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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 13.3 s]
(4) IRSwT
(5) IntTRSCompressionProof [EQUIVALENT, 28 ms]
(6) IRSwT
(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
(8) IRSwT
(9) TempFilterProof [SOUND, 55 ms]
(10) IntTRS
(11) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(12) IntTRS
(13) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(14) YES


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(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 && oldX3HAT0 = oldX3HATpost && x2HATpost = 1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x5 = x14 && x4 = x13 && x3 = x12 && x17 = x11 && x16 = x10 && x15 = x9 && x11 = x8 && x10 = x7 && x9 = x6
l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x35 = x30 && x34 = 1 + x28 && x33 = x27 && x30 = x30 && x29 = x26 && x28 = x25 && x27 = x24
l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x50 && x53 = x47 && x52 = x46 && x51 = x45 && x48 <= x49 && x49 = x49 && x48 = x48 && x47 = x44 && x46 = x43 && x45 = x42
l5(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x68 && x71 = x65 && x70 = x64 && x69 = x63 && 1 + x67 <= x66 && x67 = x67 && x66 = x66 && x65 = x62 && x64 = x61 && x63 = x60
l6(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l7(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x89 = x86 && x88 = x85 && x87 = x84 && x86 = x86 && x85 = x85 && x84 = x84 && x83 = x80 && x82 = x79 && x81 = x78
l1(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l3(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x95 = x104 && x94 = x103 && x93 = x102 && x107 = x101 && x106 = x100 && x105 = x99 && x99 - x100 <= x101 && x101 = x98 && x100 = x97 && x99 = x96
l1(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x112 = x121 && x111 = x120 && x125 = x119 && x124 = x118 && x123 = x117 && 1 + x119 <= x117 - x118 && x119 = x116 && x118 = x115 && x117 = x114
l4(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l6(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x131 = x140 && x130 = x139 && x143 = x138 && x142 = x136 && x141 = x135 && x135 <= x136 && x138 = x138 && x137 = x134 && x136 = x133 && x135 = x132
l4(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l1(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x149 = x158 && x148 = x157 && x147 = x156 && x161 = 0 && x160 = x154 && x159 = x153 && 1 + x154 <= x153 && x155 = x152 && x154 = x151 && x153 = x150
l8(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l4(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x167 = x176 && x166 = x175 && x179 = x174 && x178 = 1 && x177 = x171 && x174 = x174 && x173 = x170 && x172 = x169 && x171 = x168
l9(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l8(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x185 = x194 && x197 = x193 && x196 = x192 && x195 = x189 && x193 = x193 && x192 = x192 && x191 = x188 && x190 = x187 && x189 = x186
l9(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l0(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207
l9(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l2(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
l9(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l3(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
l9(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l5(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
l9(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l6(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
l9(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l1(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
l9(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l4(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
l9(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
l9(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l7(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
Start term: l10(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0)

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(1) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
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(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 && oldX3HAT0 = oldX3HATpost && x2HATpost = 1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x5 = x14 && x4 = x13 && x3 = x12 && x17 = x11 && x16 = x10 && x15 = x9 && x11 = x8 && x10 = x7 && x9 = x6
l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x35 = x30 && x34 = 1 + x28 && x33 = x27 && x30 = x30 && x29 = x26 && x28 = x25 && x27 = x24
l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x50 && x53 = x47 && x52 = x46 && x51 = x45 && x48 <= x49 && x49 = x49 && x48 = x48 && x47 = x44 && x46 = x43 && x45 = x42
l5(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x68 && x71 = x65 && x70 = x64 && x69 = x63 && 1 + x67 <= x66 && x67 = x67 && x66 = x66 && x65 = x62 && x64 = x61 && x63 = x60
l6(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l7(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x89 = x86 && x88 = x85 && x87 = x84 && x86 = x86 && x85 = x85 && x84 = x84 && x83 = x80 && x82 = x79 && x81 = x78
l1(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l3(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x95 = x104 && x94 = x103 && x93 = x102 && x107 = x101 && x106 = x100 && x105 = x99 && x99 - x100 <= x101 && x101 = x98 && x100 = x97 && x99 = x96
l1(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x112 = x121 && x111 = x120 && x125 = x119 && x124 = x118 && x123 = x117 && 1 + x119 <= x117 - x118 && x119 = x116 && x118 = x115 && x117 = x114
l4(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l6(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x131 = x140 && x130 = x139 && x143 = x138 && x142 = x136 && x141 = x135 && x135 <= x136 && x138 = x138 && x137 = x134 && x136 = x133 && x135 = x132
l4(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l1(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x149 = x158 && x148 = x157 && x147 = x156 && x161 = 0 && x160 = x154 && x159 = x153 && 1 + x154 <= x153 && x155 = x152 && x154 = x151 && x153 = x150
l8(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l4(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x167 = x176 && x166 = x175 && x179 = x174 && x178 = 1 && x177 = x171 && x174 = x174 && x173 = x170 && x172 = x169 && x171 = x168
l9(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l8(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x185 = x194 && x197 = x193 && x196 = x192 && x195 = x189 && x193 = x193 && x192 = x192 && x191 = x188 && x190 = x187 && x189 = x186
l9(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l0(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207
l9(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l2(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
l9(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l3(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
l9(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l5(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
l9(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l6(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
l9(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l1(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
l9(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l4(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
l9(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
l9(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l7(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
Start term: l10(oldX0HAT0, oldX1HAT0, oldX2HAT0, oldX3HAT0, oldX4HAT0, oldX5HAT0, x0HAT0, x1HAT0, x2HAT0)

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(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 && oldX3HAT0 = oldX3HATpost && x2HATpost = 1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
(2) l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x5 = x14 && x4 = x13 && x3 = x12 && x17 = x11 && x16 = x10 && x15 = x9 && x11 = x8 && x10 = x7 && x9 = x6
(3) l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x35 = x30 && x34 = 1 + x28 && x33 = x27 && x30 = x30 && x29 = x26 && x28 = x25 && x27 = x24
(4) l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x50 && x53 = x47 && x52 = x46 && x51 = x45 && x48 <= x49 && x49 = x49 && x48 = x48 && x47 = x44 && x46 = x43 && x45 = x42
(5) l5(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x68 && x71 = x65 && x70 = x64 && x69 = x63 && 1 + x67 <= x66 && x67 = x67 && x66 = x66 && x65 = x62 && x64 = x61 && x63 = x60
(6) l6(x72, x73, x74, x75, x76, x77, x78, x79, x80) -> l7(x81, x82, x83, x84, x85, x86, x87, x88, x89) :|: x89 = x86 && x88 = x85 && x87 = x84 && x86 = x86 && x85 = x85 && x84 = x84 && x83 = x80 && x82 = x79 && x81 = x78
(7) l1(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l3(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x95 = x104 && x94 = x103 && x93 = x102 && x107 = x101 && x106 = x100 && x105 = x99 && x99 - x100 <= x101 && x101 = x98 && x100 = x97 && x99 = x96
(8) l1(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x112 = x121 && x111 = x120 && x125 = x119 && x124 = x118 && x123 = x117 && 1 + x119 <= x117 - x118 && x119 = x116 && x118 = x115 && x117 = x114
(9) l4(x126, x127, x128, x129, x130, x131, x132, x133, x134) -> l6(x135, x136, x137, x138, x139, x140, x141, x142, x143) :|: x131 = x140 && x130 = x139 && x143 = x138 && x142 = x136 && x141 = x135 && x135 <= x136 && x138 = x138 && x137 = x134 && x136 = x133 && x135 = x132
(10) l4(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l1(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x149 = x158 && x148 = x157 && x147 = x156 && x161 = 0 && x160 = x154 && x159 = x153 && 1 + x154 <= x153 && x155 = x152 && x154 = x151 && x153 = x150
(11) l8(x162, x163, x164, x165, x166, x167, x168, x169, x170) -> l4(x171, x172, x173, x174, x175, x176, x177, x178, x179) :|: x167 = x176 && x166 = x175 && x179 = x174 && x178 = 1 && x177 = x171 && x174 = x174 && x173 = x170 && x172 = x169 && x171 = x168
(12) l9(x180, x181, x182, x183, x184, x185, x186, x187, x188) -> l8(x189, x190, x191, x192, x193, x194, x195, x196, x197) :|: x185 = x194 && x197 = x193 && x196 = x192 && x195 = x189 && x193 = x193 && x192 = x192 && x191 = x188 && x190 = x187 && x189 = x186
(13) l9(x198, x199, x200, x201, x202, x203, x204, x205, x206) -> l0(x207, x208, x209, x210, x211, x212, x213, x214, x215) :|: x206 = x215 && x205 = x214 && x204 = x213 && x203 = x212 && x202 = x211 && x201 = x210 && x200 = x209 && x199 = x208 && x198 = x207
(14) l9(x216, x217, x218, x219, x220, x221, x222, x223, x224) -> l2(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) l9(x234, x235, x236, x237, x238, x239, x240, x241, x242) -> l3(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) l9(x252, x253, x254, x255, x256, x257, x258, x259, x260) -> l5(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) l9(x270, x271, x272, x273, x274, x275, x276, x277, x278) -> l6(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) l9(x288, x289, x290, x291, x292, x293, x294, x295, x296) -> l1(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) l9(x306, x307, x308, x309, x310, x311, x312, x313, x314) -> l4(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) l9(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) l9(x342, x343, x344, x345, x346, x347, x348, x349, x350) -> l7(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

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

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

(4)
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 && oldX3HAT0 = oldX3HATpost && x2HATpost = 1 + oldX2HATpost && x1HATpost = oldX1HATpost && x0HATpost = oldX0HATpost && oldX2HATpost = x2HAT0 && oldX1HATpost = x1HAT0 && oldX0HATpost = x0HAT0
(2) l5(x36, x37, x38, x39, x40, x41, x42, x43, x44) -> l0(x45, x46, x47, x48, x49, x50, x51, x52, x53) :|: x41 = x50 && x53 = x47 && x52 = x46 && x51 = x45 && x48 <= x49 && x49 = x49 && x48 = x48 && x47 = x44 && x46 = x43 && x45 = x42
(3) l2(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l0(x9, x10, x11, x12, x13, x14, x15, x16, x17) :|: x5 = x14 && x4 = x13 && x3 = x12 && x17 = x11 && x16 = x10 && x15 = x9 && x11 = x8 && x10 = x7 && x9 = x6
(4) l5(x54, x55, x56, x57, x58, x59, x60, x61, x62) -> l2(x63, x64, x65, x66, x67, x68, x69, x70, x71) :|: x59 = x68 && x71 = x65 && x70 = x64 && x69 = x63 && 1 + x67 <= x66 && x67 = x67 && x66 = x66 && x65 = x62 && x64 = x61 && x63 = x60
(5) l1(x108, x109, x110, x111, x112, x113, x114, x115, x116) -> l5(x117, x118, x119, x120, x121, x122, x123, x124, x125) :|: x113 = x122 && x112 = x121 && x111 = x120 && x125 = x119 && x124 = x118 && x123 = x117 && 1 + x119 <= x117 - x118 && x119 = x116 && x118 = x115 && x117 = x114
(6) l4(x144, x145, x146, x147, x148, x149, x150, x151, x152) -> l1(x153, x154, x155, x156, x157, x158, x159, x160, x161) :|: x149 = x158 && x148 = x157 && x147 = x156 && x161 = 0 && x160 = x154 && x159 = x153 && 1 + x154 <= x153 && x155 = x152 && x154 = x151 && x153 = x150
(7) l3(x18, x19, x20, x21, x22, x23, x24, x25, x26) -> l4(x27, x28, x29, x30, x31, x32, x33, x34, x35) :|: x23 = x32 && x22 = x31 && x35 = x30 && x34 = 1 + x28 && x33 = x27 && x30 = x30 && x29 = x26 && x28 = x25 && x27 = x24
(8) l1(x90, x91, x92, x93, x94, x95, x96, x97, x98) -> l3(x99, x100, x101, x102, x103, x104, x105, x106, x107) :|: x95 = x104 && x94 = x103 && x93 = x102 && x107 = x101 && x106 = x100 && x105 = x99 && x99 - x100 <= x101 && x101 = x98 && x100 = x97 && x99 = x96

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

This digraph is fully evaluated!

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

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

(6)
Obligation:
Rules:
l1(x108:0, x109:0, x110:0, x111:0, x112:0, oldX5HATpost:0, oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0) -> l1(oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0, oldX3HATpost:0, oldX4HATpost:0, oldX5HATpost:0, oldX0HATpost:0, oldX1HATpost:0, 1 + oldX2HATpost:0) :|: oldX0HATpost:0 - oldX1HATpost:0 >= 1 + oldX2HATpost:0 && oldX4HATpost:0 >= oldX3HATpost:0
l1(x90:0, x91:0, x92:0, x102:0, x103:0, x104:0, x105:0, x100:0, x101:0) -> l1(x105:0, 1 + x100:0, x155:0, x155:0, x103:0, x104:0, x105:0, 1 + x100:0, 0) :|: x105:0 - x100:0 <= x101:0 && x105:0 >= 1 + (1 + x100:0)
l1(x, x1, x2, x3, x4, x5, x6, x7, x8) -> l1(x6, x7, x8, x9, x10, x5, x6, x7, 1 + x8) :|: x6 - x7 >= 1 + x8 && x9 >= 1 + x10

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

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

   l1(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> l1(x7, x8, x9)

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

(8)
Obligation:
Rules:
l1(oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0) -> l1(oldX0HATpost:0, oldX1HATpost:0, 1 + oldX2HATpost:0) :|: oldX0HATpost:0 - oldX1HATpost:0 >= 1 + oldX2HATpost:0 && oldX4HATpost:0 >= oldX3HATpost:0
l1(x105:0, x100:0, x101:0) -> l1(x105:0, 1 + x100:0, 0) :|: x105:0 - x100:0 <= x101:0 && x105:0 >= 1 + (1 + x100:0)
l1(x6, x7, x8) -> l1(x6, x7, 1 + x8) :|: x6 - x7 >= 1 + x8 && x9 >= 1 + x10

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

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

(10)
Obligation:
Rules:
l1(oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0) -> l1(oldX0HATpost:0, oldX1HATpost:0, c) :|: c = 1 + oldX2HATpost:0 && (oldX0HATpost:0 - oldX1HATpost:0 >= 1 + oldX2HATpost:0 && oldX4HATpost:0 >= oldX3HATpost:0)
l1(x105:0, x100:0, x101:0) -> l1(x105:0, c1, c2) :|: c2 = 0 && c1 = 1 + x100:0 && (x105:0 - x100:0 <= x101:0 && x105:0 >= 1 + (1 + x100:0))
l1(x6, x7, x8) -> l1(x6, x7, c3) :|: c3 = 1 + x8 && (x6 - x7 >= 1 + x8 && x9 >= 1 + x10)

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

(11) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l1(x, x1, x2)] = -2 + x - x1

The following rules are decreasing:
l1(x105:0, x100:0, x101:0) -> l1(x105:0, c1, c2) :|: c2 = 0 && c1 = 1 + x100:0 && (x105:0 - x100:0 <= x101:0 && x105:0 >= 1 + (1 + x100:0))
The following rules are bounded:
l1(x105:0, x100:0, x101:0) -> l1(x105:0, c1, c2) :|: c2 = 0 && c1 = 1 + x100:0 && (x105:0 - x100:0 <= x101:0 && x105:0 >= 1 + (1 + x100:0))

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

(12)
Obligation:
Rules:
l1(oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0) -> l1(oldX0HATpost:0, oldX1HATpost:0, c) :|: c = 1 + oldX2HATpost:0 && (oldX0HATpost:0 - oldX1HATpost:0 >= 1 + oldX2HATpost:0 && oldX4HATpost:0 >= oldX3HATpost:0)
l1(x6, x7, x8) -> l1(x6, x7, c3) :|: c3 = 1 + x8 && (x6 - x7 >= 1 + x8 && x9 >= 1 + x10)

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

(13) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[l1(x, x1, x2)] = x - x1 - x2

The following rules are decreasing:
l1(oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0) -> l1(oldX0HATpost:0, oldX1HATpost:0, c) :|: c = 1 + oldX2HATpost:0 && (oldX0HATpost:0 - oldX1HATpost:0 >= 1 + oldX2HATpost:0 && oldX4HATpost:0 >= oldX3HATpost:0)
l1(x6, x7, x8) -> l1(x6, x7, c3) :|: c3 = 1 + x8 && (x6 - x7 >= 1 + x8 && x9 >= 1 + x10)
The following rules are bounded:
l1(oldX0HATpost:0, oldX1HATpost:0, oldX2HATpost:0) -> l1(oldX0HATpost:0, oldX1HATpost:0, c) :|: c = 1 + oldX2HATpost:0 && (oldX0HATpost:0 - oldX1HATpost:0 >= 1 + oldX2HATpost:0 && oldX4HATpost:0 >= oldX3HATpost:0)
l1(x6, x7, x8) -> l1(x6, x7, c3) :|: c3 = 1 + x8 && (x6 - x7 >= 1 + x8 && x9 >= 1 + x10)

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

(14)
YES