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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 3003 ms]
(4) AND
    (5) IRSwT
        (6) IntTRSCompressionProof [EQUIVALENT, 16 ms]
        (7) IRSwT
        (8) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (9) IRSwT
        (10) TempFilterProof [SOUND, 22 ms]
        (11) IntTRS
        (12) RankingReductionPairProof [EQUIVALENT, 13 ms]
        (13) YES
    (14) IRSwT
        (15) IntTRSCompressionProof [EQUIVALENT, 25 ms]
        (16) IRSwT
        (17) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
        (18) IRSwT
        (19) TempFilterProof [SOUND, 27 ms]
        (20) IntTRS
        (21) RankingReductionPairProof [EQUIVALENT, 13 ms]
        (22) YES


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

(0)
Obligation:
Rules:
l0(constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0) -> l1(constant22HATpost, i20HATpost, lx2HATpost, tmp03HATpost, tmp1011HATpost, tmp1112HATpost, tmp1213HATpost, tmp1314HATpost, tmp14HATpost, tmp25HATpost, tmp36HATpost, tmp47HATpost, tmp58HATpost, tmp69HATpost, tmp710HATpost, z115HATpost, z216HATpost, z317HATpost, z418HATpost, z519HATpost) :|: z519HAT0 = z519HATpost && z418HAT0 = z418HATpost && z317HAT0 = z317HATpost && z216HAT0 = z216HATpost && z115HAT0 = z115HATpost && tmp710HAT0 = tmp710HATpost && tmp69HAT0 = tmp69HATpost && tmp58HAT0 = tmp58HATpost && tmp47HAT0 = tmp47HATpost && tmp36HAT0 = tmp36HATpost && tmp25HAT0 = tmp25HATpost && tmp14HAT0 = tmp14HATpost && tmp1314HAT0 = tmp1314HATpost && tmp1213HAT0 = tmp1213HATpost && tmp1112HAT0 = tmp1112HATpost && tmp1011HAT0 = tmp1011HATpost && tmp03HAT0 = tmp03HATpost && lx2HAT0 = lx2HATpost && constant22HAT0 = constant22HATpost && i20HATpost = 0 && 8 <= i20HAT0
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) :|: 1 + x1 <= 8 && x23 = x23 && x40 = x40 && x28 = x28 && x41 = x41 && x29 = x29 && x42 = x42 && x30 = x30 && x43 = x43 && x24 = x23 + x30 && x27 = x23 - x30 && x25 = x28 + x29 && x26 = x28 - x29 && x44 = 4433 && x45 = x45 && x46 = 6270 && x47 = -15137 && x48 = x43 + x40 && x49 = x42 + x41 && x50 = x43 + x41 && x51 = x42 + x40 && x52 = 9633 && x39 = x39 && x53 = 2446 && x31 = x31 && x54 = 16819 && x32 = x32 && x55 = 25172 && x33 = x33 && x56 = 12299 && x34 = x34 && x57 = -7373 && x35 = x35 && x58 = -20995 && x36 = x36 && x59 = -16069 && x60 = x60 && x20 = -3196 && x61 = x61 && x37 = x60 + x39 && x38 = x61 + x39 && x21 = 1 + x1 && x2 = x22
l3(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l4(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x81 = x101 && x80 = x100 && x79 = x99 && x78 = x98 && x77 = x97 && x76 = x96 && x75 = x95 && x74 = x94 && x73 = x93 && x72 = x92 && x71 = x91 && x70 = x90 && x69 = x89 && x68 = x88 && x67 = x87 && x66 = x86 && x65 = x85 && x64 = x84 && x63 = x83 && x62 = x82 && 8 <= x63
l3(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) -> l1(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: 1 + x103 <= 8 && x125 = x125 && x142 = x142 && x130 = x130 && x143 = x143 && x131 = x131 && x144 = x144 && x132 = x132 && x145 = x145 && x126 = x125 + x132 && x129 = x125 - x132 && x127 = x130 + x131 && x128 = x130 - x131 && x146 = 4433 && x147 = x147 && x148 = 6270 && x149 = -15137 && x150 = x145 + x142 && x151 = x144 + x143 && x152 = x145 + x143 && x153 = x144 + x142 && x154 = 9633 && x141 = x141 && x155 = 2446 && x133 = x133 && x156 = 16819 && x134 = x134 && x157 = 25172 && x135 = x135 && x158 = 12299 && x136 = x136 && x159 = -7373 && x137 = x137 && x160 = -20995 && x138 = x138 && x161 = -16069 && x162 = x162 && x122 = -3196 && x163 = x163 && x139 = x162 + x141 && x140 = x163 + x141 && x123 = 1 + x103 && x104 = x124
l2(x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183) -> l0(x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: 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 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x166 = x186 && x165 = x185 && x164 = x184
l1(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223) -> l3(x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) :|: 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 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224
l5(x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l2(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283) :|: x263 = x283 && x262 = x282 && x261 = x281 && x260 = x280 && x259 = x279 && x258 = x278 && x257 = x277 && x256 = x276 && x255 = x275 && x254 = x274 && x253 = x273 && x252 = x272 && x251 = x271 && x250 = x270 && x249 = x269 && x248 = x268 && x247 = x267 && x244 = x264 && x265 = 0 && x266 = 8
l6(x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303) -> l5(x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x303 = x323 && x302 = x322 && x301 = x321 && x300 = x320 && x299 = x319 && x298 = x318 && x297 = x317 && x296 = x316 && x295 = x315 && x294 = x314 && x293 = x313 && x292 = x312 && x291 = x311 && x290 = x310 && x289 = x309 && x288 = x308 && x287 = x307 && x286 = x306 && x285 = x305 && x284 = x304
Start term: l6(constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0)

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

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

(2)
Obligation:
Rules:
l0(constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0) -> l1(constant22HATpost, i20HATpost, lx2HATpost, tmp03HATpost, tmp1011HATpost, tmp1112HATpost, tmp1213HATpost, tmp1314HATpost, tmp14HATpost, tmp25HATpost, tmp36HATpost, tmp47HATpost, tmp58HATpost, tmp69HATpost, tmp710HATpost, z115HATpost, z216HATpost, z317HATpost, z418HATpost, z519HATpost) :|: z519HAT0 = z519HATpost && z418HAT0 = z418HATpost && z317HAT0 = z317HATpost && z216HAT0 = z216HATpost && z115HAT0 = z115HATpost && tmp710HAT0 = tmp710HATpost && tmp69HAT0 = tmp69HATpost && tmp58HAT0 = tmp58HATpost && tmp47HAT0 = tmp47HATpost && tmp36HAT0 = tmp36HATpost && tmp25HAT0 = tmp25HATpost && tmp14HAT0 = tmp14HATpost && tmp1314HAT0 = tmp1314HATpost && tmp1213HAT0 = tmp1213HATpost && tmp1112HAT0 = tmp1112HATpost && tmp1011HAT0 = tmp1011HATpost && tmp03HAT0 = tmp03HATpost && lx2HAT0 = lx2HATpost && constant22HAT0 = constant22HATpost && i20HATpost = 0 && 8 <= i20HAT0
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) :|: 1 + x1 <= 8 && x23 = x23 && x40 = x40 && x28 = x28 && x41 = x41 && x29 = x29 && x42 = x42 && x30 = x30 && x43 = x43 && x24 = x23 + x30 && x27 = x23 - x30 && x25 = x28 + x29 && x26 = x28 - x29 && x44 = 4433 && x45 = x45 && x46 = 6270 && x47 = -15137 && x48 = x43 + x40 && x49 = x42 + x41 && x50 = x43 + x41 && x51 = x42 + x40 && x52 = 9633 && x39 = x39 && x53 = 2446 && x31 = x31 && x54 = 16819 && x32 = x32 && x55 = 25172 && x33 = x33 && x56 = 12299 && x34 = x34 && x57 = -7373 && x35 = x35 && x58 = -20995 && x36 = x36 && x59 = -16069 && x60 = x60 && x20 = -3196 && x61 = x61 && x37 = x60 + x39 && x38 = x61 + x39 && x21 = 1 + x1 && x2 = x22
l3(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l4(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x81 = x101 && x80 = x100 && x79 = x99 && x78 = x98 && x77 = x97 && x76 = x96 && x75 = x95 && x74 = x94 && x73 = x93 && x72 = x92 && x71 = x91 && x70 = x90 && x69 = x89 && x68 = x88 && x67 = x87 && x66 = x86 && x65 = x85 && x64 = x84 && x63 = x83 && x62 = x82 && 8 <= x63
l3(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) -> l1(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: 1 + x103 <= 8 && x125 = x125 && x142 = x142 && x130 = x130 && x143 = x143 && x131 = x131 && x144 = x144 && x132 = x132 && x145 = x145 && x126 = x125 + x132 && x129 = x125 - x132 && x127 = x130 + x131 && x128 = x130 - x131 && x146 = 4433 && x147 = x147 && x148 = 6270 && x149 = -15137 && x150 = x145 + x142 && x151 = x144 + x143 && x152 = x145 + x143 && x153 = x144 + x142 && x154 = 9633 && x141 = x141 && x155 = 2446 && x133 = x133 && x156 = 16819 && x134 = x134 && x157 = 25172 && x135 = x135 && x158 = 12299 && x136 = x136 && x159 = -7373 && x137 = x137 && x160 = -20995 && x138 = x138 && x161 = -16069 && x162 = x162 && x122 = -3196 && x163 = x163 && x139 = x162 + x141 && x140 = x163 + x141 && x123 = 1 + x103 && x104 = x124
l2(x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183) -> l0(x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: 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 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x166 = x186 && x165 = x185 && x164 = x184
l1(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223) -> l3(x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) :|: 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 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224
l5(x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l2(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283) :|: x263 = x283 && x262 = x282 && x261 = x281 && x260 = x280 && x259 = x279 && x258 = x278 && x257 = x277 && x256 = x276 && x255 = x275 && x254 = x274 && x253 = x273 && x252 = x272 && x251 = x271 && x250 = x270 && x249 = x269 && x248 = x268 && x247 = x267 && x244 = x264 && x265 = 0 && x266 = 8
l6(x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303) -> l5(x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x303 = x323 && x302 = x322 && x301 = x321 && x300 = x320 && x299 = x319 && x298 = x318 && x297 = x317 && x296 = x316 && x295 = x315 && x294 = x314 && x293 = x313 && x292 = x312 && x291 = x311 && x290 = x310 && x289 = x309 && x288 = x308 && x287 = x307 && x286 = x306 && x285 = x305 && x284 = x304
Start term: l6(constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0)

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

(3) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) l0(constant22HAT0, i20HAT0, lx2HAT0, tmp03HAT0, tmp1011HAT0, tmp1112HAT0, tmp1213HAT0, tmp1314HAT0, tmp14HAT0, tmp25HAT0, tmp36HAT0, tmp47HAT0, tmp58HAT0, tmp69HAT0, tmp710HAT0, z115HAT0, z216HAT0, z317HAT0, z418HAT0, z519HAT0) -> l1(constant22HATpost, i20HATpost, lx2HATpost, tmp03HATpost, tmp1011HATpost, tmp1112HATpost, tmp1213HATpost, tmp1314HATpost, tmp14HATpost, tmp25HATpost, tmp36HATpost, tmp47HATpost, tmp58HATpost, tmp69HATpost, tmp710HATpost, z115HATpost, z216HATpost, z317HATpost, z418HATpost, z519HATpost) :|: z519HAT0 = z519HATpost && z418HAT0 = z418HATpost && z317HAT0 = z317HATpost && z216HAT0 = z216HATpost && z115HAT0 = z115HATpost && tmp710HAT0 = tmp710HATpost && tmp69HAT0 = tmp69HATpost && tmp58HAT0 = tmp58HATpost && tmp47HAT0 = tmp47HATpost && tmp36HAT0 = tmp36HATpost && tmp25HAT0 = tmp25HATpost && tmp14HAT0 = tmp14HATpost && tmp1314HAT0 = tmp1314HATpost && tmp1213HAT0 = tmp1213HATpost && tmp1112HAT0 = tmp1112HATpost && tmp1011HAT0 = tmp1011HATpost && tmp03HAT0 = tmp03HATpost && lx2HAT0 = lx2HATpost && constant22HAT0 = constant22HATpost && i20HATpost = 0 && 8 <= i20HAT0
(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) :|: 1 + x1 <= 8 && x23 = x23 && x40 = x40 && x28 = x28 && x41 = x41 && x29 = x29 && x42 = x42 && x30 = x30 && x43 = x43 && x24 = x23 + x30 && x27 = x23 - x30 && x25 = x28 + x29 && x26 = x28 - x29 && x44 = 4433 && x45 = x45 && x46 = 6270 && x47 = -15137 && x48 = x43 + x40 && x49 = x42 + x41 && x50 = x43 + x41 && x51 = x42 + x40 && x52 = 9633 && x39 = x39 && x53 = 2446 && x31 = x31 && x54 = 16819 && x32 = x32 && x55 = 25172 && x33 = x33 && x56 = 12299 && x34 = x34 && x57 = -7373 && x35 = x35 && x58 = -20995 && x36 = x36 && x59 = -16069 && x60 = x60 && x20 = -3196 && x61 = x61 && x37 = x60 + x39 && x38 = x61 + x39 && x21 = 1 + x1 && x2 = x22
(3) l3(x62, x63, x64, x65, x66, x67, x68, x69, x70, x71, x72, x73, x74, x75, x76, x77, x78, x79, x80, x81) -> l4(x82, x83, x84, x85, x86, x87, x88, x89, x90, x91, x92, x93, x94, x95, x96, x97, x98, x99, x100, x101) :|: x81 = x101 && x80 = x100 && x79 = x99 && x78 = x98 && x77 = x97 && x76 = x96 && x75 = x95 && x74 = x94 && x73 = x93 && x72 = x92 && x71 = x91 && x70 = x90 && x69 = x89 && x68 = x88 && x67 = x87 && x66 = x86 && x65 = x85 && x64 = x84 && x63 = x83 && x62 = x82 && 8 <= x63
(4) l3(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) -> l1(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: 1 + x103 <= 8 && x125 = x125 && x142 = x142 && x130 = x130 && x143 = x143 && x131 = x131 && x144 = x144 && x132 = x132 && x145 = x145 && x126 = x125 + x132 && x129 = x125 - x132 && x127 = x130 + x131 && x128 = x130 - x131 && x146 = 4433 && x147 = x147 && x148 = 6270 && x149 = -15137 && x150 = x145 + x142 && x151 = x144 + x143 && x152 = x145 + x143 && x153 = x144 + x142 && x154 = 9633 && x141 = x141 && x155 = 2446 && x133 = x133 && x156 = 16819 && x134 = x134 && x157 = 25172 && x135 = x135 && x158 = 12299 && x136 = x136 && x159 = -7373 && x137 = x137 && x160 = -20995 && x138 = x138 && x161 = -16069 && x162 = x162 && x122 = -3196 && x163 = x163 && x139 = x162 + x141 && x140 = x163 + x141 && x123 = 1 + x103 && x104 = x124
(5) l2(x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183) -> l0(x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: 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 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x166 = x186 && x165 = x185 && x164 = x184
(6) l1(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223) -> l3(x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) :|: 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 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224
(7) l5(x244, x245, x246, x247, x248, x249, x250, x251, x252, x253, x254, x255, x256, x257, x258, x259, x260, x261, x262, x263) -> l2(x264, x265, x266, x267, x268, x269, x270, x271, x272, x273, x274, x275, x276, x277, x278, x279, x280, x281, x282, x283) :|: x263 = x283 && x262 = x282 && x261 = x281 && x260 = x280 && x259 = x279 && x258 = x278 && x257 = x277 && x256 = x276 && x255 = x275 && x254 = x274 && x253 = x273 && x252 = x272 && x251 = x271 && x250 = x270 && x249 = x269 && x248 = x268 && x247 = x267 && x244 = x264 && x265 = 0 && x266 = 8
(8) l6(x284, x285, x286, x287, x288, x289, x290, x291, x292, x293, x294, x295, x296, x297, x298, x299, x300, x301, x302, x303) -> l5(x304, x305, x306, x307, x308, x309, x310, x311, x312, x313, x314, x315, x316, x317, x318, x319, x320, x321, x322, x323) :|: x303 = x323 && x302 = x322 && x301 = x321 && x300 = x320 && x299 = x319 && x298 = x318 && x297 = x317 && x296 = x316 && x295 = x315 && x294 = x314 && x293 = x313 && x292 = x312 && x291 = x311 && x290 = x310 && x289 = x309 && x288 = x308 && x287 = x307 && x286 = x306 && x285 = x305 && x284 = x304

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

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

(4)
Complex Obligation (AND)

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

(5)
Obligation:

Termination digraph:
Nodes:
(1) l0(x, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19) -> l2(x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39) :|: 1 + x1 <= 8 && x23 = x23 && x40 = x40 && x28 = x28 && x41 = x41 && x29 = x29 && x42 = x42 && x30 = x30 && x43 = x43 && x24 = x23 + x30 && x27 = x23 - x30 && x25 = x28 + x29 && x26 = x28 - x29 && x44 = 4433 && x45 = x45 && x46 = 6270 && x47 = -15137 && x48 = x43 + x40 && x49 = x42 + x41 && x50 = x43 + x41 && x51 = x42 + x40 && x52 = 9633 && x39 = x39 && x53 = 2446 && x31 = x31 && x54 = 16819 && x32 = x32 && x55 = 25172 && x33 = x33 && x56 = 12299 && x34 = x34 && x57 = -7373 && x35 = x35 && x58 = -20995 && x36 = x36 && x59 = -16069 && x60 = x60 && x20 = -3196 && x61 = x61 && x37 = x60 + x39 && x38 = x61 + x39 && x21 = 1 + x1 && x2 = x22
(2) l2(x164, x165, x166, x167, x168, x169, x170, x171, x172, x173, x174, x175, x176, x177, x178, x179, x180, x181, x182, x183) -> l0(x184, x185, x186, x187, x188, x189, x190, x191, x192, x193, x194, x195, x196, x197, x198, x199, x200, x201, x202, x203) :|: 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 && x170 = x190 && x169 = x189 && x168 = x188 && x167 = x187 && x166 = x186 && x165 = x185 && x164 = x184

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

This digraph is fully evaluated!

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

(7)
Obligation:
Rules:
l0(x:0, x1:0, x186:0, x3:0, x4:0, x5:0, x6:0, x7:0, x8:0, x9:0, x10:0, x11:0, x12:0, x13:0, x14:0, x15:0, x16:0, x17:0, x18:0, x19:0) -> l0(-3196, 1 + x1:0, x186:0, x187:0, x187:0 + x194:0, x192:0 + x193:0, x192:0 - x193:0, x187:0 - x194:0, x192:0, x193:0, x194:0, x195:0, x196:0, x197:0, x198:0, x199:0, x200:0, x60:0 + x203:0, x61:0 + x203:0, x203:0) :|: x1:0 < 8

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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 < 8

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

(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 < 8

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

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

The following rules are decreasing:
l0(x1:0) -> l0(c) :|: c = 1 + x1:0 && x1:0 < 8

The following rules are bounded:
l0(x1:0) -> l0(c) :|: c = 1 + x1:0 && x1:0 < 8


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

(13)
YES

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

(14)
Obligation:

Termination digraph:
Nodes:
(1) l1(x204, x205, x206, x207, x208, x209, x210, x211, x212, x213, x214, x215, x216, x217, x218, x219, x220, x221, x222, x223) -> l3(x224, x225, x226, x227, x228, x229, x230, x231, x232, x233, x234, x235, x236, x237, x238, x239, x240, x241, x242, x243) :|: 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 && x210 = x230 && x209 = x229 && x208 = x228 && x207 = x227 && x206 = x226 && x205 = x225 && x204 = x224
(2) l3(x102, x103, x104, x105, x106, x107, x108, x109, x110, x111, x112, x113, x114, x115, x116, x117, x118, x119, x120, x121) -> l1(x122, x123, x124, x125, x126, x127, x128, x129, x130, x131, x132, x133, x134, x135, x136, x137, x138, x139, x140, x141) :|: 1 + x103 <= 8 && x125 = x125 && x142 = x142 && x130 = x130 && x143 = x143 && x131 = x131 && x144 = x144 && x132 = x132 && x145 = x145 && x126 = x125 + x132 && x129 = x125 - x132 && x127 = x130 + x131 && x128 = x130 - x131 && x146 = 4433 && x147 = x147 && x148 = 6270 && x149 = -15137 && x150 = x145 + x142 && x151 = x144 + x143 && x152 = x145 + x143 && x153 = x144 + x142 && x154 = 9633 && x141 = x141 && x155 = 2446 && x133 = x133 && x156 = 16819 && x134 = x134 && x157 = 25172 && x135 = x135 && x158 = 12299 && x136 = x136 && x159 = -7373 && x137 = x137 && x160 = -20995 && x138 = x138 && x161 = -16069 && x162 = x162 && x122 = -3196 && x163 = x163 && x139 = x162 + x141 && x140 = x163 + x141 && x123 = 1 + x103 && x104 = x124

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

This digraph is fully evaluated!

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

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

(16)
Obligation:
Rules:
l1(x204:0, x205:0, x124:0, x207:0, x208:0, x209:0, x210:0, x211:0, x212:0, x213:0, x214:0, x215:0, x216:0, x217:0, x218:0, x219:0, x220:0, x221:0, x222:0, x223:0) -> l1(-3196, 1 + x205:0, x124:0, x125:0, x125:0 + x132:0, x130:0 + x131:0, x130:0 - x131:0, x125:0 - x132:0, x130:0, x131:0, x132:0, x133:0, x134:0, x135:0, x136:0, x137:0, x138:0, x162:0 + x141:0, x163:0 + x141:0, x141:0) :|: x205:0 < 8

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

   l1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20) -> l1(x2)

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

(18)
Obligation:
Rules:
l1(x205:0) -> l1(1 + x205:0) :|: x205:0 < 8

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

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

(20)
Obligation:
Rules:
l1(x205:0) -> l1(c) :|: c = 1 + x205:0 && x205:0 < 8

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

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

The following rules are decreasing:
l1(x205:0) -> l1(c) :|: c = 1 + x205:0 && x205:0 < 8

The following rules are bounded:
l1(x205:0) -> l1(c) :|: c = 1 + x205:0 && x205:0 < 8


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

(22)
YES