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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 5904 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 12 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 7 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 3 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 16 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 32 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 21 ms]
        (22) YES
    (23) IRSwT
        (24) IntTRSCompressionProof [EQUIVALENT, 11 ms]
        (25) IRSwT
        (26) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (27) IRSwT
        (28) TempFilterProof [SOUND, 7 ms]
        (29) IntTRS
        (30) RankingReductionPairProof [EQUIVALENT, 3 ms]
        (31) YES


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

(0)
Obligation:
Rules:
l0(ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0) -> l1(ctr23HATpost, iHATpost, seedHATpost, tmp05HATpost, tmp1013HATpost, tmp1114HATpost, tmp1215HATpost, tmp1316HATpost, tmp16HATpost, tmp27HATpost, tmp38HATpost, tmp49HATpost, tmp510HATpost, tmp611HATpost, tmp712HATpost, z117HATpost, z218HATpost, z319HATpost, z420HATpost, z521HATpost) :|: z521HAT0 = z521HATpost && z420HAT0 = z420HATpost && z319HAT0 = z319HATpost && z218HAT0 = z218HATpost && z117HAT0 = z117HATpost && tmp712HAT0 = tmp712HATpost && tmp611HAT0 = tmp611HATpost && tmp510HAT0 = tmp510HATpost && tmp49HAT0 = tmp49HATpost && tmp38HAT0 = tmp38HATpost && tmp27HAT0 = tmp27HATpost && tmp16HAT0 = tmp16HATpost && tmp1316HAT0 = tmp1316HATpost && tmp1215HAT0 = tmp1215HATpost && tmp1114HAT0 = tmp1114HATpost && tmp1013HAT0 = tmp1013HATpost && tmp05HAT0 = tmp05HATpost && seedHAT0 = seedHATpost && iHAT0 = iHATpost && ctr23HATpost = 7 && 64 <= iHAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x17 = x37 && x16 = x36 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x = x20 && x21 = 1 + x1 && x22 = x22 && 1 + x1 <= 64
l3(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l4(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x59 = x79 && x58 = x78 && x57 = x77 && x56 = x76 && x55 = x75 && x54 = x74 && x53 = x73 && x52 = x72 && x51 = x71 && x50 = x70 && x49 = x69 && x48 = x68 && x47 = x67 && x46 = x66 && x45 = x65 && x44 = x64 && x43 = x63 && x42 = x62 && x41 = x61 && x40 = x60 && 1 + x40 <= 0
l3(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: 0 <= x80 && x103 = x103 && x120 = x120 && x108 = x108 && x121 = x121 && x109 = x109 && x122 = x122 && x110 = x110 && x123 = x123 && x104 = x103 + x110 && x107 = x103 - x110 && x105 = x108 + x109 && x106 = x108 - x109 && x124 = x124 && x125 = x123 + x120 && x126 = x122 + x121 && x127 = x123 + x121 && x128 = x122 + x120 && x119 = x119 && x111 = x111 && x112 = x112 && x113 = x113 && x114 = x114 && x115 = x115 && x116 = x116 && x129 = x129 && x130 = x130 && x117 = x129 + x119 && x118 = x130 + x119 && x100 = -1 + x80 && x81 = x101 && x82 = x102
l2(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l0(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) :|: x150 = x170 && x149 = x169 && x148 = x168 && x147 = x167 && x146 = x166 && x145 = x165 && x144 = x164 && x143 = x163 && x142 = x162 && x141 = x161 && x140 = x160 && x139 = x159 && x138 = x158 && x137 = x157 && x136 = x156 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151
l1(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l6(x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210) :|: x190 = x210 && x189 = x209 && x188 = x208 && x187 = x207 && x186 = x206 && x185 = x205 && x184 = x204 && x183 = x203 && x182 = x202 && x181 = x201 && x180 = x200 && x179 = x199 && x178 = x198 && x177 = x197 && x176 = x196 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191
l5(x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l3(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250) :|: x230 = x250 && x229 = x249 && x228 = x248 && x227 = x247 && x226 = x246 && x225 = x245 && x224 = x244 && x223 = x243 && x222 = x242 && x221 = x241 && x220 = x240 && x219 = x239 && x218 = x238 && x217 = x237 && x216 = x236 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231
l6(x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270) -> l5(x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290) :|: x270 = x290 && x269 = x289 && x268 = x288 && x267 = x287 && x266 = x286 && x265 = x285 && x264 = x284 && x263 = x283 && x262 = x282 && x261 = x281 && x260 = x280 && x259 = x279 && x258 = x278 && x257 = x277 && x256 = x276 && x255 = x275 && x254 = x274 && x253 = x273 && x252 = x272 && x271 = 7 && 1 + x251 <= 0
l6(x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310) -> l1(x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330) :|: 0 <= x291 && x314 = x314 && x331 = x331 && x319 = x319 && x332 = x332 && x320 = x320 && x333 = x333 && x321 = x321 && x334 = x334 && x315 = x314 + x321 && x318 = x314 - x321 && x316 = x319 + x320 && x317 = x319 - x320 && x335 = x335 && x336 = x334 + x331 && x337 = x333 + x332 && x338 = x334 + x332 && x339 = x333 + x331 && x330 = x330 && x322 = x322 && x323 = x323 && x324 = x324 && x325 = x325 && x326 = x326 && x327 = x327 && x340 = x340 && x341 = x341 && x328 = x340 + x330 && x329 = x341 + x330 && x311 = -1 + x291 && x292 = x312 && x293 = x313
l7(x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361) -> l2(x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377, x378, x379, x380, x381) :|: x361 = x381 && x360 = x380 && x359 = x379 && x358 = x378 && x357 = x377 && x356 = x376 && x355 = x375 && x354 = x374 && x353 = x373 && x352 = x372 && x351 = x371 && x350 = x370 && x349 = x369 && x348 = x368 && x347 = x367 && x346 = x366 && x345 = x365 && x342 = x362 && x363 = 0 && x364 = 0
l8(x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401) -> l7(x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421) :|: x401 = x421 && x400 = x420 && x399 = x419 && x398 = x418 && x397 = x417 && x396 = x416 && x395 = x415 && x394 = x414 && x393 = x413 && x392 = x412 && x391 = x411 && x390 = x410 && x389 = x409 && x388 = x408 && x387 = x407 && x386 = x406 && x385 = x405 && x384 = x404 && x383 = x403 && x382 = x402
Start term: l8(ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0)

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

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

(2)
Obligation:
Rules:
l0(ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0) -> l1(ctr23HATpost, iHATpost, seedHATpost, tmp05HATpost, tmp1013HATpost, tmp1114HATpost, tmp1215HATpost, tmp1316HATpost, tmp16HATpost, tmp27HATpost, tmp38HATpost, tmp49HATpost, tmp510HATpost, tmp611HATpost, tmp712HATpost, z117HATpost, z218HATpost, z319HATpost, z420HATpost, z521HATpost) :|: z521HAT0 = z521HATpost && z420HAT0 = z420HATpost && z319HAT0 = z319HATpost && z218HAT0 = z218HATpost && z117HAT0 = z117HATpost && tmp712HAT0 = tmp712HATpost && tmp611HAT0 = tmp611HATpost && tmp510HAT0 = tmp510HATpost && tmp49HAT0 = tmp49HATpost && tmp38HAT0 = tmp38HATpost && tmp27HAT0 = tmp27HATpost && tmp16HAT0 = tmp16HATpost && tmp1316HAT0 = tmp1316HATpost && tmp1215HAT0 = tmp1215HATpost && tmp1114HAT0 = tmp1114HATpost && tmp1013HAT0 = tmp1013HATpost && tmp05HAT0 = tmp05HATpost && seedHAT0 = seedHATpost && iHAT0 = iHATpost && ctr23HATpost = 7 && 64 <= iHAT0
l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x17 = x37 && x16 = x36 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x = x20 && x21 = 1 + x1 && x22 = x22 && 1 + x1 <= 64
l3(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l4(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x59 = x79 && x58 = x78 && x57 = x77 && x56 = x76 && x55 = x75 && x54 = x74 && x53 = x73 && x52 = x72 && x51 = x71 && x50 = x70 && x49 = x69 && x48 = x68 && x47 = x67 && x46 = x66 && x45 = x65 && x44 = x64 && x43 = x63 && x42 = x62 && x41 = x61 && x40 = x60 && 1 + x40 <= 0
l3(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: 0 <= x80 && x103 = x103 && x120 = x120 && x108 = x108 && x121 = x121 && x109 = x109 && x122 = x122 && x110 = x110 && x123 = x123 && x104 = x103 + x110 && x107 = x103 - x110 && x105 = x108 + x109 && x106 = x108 - x109 && x124 = x124 && x125 = x123 + x120 && x126 = x122 + x121 && x127 = x123 + x121 && x128 = x122 + x120 && x119 = x119 && x111 = x111 && x112 = x112 && x113 = x113 && x114 = x114 && x115 = x115 && x116 = x116 && x129 = x129 && x130 = x130 && x117 = x129 + x119 && x118 = x130 + x119 && x100 = -1 + x80 && x81 = x101 && x82 = x102
l2(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l0(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) :|: x150 = x170 && x149 = x169 && x148 = x168 && x147 = x167 && x146 = x166 && x145 = x165 && x144 = x164 && x143 = x163 && x142 = x162 && x141 = x161 && x140 = x160 && x139 = x159 && x138 = x158 && x137 = x157 && x136 = x156 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151
l1(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l6(x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210) :|: x190 = x210 && x189 = x209 && x188 = x208 && x187 = x207 && x186 = x206 && x185 = x205 && x184 = x204 && x183 = x203 && x182 = x202 && x181 = x201 && x180 = x200 && x179 = x199 && x178 = x198 && x177 = x197 && x176 = x196 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191
l5(x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l3(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250) :|: x230 = x250 && x229 = x249 && x228 = x248 && x227 = x247 && x226 = x246 && x225 = x245 && x224 = x244 && x223 = x243 && x222 = x242 && x221 = x241 && x220 = x240 && x219 = x239 && x218 = x238 && x217 = x237 && x216 = x236 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231
l6(x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270) -> l5(x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290) :|: x270 = x290 && x269 = x289 && x268 = x288 && x267 = x287 && x266 = x286 && x265 = x285 && x264 = x284 && x263 = x283 && x262 = x282 && x261 = x281 && x260 = x280 && x259 = x279 && x258 = x278 && x257 = x277 && x256 = x276 && x255 = x275 && x254 = x274 && x253 = x273 && x252 = x272 && x271 = 7 && 1 + x251 <= 0
l6(x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310) -> l1(x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330) :|: 0 <= x291 && x314 = x314 && x331 = x331 && x319 = x319 && x332 = x332 && x320 = x320 && x333 = x333 && x321 = x321 && x334 = x334 && x315 = x314 + x321 && x318 = x314 - x321 && x316 = x319 + x320 && x317 = x319 - x320 && x335 = x335 && x336 = x334 + x331 && x337 = x333 + x332 && x338 = x334 + x332 && x339 = x333 + x331 && x330 = x330 && x322 = x322 && x323 = x323 && x324 = x324 && x325 = x325 && x326 = x326 && x327 = x327 && x340 = x340 && x341 = x341 && x328 = x340 + x330 && x329 = x341 + x330 && x311 = -1 + x291 && x292 = x312 && x293 = x313
l7(x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361) -> l2(x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377, x378, x379, x380, x381) :|: x361 = x381 && x360 = x380 && x359 = x379 && x358 = x378 && x357 = x377 && x356 = x376 && x355 = x375 && x354 = x374 && x353 = x373 && x352 = x372 && x351 = x371 && x350 = x370 && x349 = x369 && x348 = x368 && x347 = x367 && x346 = x366 && x345 = x365 && x342 = x362 && x363 = 0 && x364 = 0
l8(x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401) -> l7(x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421) :|: x401 = x421 && x400 = x420 && x399 = x419 && x398 = x418 && x397 = x417 && x396 = x416 && x395 = x415 && x394 = x414 && x393 = x413 && x392 = x412 && x391 = x411 && x390 = x410 && x389 = x409 && x388 = x408 && x387 = x407 && x386 = x406 && x385 = x405 && x384 = x404 && x383 = x403 && x382 = x402
Start term: l8(ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(ctr23HAT0, iHAT0, seedHAT0, tmp05HAT0, tmp1013HAT0, tmp1114HAT0, tmp1215HAT0, tmp1316HAT0, tmp16HAT0, tmp27HAT0, tmp38HAT0, tmp49HAT0, tmp510HAT0, tmp611HAT0, tmp712HAT0, z117HAT0, z218HAT0, z319HAT0, z420HAT0, z521HAT0) -> l1(ctr23HATpost, iHATpost, seedHATpost, tmp05HATpost, tmp1013HATpost, tmp1114HATpost, tmp1215HATpost, tmp1316HATpost, tmp16HATpost, tmp27HATpost, tmp38HATpost, tmp49HATpost, tmp510HATpost, tmp611HATpost, tmp712HATpost, z117HATpost, z218HATpost, z319HATpost, z420HATpost, z521HATpost) :|: z521HAT0 = z521HATpost && z420HAT0 = z420HATpost && z319HAT0 = z319HATpost && z218HAT0 = z218HATpost && z117HAT0 = z117HATpost && tmp712HAT0 = tmp712HATpost && tmp611HAT0 = tmp611HATpost && tmp510HAT0 = tmp510HATpost && tmp49HAT0 = tmp49HATpost && tmp38HAT0 = tmp38HATpost && tmp27HAT0 = tmp27HATpost && tmp16HAT0 = tmp16HATpost && tmp1316HAT0 = tmp1316HATpost && tmp1215HAT0 = tmp1215HATpost && tmp1114HAT0 = tmp1114HATpost && tmp1013HAT0 = tmp1013HATpost && tmp05HAT0 = tmp05HATpost && seedHAT0 = seedHATpost && iHAT0 = iHATpost && ctr23HATpost = 7 && 64 <= iHAT0
(2) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x17 = x37 && x16 = x36 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x = x20 && x21 = 1 + x1 && x22 = x22 && 1 + x1 <= 64
(3) l3(x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58, x59) -> l4(x60, x61, x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) :|: x59 = x79 && x58 = x78 && x57 = x77 && x56 = x76 && x55 = x75 && x54 = x74 && x53 = x73 && x52 = x72 && x51 = x71 && x50 = x70 && x49 = x69 && x48 = x68 && x47 = x67 && x46 = x66 && x45 = x65 && x44 = x64 && x43 = x63 && x42 = x62 && x41 = x61 && x40 = x60 && 1 + x40 <= 0
(4) l3(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: 0 <= x80 && x103 = x103 && x120 = x120 && x108 = x108 && x121 = x121 && x109 = x109 && x122 = x122 && x110 = x110 && x123 = x123 && x104 = x103 + x110 && x107 = x103 - x110 && x105 = x108 + x109 && x106 = x108 - x109 && x124 = x124 && x125 = x123 + x120 && x126 = x122 + x121 && x127 = x123 + x121 && x128 = x122 + x120 && x119 = x119 && x111 = x111 && x112 = x112 && x113 = x113 && x114 = x114 && x115 = x115 && x116 = x116 && x129 = x129 && x130 = x130 && x117 = x129 + x119 && x118 = x130 + x119 && x100 = -1 + x80 && x81 = x101 && x82 = x102
(5) l2(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l0(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) :|: x150 = x170 && x149 = x169 && x148 = x168 && x147 = x167 && x146 = x166 && x145 = x165 && x144 = x164 && x143 = x163 && x142 = x162 && x141 = x161 && x140 = x160 && x139 = x159 && x138 = x158 && x137 = x157 && x136 = x156 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151
(6) l1(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l6(x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210) :|: x190 = x210 && x189 = x209 && x188 = x208 && x187 = x207 && x186 = x206 && x185 = x205 && x184 = x204 && x183 = x203 && x182 = x202 && x181 = x201 && x180 = x200 && x179 = x199 && x178 = x198 && x177 = x197 && x176 = x196 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191
(7) l5(x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l3(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250) :|: x230 = x250 && x229 = x249 && x228 = x248 && x227 = x247 && x226 = x246 && x225 = x245 && x224 = x244 && x223 = x243 && x222 = x242 && x221 = x241 && x220 = x240 && x219 = x239 && x218 = x238 && x217 = x237 && x216 = x236 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231
(8) l6(x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263, x264, x265, x266, x267, x268, x269, x270) -> l5(x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283, x284, x285, x286, x287, x288, x289, x290) :|: x270 = x290 && x269 = x289 && x268 = x288 && x267 = x287 && x266 = x286 && x265 = x285 && x264 = x284 && x263 = x283 && x262 = x282 && x261 = x281 && x260 = x280 && x259 = x279 && x258 = x278 && x257 = x277 && x256 = x276 && x255 = x275 && x254 = x274 && x253 = x273 && x252 = x272 && x271 = 7 && 1 + x251 <= 0
(9) l6(x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310) -> l1(x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330) :|: 0 <= x291 && x314 = x314 && x331 = x331 && x319 = x319 && x332 = x332 && x320 = x320 && x333 = x333 && x321 = x321 && x334 = x334 && x315 = x314 + x321 && x318 = x314 - x321 && x316 = x319 + x320 && x317 = x319 - x320 && x335 = x335 && x336 = x334 + x331 && x337 = x333 + x332 && x338 = x334 + x332 && x339 = x333 + x331 && x330 = x330 && x322 = x322 && x323 = x323 && x324 = x324 && x325 = x325 && x326 = x326 && x327 = x327 && x340 = x340 && x341 = x341 && x328 = x340 + x330 && x329 = x341 + x330 && x311 = -1 + x291 && x292 = x312 && x293 = x313
(10) l7(x342, x343, x344, x345, x346, x347, x348, x349, x350, x351, x352, x353, x354, x355, x356, x357, x358, x359, x360, x361) -> l2(x362, x363, x364, x365, x366, x367, x368, x369, x370, x371, x372, x373, x374, x375, x376, x377, x378, x379, x380, x381) :|: x361 = x381 && x360 = x380 && x359 = x379 && x358 = x378 && x357 = x377 && x356 = x376 && x355 = x375 && x354 = x374 && x353 = x373 && x352 = x372 && x351 = x371 && x350 = x370 && x349 = x369 && x348 = x368 && x347 = x367 && x346 = x366 && x345 = x365 && x342 = x362 && x363 = 0 && x364 = 0
(11) l8(x382, x383, x384, x385, x386, x387, x388, x389, x390, x391, x392, x393, x394, x395, x396, x397, x398, x399, x400, x401) -> l7(x402, x403, x404, x405, x406, x407, x408, x409, x410, x411, x412, x413, x414, x415, x416, x417, x418, x419, x420, x421) :|: x401 = x421 && x400 = x420 && x399 = x419 && x398 = x418 && x397 = x417 && x396 = x416 && x395 = x415 && x394 = x414 && x393 = x413 && x392 = x412 && x391 = x411 && x390 = x410 && x389 = x409 && x388 = x408 && x387 = x407 && x386 = x406 && x385 = x405 && x384 = x404 && x383 = x403 && x382 = x402

Arcs:
(1) -> (6)
(2) -> (5)
(4) -> (7)
(5) -> (1), (2)
(6) -> (8), (9)
(7) -> (3), (4)
(8) -> (7)
(9) -> (6)
(10) -> (5)
(11) -> (10)

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) -> l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: x19 = x39 && x18 = x38 && x17 = x37 && x16 = x36 && x15 = x35 && x14 = x34 && x13 = x33 && x12 = x32 && x11 = x31 && x10 = x30 && x9 = x29 && x8 = x28 && x7 = x27 && x6 = x26 && x5 = x25 && x4 = x24 && x3 = x23 && x = x20 && x21 = 1 + x1 && x22 = x22 && 1 + x1 <= 64
(2) l2(x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141, x142, x143, x144, x145, x146, x147, x148, x149, x150) -> l0(x151, x152, x153, x154, x155, x156, x157, x158, x159, x160, x161, x162, x163, x164, x165, x166, x167, x168, x169, x170) :|: x150 = x170 && x149 = x169 && x148 = x168 && x147 = x167 && x146 = x166 && x145 = x165 && x144 = x164 && x143 = x163 && x142 = x162 && x141 = x161 && x140 = x160 && x139 = x159 && x138 = x158 && x137 = x157 && x136 = x156 && x135 = x155 && x134 = x154 && x133 = x153 && x132 = x152 && x131 = x151

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

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
l0(x151:0, x1:0, x2:0, x154:0, x155:0, x156:0, x157:0, x158:0, x159:0, x160:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0, x167:0, x168:0, x169:0, x170:0) -> l0(x151:0, 1 + x1:0, x153:0, x154:0, x155:0, x156:0, x157:0, x158:0, x159:0, x160:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0, x167:0, x168:0, x169:0, x170:0) :|: x1:0 < 64

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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) -> l0(x2)

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(9)
Obligation:
Rules:
l0(x1:0) -> l0(1 + x1:0) :|: x1:0 < 64

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

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

(11)
Obligation:
Rules:
l0(x1:0) -> l0(c) :|: c = 1 + x1:0 && x1:0 < 64

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

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

The following rules are decreasing:
l0(x1:0) -> l0(c) :|: c = 1 + x1:0 && x1:0 < 64

The following rules are bounded:
l0(x1:0) -> l0(c) :|: c = 1 + x1:0 && x1:0 < 64


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) l1(x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183, x184, x185, x186, x187, x188, x189, x190) -> l6(x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203, x204, x205, x206, x207, x208, x209, x210) :|: x190 = x210 && x189 = x209 && x188 = x208 && x187 = x207 && x186 = x206 && x185 = x205 && x184 = x204 && x183 = x203 && x182 = x202 && x181 = x201 && x180 = x200 && x179 = x199 && x178 = x198 && x177 = x197 && x176 = x196 && x175 = x195 && x174 = x194 && x173 = x193 && x172 = x192 && x171 = x191
(2) l6(x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303, x304, x305, x306, x307, x308, x309, x310) -> l1(x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323, x324, x325, x326, x327, x328, x329, x330) :|: 0 <= x291 && x314 = x314 && x331 = x331 && x319 = x319 && x332 = x332 && x320 = x320 && x333 = x333 && x321 = x321 && x334 = x334 && x315 = x314 + x321 && x318 = x314 - x321 && x316 = x319 + x320 && x317 = x319 - x320 && x335 = x335 && x336 = x334 + x331 && x337 = x333 + x332 && x338 = x334 + x332 && x339 = x333 + x331 && x330 = x330 && x322 = x322 && x323 = x323 && x324 = x324 && x325 = x325 && x326 = x326 && x327 = x327 && x340 = x340 && x341 = x341 && x328 = x340 + x330 && x329 = x341 + x330 && x311 = -1 + x291 && x292 = x312 && x293 = x313

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
l1(x171:0, x172:0, x173:0, x174:0, x175:0, x176:0, x177:0, x178:0, x179:0, x180:0, x181:0, x182:0, x183:0, x184:0, x185:0, x186:0, x187:0, x188:0, x189:0, x190:0) -> l1(-1 + x171:0, x172:0, x173:0, x314:0, x314:0 + x321:0, x319:0 + x320:0, x319:0 - x320:0, x314:0 - x321:0, x319:0, x320:0, x321:0, x322:0, x323:0, x324:0, x325:0, x326:0, x327:0, x340:0 + x330:0, x341:0 + x330:0, x330:0) :|: x171:0 > -1

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

(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) -> l1(x1)

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(18)
Obligation:
Rules:
l1(x171:0) -> l1(-1 + x171:0) :|: x171:0 > -1

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

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

(20)
Obligation:
Rules:
l1(x171:0) -> l1(c) :|: c = -1 + x171:0 && x171:0 > -1

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

(21) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l1 ] = l1_1

The following rules are decreasing:
l1(x171:0) -> l1(c) :|: c = -1 + x171:0 && x171:0 > -1

The following rules are bounded:
l1(x171:0) -> l1(c) :|: c = -1 + x171:0 && x171:0 > -1


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

(22)
YES

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

(23)
Obligation:

Termination digraph:
Nodes:
(1) l5(x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223, x224, x225, x226, x227, x228, x229, x230) -> l3(x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243, x244, x245, x246, x247, x248, x249, x250) :|: x230 = x250 && x229 = x249 && x228 = x248 && x227 = x247 && x226 = x246 && x225 = x245 && x224 = x244 && x223 = x243 && x222 = x242 && x221 = x241 && x220 = x240 && x219 = x239 && x218 = x238 && x217 = x237 && x216 = x236 && x215 = x235 && x214 = x234 && x213 = x233 && x212 = x232 && x211 = x231
(2) l3(x80, x81, x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99) -> l5(x100, x101, x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119) :|: 0 <= x80 && x103 = x103 && x120 = x120 && x108 = x108 && x121 = x121 && x109 = x109 && x122 = x122 && x110 = x110 && x123 = x123 && x104 = x103 + x110 && x107 = x103 - x110 && x105 = x108 + x109 && x106 = x108 - x109 && x124 = x124 && x125 = x123 + x120 && x126 = x122 + x121 && x127 = x123 + x121 && x128 = x122 + x120 && x119 = x119 && x111 = x111 && x112 = x112 && x113 = x113 && x114 = x114 && x115 = x115 && x116 = x116 && x129 = x129 && x130 = x130 && x117 = x129 + x119 && x118 = x130 + x119 && x100 = -1 + x80 && x81 = x101 && x82 = x102

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

This digraph is fully evaluated!

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

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

(25)
Obligation:
Rules:
l5(x211:0, x101:0, x102:0, x214:0, x215:0, x216:0, x217:0, x218:0, x219:0, x220:0, x221:0, x222:0, x223:0, x224:0, x225:0, x226:0, x227:0, x228:0, x229:0, x230:0) -> l5(-1 + x211:0, x101:0, x102:0, x103:0, x103:0 + x110:0, x108:0 + x109:0, x108:0 - x109:0, x103:0 - x110:0, x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0, x129:0 + x119:0, x130:0 + x119:0, x119:0) :|: x211:0 > -1

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

(26) 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, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> l5(x1)

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

(27)
Obligation:
Rules:
l5(x211:0) -> l5(-1 + x211:0) :|: x211:0 > -1

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

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

(29)
Obligation:
Rules:
l5(x211:0) -> l5(c) :|: c = -1 + x211:0 && x211:0 > -1

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

(30) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ l5 ] = l5_1

The following rules are decreasing:
l5(x211:0) -> l5(c) :|: c = -1 + x211:0 && x211:0 > -1

The following rules are bounded:
l5(x211:0) -> l5(c) :|: c = -1 + x211:0 && x211:0 > -1


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(31)
YES