# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l22, l7, l11, l13, l3, l20, l18, l17, l2, l21, l14, l9, l23, l4, l6, l10, l8, l16, l15, l0, l12, l19
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _iHAT0 ∧ x2 = _jHAT0 ∧ x3 = _mHAT0 ∧ x4 = _nHAT0 ∧ x5 = _tmpHAT0 ∧ x6 = _tmp___0HAT0 ∧ x7 = _xHAT0 ∧ x8 = _yHAT0 ∧ x1 = _iHATpost ∧ x2 = _jHATpost ∧ x3 = _mHATpost ∧ x4 = _nHATpost ∧ x5 = _tmpHATpost ∧ x6 = _tmp___0HATpost ∧ x7 = _xHATpost ∧ x8 = _yHATpost ∧ _yHAT0 = _yHATpost ∧ _xHAT0 = _xHATpost ∧ _tmp___0HAT0 = _tmp___0HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _nHAT0 = _nHATpost ∧ _mHAT0 = _mHATpost ∧ _jHAT0 = _jHATpost ∧ _iHAT0 = _iHATpost ∧ _nHAT0 ≤ _mHAT0 l0 2 l2: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x1 = _x8 ∧ x2 = _x9 ∧ x3 = _x10 ∧ x4 = _x11 ∧ x5 = _x12 ∧ x6 = _x13 ∧ x7 = _x14 ∧ x8 = _x15 ∧ _x7 = _x15 ∧ _x5 = _x13 ∧ _x4 = _x12 ∧ _x3 = _x11 ∧ _x2 = _x10 ∧ _x1 = _x9 ∧ _x8 = _x2 ∧ _x14 = 0 ∧ 1 + _x2 ≤ _x3 l2 3 l3: x1 = _x16 ∧ x2 = _x17 ∧ x3 = _x18 ∧ x4 = _x19 ∧ x5 = _x20 ∧ x6 = _x21 ∧ x7 = _x22 ∧ x8 = _x23 ∧ x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x4 = _x27 ∧ x5 = _x28 ∧ x6 = _x29 ∧ x7 = _x30 ∧ x8 = _x31 ∧ _x23 = _x31 ∧ _x22 = _x30 ∧ _x21 = _x29 ∧ _x20 = _x28 ∧ _x19 = _x27 ∧ _x18 = _x26 ∧ _x17 = _x25 ∧ _x16 = _x24 l4 4 l5: x1 = _x32 ∧ x2 = _x33 ∧ x3 = _x34 ∧ x4 = _x35 ∧ x5 = _x36 ∧ x6 = _x37 ∧ x7 = _x38 ∧ x8 = _x39 ∧ x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x7 = _x46 ∧ x8 = _x47 ∧ _x39 = _x47 ∧ _x38 = _x46 ∧ _x37 = _x45 ∧ _x36 = _x44 ∧ _x35 = _x43 ∧ _x34 = _x42 ∧ _x33 = _x41 ∧ _x32 = _x40 l6 5 l7: x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x4 = _x51 ∧ x5 = _x52 ∧ x6 = _x53 ∧ x7 = _x54 ∧ x8 = _x55 ∧ x1 = _x56 ∧ x2 = _x57 ∧ x3 = _x58 ∧ x4 = _x59 ∧ x5 = _x60 ∧ x6 = _x61 ∧ x7 = _x62 ∧ x8 = _x63 ∧ _x55 = _x63 ∧ _x54 = _x62 ∧ _x53 = _x61 ∧ _x52 = _x60 ∧ _x51 = _x59 ∧ _x49 = _x57 ∧ _x48 = _x56 ∧ _x58 = 1 + _x50 l8 6 l9: x1 = _x64 ∧ x2 = _x65 ∧ x3 = _x66 ∧ x4 = _x67 ∧ x5 = _x68 ∧ x6 = _x69 ∧ x7 = _x70 ∧ x8 = _x71 ∧ x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x6 = _x77 ∧ x7 = _x78 ∧ x8 = _x79 ∧ _x71 = _x79 ∧ _x70 = _x78 ∧ _x69 = _x77 ∧ _x68 = _x76 ∧ _x67 = _x75 ∧ _x66 = _x74 ∧ _x65 = _x73 ∧ _x72 = 1 + _x64 l10 7 l11: x1 = _x80 ∧ x2 = _x81 ∧ x3 = _x82 ∧ x4 = _x83 ∧ x5 = _x84 ∧ x6 = _x85 ∧ x7 = _x86 ∧ x8 = _x87 ∧ x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x90 ∧ x4 = _x91 ∧ x5 = _x92 ∧ x6 = _x93 ∧ x7 = _x94 ∧ x8 = _x95 ∧ _x87 = _x95 ∧ _x86 = _x94 ∧ _x85 = _x93 ∧ _x84 = _x92 ∧ _x83 = _x91 ∧ _x82 = _x90 ∧ _x81 = _x89 ∧ _x80 = _x88 l12 8 l8: x1 = _x96 ∧ x2 = _x97 ∧ x3 = _x98 ∧ x4 = _x99 ∧ x5 = _x100 ∧ x6 = _x101 ∧ x7 = _x102 ∧ x8 = _x103 ∧ x1 = _x104 ∧ x2 = _x105 ∧ x3 = _x106 ∧ x4 = _x107 ∧ x5 = _x108 ∧ x6 = _x109 ∧ x7 = _x110 ∧ x8 = _x111 ∧ _x103 = _x111 ∧ _x102 = _x110 ∧ _x101 = _x109 ∧ _x100 = _x108 ∧ _x99 = _x107 ∧ _x98 = _x106 ∧ _x97 = _x105 ∧ _x96 = _x104 ∧ 1 + _x99 ≤ _x97 l12 9 l13: x1 = _x112 ∧ x2 = _x113 ∧ x3 = _x114 ∧ x4 = _x115 ∧ x5 = _x116 ∧ x6 = _x117 ∧ x7 = _x118 ∧ x8 = _x119 ∧ x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x4 = _x123 ∧ x5 = _x124 ∧ x6 = _x125 ∧ x7 = _x126 ∧ x8 = _x127 ∧ _x119 = _x127 ∧ _x118 = _x126 ∧ _x117 = _x125 ∧ _x116 = _x124 ∧ _x115 = _x123 ∧ _x114 = _x122 ∧ _x112 = _x120 ∧ _x121 = 1 + _x113 ∧ _x113 ≤ _x115 l14 10 l13: x1 = _x128 ∧ x2 = _x129 ∧ x3 = _x130 ∧ x4 = _x131 ∧ x5 = _x132 ∧ x6 = _x133 ∧ x7 = _x134 ∧ x8 = _x135 ∧ x1 = _x136 ∧ x2 = _x137 ∧ x3 = _x138 ∧ x4 = _x139 ∧ x5 = _x140 ∧ x6 = _x141 ∧ x7 = _x142 ∧ x8 = _x143 ∧ _x135 = _x143 ∧ _x134 = _x142 ∧ _x133 = _x141 ∧ _x132 = _x140 ∧ _x131 = _x139 ∧ _x130 = _x138 ∧ _x129 = _x137 ∧ _x128 = _x136 ∧ 1 + _x131 ≤ _x129 l14 11 l15: x1 = _x144 ∧ x2 = _x145 ∧ x3 = _x146 ∧ x4 = _x147 ∧ x5 = _x148 ∧ x6 = _x149 ∧ x7 = _x150 ∧ x8 = _x151 ∧ x1 = _x152 ∧ x2 = _x153 ∧ x3 = _x154 ∧ x4 = _x155 ∧ x5 = _x156 ∧ x6 = _x157 ∧ x7 = _x158 ∧ x8 = _x159 ∧ _x151 = _x159 ∧ _x150 = _x158 ∧ _x149 = _x157 ∧ _x148 = _x156 ∧ _x147 = _x155 ∧ _x146 = _x154 ∧ _x144 = _x152 ∧ _x153 = 1 + _x145 ∧ _x145 ≤ _x147 l16 12 l15: x1 = _x160 ∧ x2 = _x161 ∧ x3 = _x162 ∧ x4 = _x163 ∧ x5 = _x164 ∧ x6 = _x165 ∧ x7 = _x166 ∧ x8 = _x167 ∧ x1 = _x168 ∧ x2 = _x169 ∧ x3 = _x170 ∧ x4 = _x171 ∧ x5 = _x172 ∧ x6 = _x173 ∧ x7 = _x174 ∧ x8 = _x175 ∧ _x166 = _x174 ∧ _x165 = _x173 ∧ _x164 = _x172 ∧ _x163 = _x171 ∧ _x162 = _x170 ∧ _x161 = _x169 ∧ _x160 = _x168 ∧ _x175 = _x175 l17 13 l8: x1 = _x176 ∧ x2 = _x177 ∧ x3 = _x178 ∧ x4 = _x179 ∧ x5 = _x180 ∧ x6 = _x181 ∧ x7 = _x182 ∧ x8 = _x183 ∧ x1 = _x184 ∧ x2 = _x185 ∧ x3 = _x186 ∧ x4 = _x187 ∧ x5 = _x188 ∧ x6 = _x189 ∧ x7 = _x190 ∧ x8 = _x191 ∧ _x183 = _x191 ∧ _x182 = _x190 ∧ _x181 = _x189 ∧ _x180 = _x188 ∧ _x179 = _x187 ∧ _x178 = _x186 ∧ _x177 = _x185 ∧ _x176 = _x184 ∧ 0 ≤ _x183 ∧ _x183 ≤ 0 l17 14 l16: x1 = _x192 ∧ x2 = _x193 ∧ x3 = _x194 ∧ x4 = _x195 ∧ x5 = _x196 ∧ x6 = _x197 ∧ x7 = _x198 ∧ x8 = _x199 ∧ x1 = _x200 ∧ x2 = _x201 ∧ x3 = _x202 ∧ x4 = _x203 ∧ x5 = _x204 ∧ x6 = _x205 ∧ x7 = _x206 ∧ x8 = _x207 ∧ _x199 = _x207 ∧ _x198 = _x206 ∧ _x197 = _x205 ∧ _x196 = _x204 ∧ _x195 = _x203 ∧ _x194 = _x202 ∧ _x193 = _x201 ∧ _x192 = _x200 ∧ 1 ≤ _x199 l17 15 l16: x1 = _x208 ∧ x2 = _x209 ∧ x3 = _x210 ∧ x4 = _x211 ∧ x5 = _x212 ∧ x6 = _x213 ∧ x7 = _x214 ∧ x8 = _x215 ∧ x1 = _x216 ∧ x2 = _x217 ∧ x3 = _x218 ∧ x4 = _x219 ∧ x5 = _x220 ∧ x6 = _x221 ∧ x7 = _x222 ∧ x8 = _x223 ∧ _x215 = _x223 ∧ _x214 = _x222 ∧ _x213 = _x221 ∧ _x212 = _x220 ∧ _x211 = _x219 ∧ _x210 = _x218 ∧ _x209 = _x217 ∧ _x208 = _x216 ∧ 1 + _x215 ≤ 0 l9 16 l18: x1 = _x224 ∧ x2 = _x225 ∧ x3 = _x226 ∧ x4 = _x227 ∧ x5 = _x228 ∧ x6 = _x229 ∧ x7 = _x230 ∧ x8 = _x231 ∧ x1 = _x232 ∧ x2 = _x233 ∧ x3 = _x234 ∧ x4 = _x235 ∧ x5 = _x236 ∧ x6 = _x237 ∧ x7 = _x238 ∧ x8 = _x239 ∧ _x231 = _x239 ∧ _x230 = _x238 ∧ _x229 = _x237 ∧ _x228 = _x236 ∧ _x227 = _x235 ∧ _x226 = _x234 ∧ _x225 = _x233 ∧ _x224 = _x232 l18 17 l6: x1 = _x240 ∧ x2 = _x241 ∧ x3 = _x242 ∧ x4 = _x243 ∧ x5 = _x244 ∧ x6 = _x245 ∧ x7 = _x246 ∧ x8 = _x247 ∧ x1 = _x248 ∧ x2 = _x249 ∧ x3 = _x250 ∧ x4 = _x251 ∧ x5 = _x252 ∧ x6 = _x253 ∧ x7 = _x254 ∧ x8 = _x255 ∧ _x247 = _x255 ∧ _x246 = _x254 ∧ _x245 = _x253 ∧ _x244 = _x252 ∧ _x243 = _x251 ∧ _x242 = _x250 ∧ _x241 = _x249 ∧ _x240 = _x248 ∧ 1 + _x243 ≤ _x240 l18 18 l17: x1 = _x256 ∧ x2 = _x257 ∧ x3 = _x258 ∧ x4 = _x259 ∧ x5 = _x260 ∧ x6 = _x261 ∧ x7 = _x262 ∧ x8 = _x263 ∧ x1 = _x264 ∧ x2 = _x265 ∧ x3 = _x266 ∧ x4 = _x267 ∧ x5 = _x268 ∧ x6 = _x269 ∧ x7 = _x270 ∧ x8 = _x271 ∧ _x262 = _x270 ∧ _x261 = _x269 ∧ _x260 = _x268 ∧ _x259 = _x267 ∧ _x258 = _x266 ∧ _x257 = _x265 ∧ _x256 = _x264 ∧ _x271 = _x271 ∧ _x256 ≤ _x259 l19 19 l6: x1 = _x272 ∧ x2 = _x273 ∧ x3 = _x274 ∧ x4 = _x275 ∧ x5 = _x276 ∧ x6 = _x277 ∧ x7 = _x278 ∧ x8 = _x279 ∧ x1 = _x280 ∧ x2 = _x281 ∧ x3 = _x282 ∧ x4 = _x283 ∧ x5 = _x284 ∧ x6 = _x285 ∧ x7 = _x286 ∧ x8 = _x287 ∧ _x279 = _x287 ∧ _x278 = _x286 ∧ _x277 = _x285 ∧ _x276 = _x284 ∧ _x275 = _x283 ∧ _x274 = _x282 ∧ _x273 = _x281 ∧ _x272 = _x280 ∧ 0 ≤ _x278 ∧ _x278 ≤ 0 l19 20 l9: x1 = _x288 ∧ x2 = _x289 ∧ x3 = _x290 ∧ x4 = _x291 ∧ x5 = _x292 ∧ x6 = _x293 ∧ x7 = _x294 ∧ x8 = _x295 ∧ x1 = _x296 ∧ x2 = _x297 ∧ x3 = _x298 ∧ x4 = _x299 ∧ x5 = _x300 ∧ x6 = _x301 ∧ x7 = _x302 ∧ x8 = _x303 ∧ _x295 = _x303 ∧ _x294 = _x302 ∧ _x293 = _x301 ∧ _x292 = _x300 ∧ _x291 = _x299 ∧ _x290 = _x298 ∧ _x289 = _x297 ∧ _x288 = _x296 ∧ 1 ≤ _x294 l19 21 l9: x1 = _x304 ∧ x2 = _x305 ∧ x3 = _x306 ∧ x4 = _x307 ∧ x5 = _x308 ∧ x6 = _x309 ∧ x7 = _x310 ∧ x8 = _x311 ∧ x1 = _x312 ∧ x2 = _x313 ∧ x3 = _x314 ∧ x4 = _x315 ∧ x5 = _x316 ∧ x6 = _x317 ∧ x7 = _x318 ∧ x8 = _x319 ∧ _x311 = _x319 ∧ _x310 = _x318 ∧ _x309 = _x317 ∧ _x308 = _x316 ∧ _x307 = _x315 ∧ _x306 = _x314 ∧ _x305 = _x313 ∧ _x304 = _x312 ∧ 1 + _x310 ≤ 0 l15 22 l14: x1 = _x320 ∧ x2 = _x321 ∧ x3 = _x322 ∧ x4 = _x323 ∧ x5 = _x324 ∧ x6 = _x325 ∧ x7 = _x326 ∧ x8 = _x327 ∧ x1 = _x328 ∧ x2 = _x329 ∧ x3 = _x330 ∧ x4 = _x331 ∧ x5 = _x332 ∧ x6 = _x333 ∧ x7 = _x334 ∧ x8 = _x335 ∧ _x327 = _x335 ∧ _x326 = _x334 ∧ _x325 = _x333 ∧ _x324 = _x332 ∧ _x323 = _x331 ∧ _x322 = _x330 ∧ _x321 = _x329 ∧ _x320 = _x328 l11 23 l19: x1 = _x336 ∧ x2 = _x337 ∧ x3 = _x338 ∧ x4 = _x339 ∧ x5 = _x340 ∧ x6 = _x341 ∧ x7 = _x342 ∧ x8 = _x343 ∧ x1 = _x344 ∧ x2 = _x345 ∧ x3 = _x346 ∧ x4 = _x347 ∧ x5 = _x348 ∧ x6 = _x349 ∧ x7 = _x350 ∧ x8 = _x351 ∧ _x343 = _x351 ∧ _x342 = _x350 ∧ _x341 = _x349 ∧ _x340 = _x348 ∧ _x339 = _x347 ∧ _x338 = _x346 ∧ _x337 = _x345 ∧ _x336 = _x344 ∧ 1 + _x339 ≤ _x337 l11 24 l10: x1 = _x352 ∧ x2 = _x353 ∧ x3 = _x354 ∧ x4 = _x355 ∧ x5 = _x356 ∧ x6 = _x357 ∧ x7 = _x358 ∧ x8 = _x359 ∧ x1 = _x360 ∧ x2 = _x361 ∧ x3 = _x362 ∧ x4 = _x363 ∧ x5 = _x364 ∧ x6 = _x365 ∧ x7 = _x366 ∧ x8 = _x367 ∧ _x358 = _x366 ∧ _x357 = _x365 ∧ _x356 = _x364 ∧ _x355 = _x363 ∧ _x354 = _x362 ∧ _x352 = _x360 ∧ _x361 = 1 + _x353 ∧ _x367 = _x367 ∧ _x353 ≤ _x355 l5 25 l10: x1 = _x368 ∧ x2 = _x369 ∧ x3 = _x370 ∧ x4 = _x371 ∧ x5 = _x372 ∧ x6 = _x373 ∧ x7 = _x374 ∧ x8 = _x375 ∧ x1 = _x376 ∧ x2 = _x377 ∧ x3 = _x378 ∧ x4 = _x379 ∧ x5 = _x380 ∧ x6 = _x381 ∧ x7 = _x382 ∧ x8 = _x383 ∧ _x375 = _x383 ∧ _x374 = _x382 ∧ _x373 = _x381 ∧ _x372 = _x380 ∧ _x371 = _x379 ∧ _x370 = _x378 ∧ _x369 = _x377 ∧ _x368 = _x376 ∧ 1 + _x371 ≤ _x369 l5 26 l4: x1 = _x384 ∧ x2 = _x385 ∧ x3 = _x386 ∧ x4 = _x387 ∧ x5 = _x388 ∧ x6 = _x389 ∧ x7 = _x390 ∧ x8 = _x391 ∧ x1 = _x392 ∧ x2 = _x393 ∧ x3 = _x394 ∧ x4 = _x395 ∧ x5 = _x396 ∧ x6 = _x397 ∧ x7 = _x398 ∧ x8 = _x399 ∧ _x390 = _x398 ∧ _x389 = _x397 ∧ _x388 = _x396 ∧ _x387 = _x395 ∧ _x386 = _x394 ∧ _x384 = _x392 ∧ _x393 = 1 + _x385 ∧ _x399 = _x399 ∧ _x385 ≤ _x387 l20 27 l19: x1 = _x400 ∧ x2 = _x401 ∧ x3 = _x402 ∧ x4 = _x403 ∧ x5 = _x404 ∧ x6 = _x405 ∧ x7 = _x406 ∧ x8 = _x407 ∧ x1 = _x408 ∧ x2 = _x409 ∧ x3 = _x410 ∧ x4 = _x411 ∧ x5 = _x412 ∧ x6 = _x413 ∧ x7 = _x414 ∧ x8 = _x415 ∧ _x407 = _x415 ∧ _x406 = _x414 ∧ _x405 = _x413 ∧ _x404 = _x412 ∧ _x403 = _x411 ∧ _x402 = _x410 ∧ _x401 = _x409 ∧ _x400 = _x408 ∧ _x402 ≤ _x400 ∧ _x400 ≤ _x402 l20 28 l4: x1 = _x416 ∧ x2 = _x417 ∧ x3 = _x418 ∧ x4 = _x419 ∧ x5 = _x420 ∧ x6 = _x421 ∧ x7 = _x422 ∧ x8 = _x423 ∧ x1 = _x424 ∧ x2 = _x425 ∧ x3 = _x426 ∧ x4 = _x427 ∧ x5 = _x428 ∧ x6 = _x429 ∧ x7 = _x430 ∧ x8 = _x431 ∧ _x423 = _x431 ∧ _x422 = _x430 ∧ _x421 = _x429 ∧ _x420 = _x428 ∧ _x419 = _x427 ∧ _x418 = _x426 ∧ _x417 = _x425 ∧ _x416 = _x424 ∧ 1 + _x418 ≤ _x416 l20 29 l4: x1 = _x432 ∧ x2 = _x433 ∧ x3 = _x434 ∧ x4 = _x435 ∧ x5 = _x436 ∧ x6 = _x437 ∧ x7 = _x438 ∧ x8 = _x439 ∧ x1 = _x440 ∧ x2 = _x441 ∧ x3 = _x442 ∧ x4 = _x443 ∧ x5 = _x444 ∧ x6 = _x445 ∧ x7 = _x446 ∧ x8 = _x447 ∧ _x439 = _x447 ∧ _x438 = _x446 ∧ _x437 = _x445 ∧ _x436 = _x444 ∧ _x435 = _x443 ∧ _x434 = _x442 ∧ _x433 = _x441 ∧ _x432 = _x440 ∧ 1 + _x432 ≤ _x434 l13 30 l12: x1 = _x448 ∧ x2 = _x449 ∧ x3 = _x450 ∧ x4 = _x451 ∧ x5 = _x452 ∧ x6 = _x453 ∧ x7 = _x454 ∧ x8 = _x455 ∧ x1 = _x456 ∧ x2 = _x457 ∧ x3 = _x458 ∧ x4 = _x459 ∧ x5 = _x460 ∧ x6 = _x461 ∧ x7 = _x462 ∧ x8 = _x463 ∧ _x455 = _x463 ∧ _x454 = _x462 ∧ _x453 = _x461 ∧ _x452 = _x460 ∧ _x451 = _x459 ∧ _x450 = _x458 ∧ _x449 = _x457 ∧ _x448 = _x456 l21 31 l2: x1 = _x464 ∧ x2 = _x465 ∧ x3 = _x466 ∧ x4 = _x467 ∧ x5 = _x468 ∧ x6 = _x469 ∧ x7 = _x470 ∧ x8 = _x471 ∧ x1 = _x472 ∧ x2 = _x473 ∧ x3 = _x474 ∧ x4 = _x475 ∧ x5 = _x476 ∧ x6 = _x477 ∧ x7 = _x478 ∧ x8 = _x479 ∧ _x471 = _x479 ∧ _x470 = _x478 ∧ _x469 = _x477 ∧ _x468 = _x476 ∧ _x467 = _x475 ∧ _x466 = _x474 ∧ _x464 = _x472 ∧ _x473 = 1 + _x465 l22 32 l21: x1 = _x480 ∧ x2 = _x481 ∧ x3 = _x482 ∧ x4 = _x483 ∧ x5 = _x484 ∧ x6 = _x485 ∧ x7 = _x486 ∧ x8 = _x487 ∧ x1 = _x488 ∧ x2 = _x489 ∧ x3 = _x490 ∧ x4 = _x491 ∧ x5 = _x492 ∧ x6 = _x493 ∧ x7 = _x494 ∧ x8 = _x495 ∧ _x487 = _x495 ∧ _x486 = _x494 ∧ _x485 = _x493 ∧ _x484 = _x492 ∧ _x483 = _x491 ∧ _x482 = _x490 ∧ _x481 = _x489 ∧ _x480 = _x488 ∧ _x484 ≤ _x485 l22 33 l21: x1 = _x496 ∧ x2 = _x497 ∧ x3 = _x498 ∧ x4 = _x499 ∧ x5 = _x500 ∧ x6 = _x501 ∧ x7 = _x502 ∧ x8 = _x503 ∧ x1 = _x504 ∧ x2 = _x505 ∧ x3 = _x506 ∧ x4 = _x507 ∧ x5 = _x508 ∧ x6 = _x509 ∧ x7 = _x510 ∧ x8 = _x511 ∧ _x503 = _x511 ∧ _x501 = _x509 ∧ _x500 = _x508 ∧ _x499 = _x507 ∧ _x498 = _x506 ∧ _x497 = _x505 ∧ _x504 = _x497 ∧ _x510 = _x510 ∧ 1 + _x501 ≤ _x500 l3 34 l20: x1 = _x512 ∧ x2 = _x513 ∧ x3 = _x514 ∧ x4 = _x515 ∧ x5 = _x516 ∧ x6 = _x517 ∧ x7 = _x518 ∧ x8 = _x519 ∧ x1 = _x520 ∧ x2 = _x521 ∧ x3 = _x522 ∧ x4 = _x523 ∧ x5 = _x524 ∧ x6 = _x525 ∧ x7 = _x526 ∧ x8 = _x527 ∧ _x519 = _x527 ∧ _x518 = _x526 ∧ _x517 = _x525 ∧ _x516 = _x524 ∧ _x515 = _x523 ∧ _x514 = _x522 ∧ _x513 = _x521 ∧ _x512 = _x520 ∧ 1 + _x515 ≤ _x513 l3 35 l22: x1 = _x528 ∧ x2 = _x529 ∧ x3 = _x530 ∧ x4 = _x531 ∧ x5 = _x532 ∧ x6 = _x533 ∧ x7 = _x534 ∧ x8 = _x535 ∧ x1 = _x536 ∧ x2 = _x537 ∧ x3 = _x538 ∧ x4 = _x539 ∧ x5 = _x540 ∧ x6 = _x541 ∧ x7 = _x542 ∧ x8 = _x543 ∧ _x535 = _x543 ∧ _x534 = _x542 ∧ _x531 = _x539 ∧ _x530 = _x538 ∧ _x529 = _x537 ∧ _x528 = _x536 ∧ _x541 = _x541 ∧ _x540 = _x540 ∧ _x529 ≤ _x531 l7 36 l0: x1 = _x544 ∧ x2 = _x545 ∧ x3 = _x546 ∧ x4 = _x547 ∧ x5 = _x548 ∧ x6 = _x549 ∧ x7 = _x550 ∧ x8 = _x551 ∧ x1 = _x552 ∧ x2 = _x553 ∧ x3 = _x554 ∧ x4 = _x555 ∧ x5 = _x556 ∧ x6 = _x557 ∧ x7 = _x558 ∧ x8 = _x559 ∧ _x551 = _x559 ∧ _x550 = _x558 ∧ _x549 = _x557 ∧ _x548 = _x556 ∧ _x547 = _x555 ∧ _x546 = _x554 ∧ _x545 = _x553 ∧ _x544 = _x552 l23 37 l7: x1 = _x560 ∧ x2 = _x561 ∧ x3 = _x562 ∧ x4 = _x563 ∧ x5 = _x564 ∧ x6 = _x565 ∧ x7 = _x566 ∧ x8 = _x567 ∧ x1 = _x568 ∧ x2 = _x569 ∧ x3 = _x570 ∧ x4 = _x571 ∧ x5 = _x572 ∧ x6 = _x573 ∧ x7 = _x574 ∧ x8 = _x575 ∧ _x567 = _x575 ∧ _x566 = _x574 ∧ _x565 = _x573 ∧ _x564 = _x572 ∧ _x563 = _x571 ∧ _x562 = _x570 ∧ _x561 = _x569 ∧ _x560 = _x568

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 l5 l5 l5: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l22 l22 l22: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l7 l7 l7: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l11 l11 l11: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l13 l13 l13: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l3 l3 l3: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l20 l20 l20: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l18 l18 l18: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l17 l17 l17: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l2 l2 l2: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l21 l21 l21: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l14 l14 l14: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l9 l9 l9: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l23 l23 l23: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l4 l4 l4: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l6 l6 l6: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l10 l10 l10: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l8 l8 l8: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l16 l16 l16: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l15 l15 l15: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l0 l0 l0: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l12 l12 l12: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 l19 l19 l19: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/1

Here we consider the SCC { l5, l22, l7, l11, l3, l13, l20, l18, l17, l2, l21, l9, l14, l4, l6, l10, l8, l15, l16, l0, l19, l12 }.

### 2.1.1 Transition Removal

We remove transitions 35, 26, 24, 11, 9 using the following ranking functions, which are bounded by 0.

 l0: − x2 + x4 l2: − x2 + x4 l7: − x2 + x4 l6: − x2 + x4 l19: − x2 + x4 l18: − x2 + x4 l9: − x2 + x4 l20: − x2 + x4 l11: − x2 + x4 l10: − x2 + x4 l5: − x2 + x4 l4: − x2 + x4 l3: − x2 + x4 l21: −1 − x2 + x4 l22: −1 − x2 + x4 l8: − x2 + x4 l17: − x2 + x4 l12: − x2 + x4 l13: − x2 + x4 l14: − x2 + x4 l15: − x2 + x4 l16: − x2 + x4

### 2.1.2 Transition Removal

We remove transitions 31, 33, 32 using the following ranking functions, which are bounded by 0.

 l0: −1 l2: −1 l7: −1 l6: −1 l19: −1 l18: −1 l9: −1 l20: −1 l11: −1 l10: −1 l5: −1 l4: −1 l3: −1 l21: 0 l22: 1 l8: −1 l17: −1 l12: −1 l13: −1 l14: −1 l15: −1 l16: −1

### 2.1.3 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 0.

 l0: −12⋅x3 + 12⋅x4 l2: −12⋅x3 + 12⋅x4 − 1 l7: −12⋅x3 + 12⋅x4 + 1 l6: −12⋅x3 + 12⋅x4 − 10 l19: −12⋅x3 + 12⋅x4 − 8 l18: 12⋅x4 − 12⋅x3 − 9 l9: −12⋅x3 + 12⋅x4 − 9 l20: −12⋅x3 + 12⋅x4 − 3 l11: 12⋅x4 − 12⋅x3 − 7 l10: −12⋅x3 + 12⋅x4 − 6 l5: 12⋅x4 − 12⋅x3 − 5 l4: −12⋅x3 + 12⋅x4 − 4 l3: 12⋅x4 − 12⋅x3 − 2 l8: −12⋅x3 + 12⋅x4 − 9 l17: −12⋅x3 + 12⋅x4 − 9 l12: −12⋅x3 + 12⋅x4 − 9 l13: −12⋅x3 + 12⋅x4 − 9 l14: 12⋅x4 − 12⋅x3 − 9 l15: −12⋅x3 + 12⋅x4 − 9 l16: −12⋅x3 + 12⋅x4 − 9

### 2.1.4 Transition Removal

We remove transitions 19, 21, 20, 27, 23, 7, 25, 4, 29, 28, 34, 3 using the following ranking functions, which are bounded by 0.

 l7: −1 l0: −1 l6: −1 l19: 0 l18: −1 l9: −1 l20: 5 l11: 1 l10: 2 l5: 3 l4: 4 l3: 6 l2: 7 l8: −1 l17: −1 l12: −1 l13: −1 l14: −1 l15: −1 l16: −1

### 2.1.5 Transition Removal

We remove transitions 36, 5, 17 using the following ranking functions, which are bounded by 0.

 l7: 0 l0: −1 l6: 1 l18: 2 l9: 2 l8: 2 l17: 2 l12: 2 l13: 2 l14: 2 l15: 2 l16: 2

### 2.1.6 Transition Removal

We remove transition 18 using the following ranking functions, which are bounded by 0.

 l9: − x1 + x4 l18: − x1 + x4 l8: −1 − x1 + x4 l17: −1 − x1 + x4 l12: −1 − x1 + x4 l13: −1 − x1 + x4 l14: −1 − x1 + x4 l15: −1 − x1 + x4 l16: −1 − x1 + x4

### 2.1.7 Transition Removal

We remove transitions 16, 6, 13, 8, 30, 10, 22, 12, 15, 14 using the following ranking functions, which are bounded by 0.

 l9: 0 l18: −1 l8: 1 l17: 7 l12: 2 l13: 3 l14: 4 l15: 5 l16: 6

### 2.1.8 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

## Tool configuration

AProVE

• version: AProVE Commit ID: unknown
• strategy: Statistics for single proof: 100.00 % (11 real / 0 unknown / 0 assumptions / 11 total proof steps)