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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 21.1 s]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 8 ms]
        (11) IntTRS
        (12) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 20 ms]
        (20) IntTRS
        (21) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (22) YES


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

(0)
Obligation:
Rules:
l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, x0HATpost, x1HATpost, x2HATpost) :|: oldX5HAT0 = oldX5HATpost && oldX4HAT0 = oldX4HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost + oldX3HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x5 = x14 && x4 = x13 && x3 = x12 && x17 = x11 && x16 = x10 && x15 = x9 && 1 + x11 <= 0 && x11 = x8 && x10 = x7 && x9 = x6
l1(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x21 = x30 && x35 = x29 && x34 = x28 && x33 = x27 && 0 <= x29 && x29 = x26 && x28 = x25 && x27 = x24
l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x50 && x40 = x49 && x39 = x48 && x53 = x45 && x52 = 0 && x51 = x45 && x47 = x44 && x46 = x43 && x45 = x42
l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l5(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x71 = x68 && x70 = x67 && x69 = x66 && x68 = x68 && x67 = x67 && x66 = x66 && x65 = x62 && x64 = x61 && x63 = x60
l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l6(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x86 && x89 = x85 && x88 = x84 && x87 = -1 + x81 && x85 = x85 && x84 = x84 && x83 = x80 && x82 = x79 && x81 = x78
l7(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l5(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x107 = x104 && x106 = x103 && x105 = x102 && x104 = x104 && x103 = x103 && x102 = x102 && x101 = x98 && x100 = x97 && x99 = x96
l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l4(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x125 = x121 && x124 = x120 && x123 = x117 && 1 <= x117 && x121 = x121 && x120 = x120 && x119 = x116 && x118 = x115 && x117 = x114
l8(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l7(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x131 = x140 && x143 = x139 && x142 = x138 && x141 = x135 && x135 <= 0 && x139 = x139 && x138 = x138 && x137 = x134 && x136 = x133 && x135 = x132
l2(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l9(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x161 = x158 && x160 = x157 && x159 = x156 && x158 = x158 && x157 = x157 && x156 = x156 && x155 = x152 && x154 = x151 && x153 = x150
l6(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l8(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x167 = x176 && x179 = x175 && x178 = x174 && x177 = x171 && x175 = x175 && x174 = x174 && x173 = x170 && x172 = x169 && x171 = x168
l10(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l11(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x197 = x194 && x196 = x193 && x195 = x192 && x194 = x194 && x193 = x193 && x192 = x192 && x191 = x188 && x190 = x187 && x189 = x186
l10(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l3(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x203 = x212 && x215 = x211 && x214 = x210 && x213 = x207 && x211 = x211 && x210 = x210 && x209 = x206 && x208 = x205 && x207 = x204
l10(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l0(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x219 = x228 && x218 = x227 && x217 = x226 && x216 = x225
l10(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l1(x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x236 = x245 && x235 = x244 && x234 = x243
l10(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l3(x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x254 = x263 && x253 = x262 && x252 = x261
l10(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l5(x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x272 = x281 && x271 = x280 && x270 = x279
l10(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l4(x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x291 = x300 && x290 = x299 && x289 = x298 && x288 = x297
l10(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l7(x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x308 = x317 && x307 = x316 && x306 = x315
l10(x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l8(x333, x334, x335, x336, x337, x338, x339, x340, x341) :|: x332 = x341 && x331 = x340 && x330 = x339 && x329 = x338 && x328 = x337 && x327 = x336 && x326 = x335 && x325 = x334 && x324 = x333
l10(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l11(x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x345 = x354 && x344 = x353 && x343 = x352 && x342 = x351
l10(x360, x361, x362, x363, x364, x365, x366, x367, x368) -> l9(x369, x370, x371, x372, x373, x374, x375, x376, x377) :|: x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x363 = x372 && x362 = x371 && x361 = x370 && x360 = x369
l10(x378, x379, x380, x381, x382, x383, x384, x385, x386) -> l2(x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x386 = x395 && x385 = x394 && x384 = x393 && x383 = x392 && x382 = x391 && x381 = x390 && x380 = x389 && x379 = x388 && x378 = x387
l10(x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l6(x405, x406, x407, x408, x409, x410, x411, x412, x413) :|: x404 = x413 && x403 = x412 && x402 = x411 && x401 = x410 && x400 = x409 && x399 = x408 && x398 = x407 && x397 = x406 && x396 = x405
l12(x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l10(x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x422 = x431 && x421 = x430 && x420 = x429 && x419 = x428 && x418 = x427 && x417 = x426 && x416 = x425 && x415 = x424 && x414 = x423
Start term: l12(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0)

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

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

(2)
Obligation:
Rules:
l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, x0HATpost, x1HATpost, x2HATpost) :|: oldX5HAT0 = oldX5HATpost && oldX4HAT0 = oldX4HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost + oldX3HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x5 = x14 && x4 = x13 && x3 = x12 && x17 = x11 && x16 = x10 && x15 = x9 && 1 + x11 <= 0 && x11 = x8 && x10 = x7 && x9 = x6
l1(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x21 = x30 && x35 = x29 && x34 = x28 && x33 = x27 && 0 <= x29 && x29 = x26 && x28 = x25 && x27 = x24
l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x50 && x40 = x49 && x39 = x48 && x53 = x45 && x52 = 0 && x51 = x45 && x47 = x44 && x46 = x43 && x45 = x42
l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l5(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x71 = x68 && x70 = x67 && x69 = x66 && x68 = x68 && x67 = x67 && x66 = x66 && x65 = x62 && x64 = x61 && x63 = x60
l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l6(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x86 && x89 = x85 && x88 = x84 && x87 = -1 + x81 && x85 = x85 && x84 = x84 && x83 = x80 && x82 = x79 && x81 = x78
l7(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l5(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x107 = x104 && x106 = x103 && x105 = x102 && x104 = x104 && x103 = x103 && x102 = x102 && x101 = x98 && x100 = x97 && x99 = x96
l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l4(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x125 = x121 && x124 = x120 && x123 = x117 && 1 <= x117 && x121 = x121 && x120 = x120 && x119 = x116 && x118 = x115 && x117 = x114
l8(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l7(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x131 = x140 && x143 = x139 && x142 = x138 && x141 = x135 && x135 <= 0 && x139 = x139 && x138 = x138 && x137 = x134 && x136 = x133 && x135 = x132
l2(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l9(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x161 = x158 && x160 = x157 && x159 = x156 && x158 = x158 && x157 = x157 && x156 = x156 && x155 = x152 && x154 = x151 && x153 = x150
l6(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l8(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x167 = x176 && x179 = x175 && x178 = x174 && x177 = x171 && x175 = x175 && x174 = x174 && x173 = x170 && x172 = x169 && x171 = x168
l10(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l11(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x197 = x194 && x196 = x193 && x195 = x192 && x194 = x194 && x193 = x193 && x192 = x192 && x191 = x188 && x190 = x187 && x189 = x186
l10(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l3(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x203 = x212 && x215 = x211 && x214 = x210 && x213 = x207 && x211 = x211 && x210 = x210 && x209 = x206 && x208 = x205 && x207 = x204
l10(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l0(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x219 = x228 && x218 = x227 && x217 = x226 && x216 = x225
l10(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l1(x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x236 = x245 && x235 = x244 && x234 = x243
l10(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l3(x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x254 = x263 && x253 = x262 && x252 = x261
l10(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l5(x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x272 = x281 && x271 = x280 && x270 = x279
l10(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l4(x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x291 = x300 && x290 = x299 && x289 = x298 && x288 = x297
l10(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l7(x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x308 = x317 && x307 = x316 && x306 = x315
l10(x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l8(x333, x334, x335, x336, x337, x338, x339, x340, x341) :|: x332 = x341 && x331 = x340 && x330 = x339 && x329 = x338 && x328 = x337 && x327 = x336 && x326 = x335 && x325 = x334 && x324 = x333
l10(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l11(x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x345 = x354 && x344 = x353 && x343 = x352 && x342 = x351
l10(x360, x361, x362, x363, x364, x365, x366, x367, x368) -> l9(x369, x370, x371, x372, x373, x374, x375, x376, x377) :|: x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x363 = x372 && x362 = x371 && x361 = x370 && x360 = x369
l10(x378, x379, x380, x381, x382, x383, x384, x385, x386) -> l2(x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x386 = x395 && x385 = x394 && x384 = x393 && x383 = x392 && x382 = x391 && x381 = x390 && x380 = x389 && x379 = x388 && x378 = x387
l10(x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l6(x405, x406, x407, x408, x409, x410, x411, x412, x413) :|: x404 = x413 && x403 = x412 && x402 = x411 && x401 = x410 && x400 = x409 && x399 = x408 && x398 = x407 && x397 = x406 && x396 = x405
l12(x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l10(x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x422 = x431 && x421 = x430 && x420 = x429 && x419 = x428 && x418 = x427 && x417 = x426 && x416 = x425 && x415 = x424 && x414 = x423
Start term: l12(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, x0HATpost, x1HATpost, x2HATpost) :|: oldX5HAT0 = oldX5HATpost && oldX4HAT0 = oldX4HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost + oldX3HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
(2) l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l2(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x5 = x14 && x4 = x13 && x3 = x12 && x17 = x11 && x16 = x10 && x15 = x9 && 1 + x11 <= 0 && x11 = x8 && x10 = x7 && x9 = x6
(3) l1(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x21 = x30 && x35 = x29 && x34 = x28 && x33 = x27 && 0 <= x29 && x29 = x26 && x28 = x25 && x27 = x24
(4) l3(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l1(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x50 && x40 = x49 && x39 = x48 && x53 = x45 && x52 = 0 && x51 = x45 && x47 = x44 && x46 = x43 && x45 = x42
(5) l4(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l5(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x71 = x68 && x70 = x67 && x69 = x66 && x68 = x68 && x67 = x67 && x66 = x66 && x65 = x62 && x64 = x61 && x63 = x60
(6) l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l6(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x86 && x89 = x85 && x88 = x84 && x87 = -1 + x81 && x85 = x85 && x84 = x84 && x83 = x80 && x82 = x79 && x81 = x78
(7) l7(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l5(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x107 = x104 && x106 = x103 && x105 = x102 && x104 = x104 && x103 = x103 && x102 = x102 && x101 = x98 && x100 = x97 && x99 = x96
(8) l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l4(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x125 = x121 && x124 = x120 && x123 = x117 && 1 <= x117 && x121 = x121 && x120 = x120 && x119 = x116 && x118 = x115 && x117 = x114
(9) l8(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l7(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x131 = x140 && x143 = x139 && x142 = x138 && x141 = x135 && x135 <= 0 && x139 = x139 && x138 = x138 && x137 = x134 && x136 = x133 && x135 = x132
(10) l2(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l9(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x161 = x158 && x160 = x157 && x159 = x156 && x158 = x158 && x157 = x157 && x156 = x156 && x155 = x152 && x154 = x151 && x153 = x150
(11) l6(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l8(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x167 = x176 && x179 = x175 && x178 = x174 && x177 = x171 && x175 = x175 && x174 = x174 && x173 = x170 && x172 = x169 && x171 = x168
(12) l10(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l11(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x197 = x194 && x196 = x193 && x195 = x192 && x194 = x194 && x193 = x193 && x192 = x192 && x191 = x188 && x190 = x187 && x189 = x186
(13) l10(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l3(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x203 = x212 && x215 = x211 && x214 = x210 && x213 = x207 && x211 = x211 && x210 = x210 && x209 = x206 && x208 = x205 && x207 = x204
(14) l10(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l0(x225, x226, x227, x228, x229, x230, x231, x232, x233) :|: x224 = x233 && x223 = x232 && x222 = x231 && x221 = x230 && x220 = x229 && x219 = x228 && x218 = x227 && x217 = x226 && x216 = x225
(15) l10(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l1(x243, x244, x245, x246, x247, x248, x249, x250, x251) :|: x242 = x251 && x241 = x250 && x240 = x249 && x239 = x248 && x238 = x247 && x237 = x246 && x236 = x245 && x235 = x244 && x234 = x243
(16) l10(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l3(x261, x262, x263, x264, x265, x266, x267, x268, x269) :|: x260 = x269 && x259 = x268 && x258 = x267 && x257 = x266 && x256 = x265 && x255 = x264 && x254 = x263 && x253 = x262 && x252 = x261
(17) l10(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l5(x279, x280, x281, x282, x283, x284, x285, x286, x287) :|: x278 = x287 && x277 = x286 && x276 = x285 && x275 = x284 && x274 = x283 && x273 = x282 && x272 = x281 && x271 = x280 && x270 = x279
(18) l10(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l4(x297, x298, x299, x300, x301, x302, x303, x304, x305) :|: x296 = x305 && x295 = x304 && x294 = x303 && x293 = x302 && x292 = x301 && x291 = x300 && x290 = x299 && x289 = x298 && x288 = x297
(19) l10(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l7(x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x314 = x323 && x313 = x322 && x312 = x321 && x311 = x320 && x310 = x319 && x309 = x318 && x308 = x317 && x307 = x316 && x306 = x315
(20) l10(x324, x325, x326, x327, x328, x329, x330, x331, x332) -> l8(x333, x334, x335, x336, x337, x338, x339, x340, x341) :|: x332 = x341 && x331 = x340 && x330 = x339 && x329 = x338 && x328 = x337 && x327 = x336 && x326 = x335 && x325 = x334 && x324 = x333
(21) l10(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l11(x351, x352, x353, x354, x355, x356, x357, x358, x359) :|: x350 = x359 && x349 = x358 && x348 = x357 && x347 = x356 && x346 = x355 && x345 = x354 && x344 = x353 && x343 = x352 && x342 = x351
(22) l10(x360, x361, x362, x363, x364, x365, x366, x367, x368) -> l9(x369, x370, x371, x372, x373, x374, x375, x376, x377) :|: x368 = x377 && x367 = x376 && x366 = x375 && x365 = x374 && x364 = x373 && x363 = x372 && x362 = x371 && x361 = x370 && x360 = x369
(23) l10(x378, x379, x380, x381, x382, x383, x384, x385, x386) -> l2(x387, x388, x389, x390, x391, x392, x393, x394, x395) :|: x386 = x395 && x385 = x394 && x384 = x393 && x383 = x392 && x382 = x391 && x381 = x390 && x380 = x389 && x379 = x388 && x378 = x387
(24) l10(x396, x397, x398, x399, x400, x401, x402, x403, x404) -> l6(x405, x406, x407, x408, x409, x410, x411, x412, x413) :|: x404 = x413 && x403 = x412 && x402 = x411 && x401 = x410 && x400 = x409 && x399 = x408 && x398 = x407 && x397 = x406 && x396 = x405
(25) l12(x414, x415, x416, x417, x418, x419, x420, x421, x422) -> l10(x423, x424, x425, x426, x427, x428, x429, x430, x431) :|: x422 = x431 && x421 = x430 && x420 = x429 && x419 = x428 && x418 = x427 && x417 = x426 && x416 = x425 && x415 = x424 && x414 = x423

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l4(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l6(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x77 = x86 && x89 = x85 && x88 = x84 && x87 = -1 + x81 && x85 = x85 && x84 = x84 && x83 = x80 && x82 = x79 && x81 = x78
(2) l8(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l4(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x125 = x121 && x124 = x120 && x123 = x117 && 1 <= x117 && x121 = x121 && x120 = x120 && x119 = x116 && x118 = x115 && x117 = x114
(3) l6(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l8(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x167 = x176 && x179 = x175 && x178 = x174 && x177 = x171 && x175 = x175 && x174 = x174 && x173 = x170 && x172 = x169 && x171 = x168

Arcs:
(1) -> (3)
(2) -> (1)
(3) -> (2)

This digraph is fully evaluated!

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

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

(7)
Obligation:
Rules:
l8(x108:0, x109:0, x110:0, x111:0, x112:0, x113:0, x114:0, x115:0, x116:0) -> l8(-1 + x114:0, x172:0, x173:0, x174:0, x175:0, x113:0, -1 + x114:0, x174:0, x175:0) :|: x114:0 > 0

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

(8) 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) -> l8(x7)

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

(9)
Obligation:
Rules:
l8(x114:0) -> l8(-1 + x114:0) :|: x114:0 > 0

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

(11)
Obligation:
Rules:
l8(x114:0) -> l8(c) :|: c = -1 + x114:0 && x114:0 > 0

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

(12) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l8(x)] = x

The following rules are decreasing:
l8(x114:0) -> l8(c) :|: c = -1 + x114:0 && x114:0 > 0
The following rules are bounded:
l8(x114:0) -> l8(c) :|: c = -1 + x114:0 && x114:0 > 0

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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) l0(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0) -> l1(oldX0HATpost, oldX1HATpost, oldX2HATpost, oldX3HATpost, oldX4HATpost, oldX5HATpost, x0HATpost, x1HATpost, x2HATpost) :|: oldX5HAT0 = oldX5HATpost && oldX4HAT0 = oldX4HATpost && x2HATpost = -1 + oldX2HATpost && x1HATpost = oldX1HATpost + oldX3HATpost && x0HATpost = oldX0HATpost && oldX3HATpost = oldX3HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
(2) l1(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l0(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x21 = x30 && x35 = x29 && x34 = x28 && x33 = x27 && 0 <= x29 && x29 = x26 && x28 = x25 && x27 = x24

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
l0(oldX0HAT0:0, oldX1HAT0:0, oldX2HAT0:0, oldX3HAT0:0, oldX4HAT0:0, oldX5HAT0:0, oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0) -> l0(oldX0HATpost:0, oldX1HATpost:0 + oldX3HATpost:0, -1 + oldX2HATpost:0, oldX3HATpost:0, oldX4HAT0:0, oldX5HAT0:0, oldX0HATpost:0, oldX1HATpost:0 + oldX3HATpost:0, -1 + oldX2HATpost:0) :|: oldX2HATpost:0 > 0

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

(17) 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) -> l0(x9)

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

(18)
Obligation:
Rules:
l0(oldX2HATpost:0) -> l0(-1 + oldX2HATpost:0) :|: oldX2HATpost:0 > 0

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

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

(20)
Obligation:
Rules:
l0(oldX2HATpost:0) -> l0(c) :|: c = -1 + oldX2HATpost:0 && oldX2HATpost:0 > 0

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

(21) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l0(x)] = x

The following rules are decreasing:
l0(oldX2HATpost:0) -> l0(c) :|: c = -1 + oldX2HATpost:0 && oldX2HATpost:0 > 0
The following rules are bounded:
l0(oldX2HATpost:0) -> l0(c) :|: c = -1 + oldX2HATpost:0 && oldX2HATpost:0 > 0

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

(22)
YES