x204 && 1 + x204 <= x202

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

This digraph is fully evaluated!

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

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

(43)
Obligation:
Rules:
l16(x212:0, x213:0, x224:0, x215:0, x216:0, x217:0, x218:0, x219:0, x220:0, x221:0) -> l16(x212:0, x213:0, 1 + x224:0, x215:0, x216:0, x217:0, x218:0, x219:0, x220:0, x221:0) :|: x212:0 >= 1 + x224:0

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

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

   l16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l16(x1, x3)

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

(45)
Obligation:
Rules:
l16(x212:0, x224:0) -> l16(x212:0, 1 + x224:0) :|: x212:0 >= 1 + x224:0

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

(46) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l16(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(47)
Obligation:
Rules:
l16(x212:0, x224:0) -> l16(x212:0, c) :|: c = 1 + x224:0 && x212:0 >= 1 + x224:0

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

(48) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l16 ] = l16_1 + -1*l16_2

The following rules are decreasing:
l16(x212:0, x224:0) -> l16(x212:0, c) :|: c = 1 + x224:0 && x212:0 >= 1 + x224:0

The following rules are bounded:
l16(x212:0, x224:0) -> l16(x212:0, c) :|: c = 1 + x224:0 && x212:0 >= 1 + x224:0


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

(49)
YES

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

(50)
Obligation:

Termination digraph:
Nodes:
(1) l12(x283, x284, x285, x286, x287, x288, x289, x290, x291, x292) -> l11(x293, x294, x295, x296, x297, x298, x299, x300, x301, x302) :|: x292 = x302 && x291 = x301 && x289 = x299 && x288 = x298 && x287 = x297 && x286 = x296 && x285 = x295 && x284 = x294 && x290 = x300 && x283 = x293
(2) l11(x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l12(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160) :|: x150 = x160 && x149 = x159 && x147 = x157 && x146 = x156 && x145 = x155 && x143 = x153 && x142 = x152 && x148 = x158 && x141 = x151 && x154 = 1 + x144 && 1 + x144 <= x141

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

This digraph is fully evaluated!

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

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

(52)
Obligation:
Rules:
l12(x151:0, x152:0, x153:0, x286:0, x155:0, x156:0, x157:0, x158:0, x159:0, x160:0) -> l12(x151:0, x152:0, x153:0, 1 + x286:0, x155:0, x156:0, x157:0, x158:0, x159:0, x160:0) :|: x151:0 >= 1 + x286:0

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

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

   l12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l12(x1, x4)

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

(54)
Obligation:
Rules:
l12(x151:0, x286:0) -> l12(x151:0, 1 + x286:0) :|: x151:0 >= 1 + x286:0

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

(55) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l12(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(56)
Obligation:
Rules:
l12(x151:0, x286:0) -> l12(x151:0, c) :|: c = 1 + x286:0 && x151:0 >= 1 + x286:0

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

(57) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l12 ] = l12_1 + -1*l12_2

The following rules are decreasing:
l12(x151:0, x286:0) -> l12(x151:0, c) :|: c = 1 + x286:0 && x151:0 >= 1 + x286:0

The following rules are bounded:
l12(x151:0, x286:0) -> l12(x151:0, c) :|: c = 1 + x286:0 && x151:0 >= 1 + x286:0


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

(58)
YES

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

(59)
Obligation:

Termination digraph:
Nodes:
(1) l8(x343, x344, x345, x346, x347, x348, x349, x350, x351, x352) -> l7(x353, x354, x355, x356, x357, x358, x359, x360, x361, x362) :|: x352 = x362 && x351 = x361 && x349 = x359 && x348 = x358 && x347 = x357 && x346 = x356 && x345 = x355 && x344 = x354 && x350 = x360 && x343 = x353
(2) l7(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89) -> l8(x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) :|: x89 = x99 && x88 = x98 && x86 = x96 && x85 = x95 && x83 = x93 && x82 = x92 && x81 = x91 && x87 = x97 && x80 = x90 && x94 = 1 + x84 && 1 + x84 <= x80

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

This digraph is fully evaluated!

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

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

(61)
Obligation:
Rules:
l8(x343:0, x344:0, x345:0, x346:0, x347:0, x348:0, x349:0, x350:0, x351:0, x352:0) -> l8(x343:0, x344:0, x345:0, x346:0, 1 + x347:0, x348:0, x349:0, x350:0, x351:0, x352:0) :|: x343:0 >= 1 + x347:0

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

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

   l8(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l8(x1, x5)

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

(63)
Obligation:
Rules:
l8(x343:0, x347:0) -> l8(x343:0, 1 + x347:0) :|: x343:0 >= 1 + x347:0

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

(64) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
l8(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(65)
Obligation:
Rules:
l8(x343:0, x347:0) -> l8(x343:0, c) :|: c = 1 + x347:0 && x343:0 >= 1 + x347:0

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

(66) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l8 ] = l8_1 + -1*l8_2

The following rules are decreasing:
l8(x343:0, x347:0) -> l8(x343:0, c) :|: c = 1 + x347:0 && x343:0 >= 1 + x347:0

The following rules are bounded:
l8(x343:0, x347:0) -> l8(x343:0, c) :|: c = 1 + x347:0 && x343:0 >= 1 + x347:0


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

(67)
YES

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

(68)
Obligation:

Termination digraph:
Nodes:
(1) l4(x404, x405, x406, x407, x408, x409, x410, x411, x412, x413) -> l2(x414, x415, x416, x417, x418, x419, x420, x421, x422, x423) :|: x413 = x423 && x412 = x422 && x410 = x420 && x409 = x419 && x408 = x418 && x407 = x417 && x406 = x416 && x405 = x415 && x411 = x421 && x404 = x414
(2) l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29) -> l4(x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x29 = x39 && x28 = x38 && x26 = x36 && x25 = x35 && x24 = x34 && x23 = x33 && x22 = x32 && x21 = x31 && x20 = x30 && x37 = 1 + x27 && 1 + x27 <= x20

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

This digraph is fully evaluated!

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

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

(70)
Obligation:
Rules:
l4(x30:0, x31:0, x32:0, x33:0, x34:0, x35:0, x36:0, x411:0, x38:0, x39:0) -> l4(x30:0, x31:0, x32:0, x33:0, x34:0, x35:0, x36:0, 1 + x411:0, x38:0, x39:0) :|: x30:0 >= 1 + x411:0

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

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

   l4(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> l4(x1, x8)

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

(72)
Obligation:
Rules:
l4(x30:0, x411:0) -> l4(x30:0, 1 + x411:0) :|: x30:0 >= 1 + x411:0

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

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

(74)
Obligation:
Rules:
l4(x30:0, x411:0) -> l4(x30:0, c) :|: c = 1 + x411:0 && x30:0 >= 1 + x411:0

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

(75) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l4 ] = l4_1 + -1*l4_2

The following rules are decreasing:
l4(x30:0, x411:0) -> l4(x30:0, c) :|: c = 1 + x411:0 && x30:0 >= 1 + x411:0

The following rules are bounded:
l4(x30:0, x411:0) -> l4(x30:0, c) :|: c = 1 + x411:0 && x30:0 >= 1 + x411:0


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

(76)
YES