# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l22, l13, l18, l17, l21, l14, l9, l25, l6, l8, l27, l0, l12, l19, l26, l7, l24, l11, l3, l20, l2, l23, l4, l10, l15, l16
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _bDomainHAT0 ∧ x2 = _bNoCaptureHAT0 ∧ x3 = _nDimHAT0 ∧ x4 = _niHAT0 ∧ x5 = _njHAT0 ∧ x6 = _tmpHAT0 ∧ x7 = _tmp___0HAT0 ∧ x8 = _tmp___1HAT0 ∧ x9 = _tmp___2HAT0 ∧ x10 = _tmp___3HAT0 ∧ x1 = _bDomainHATpost ∧ x2 = _bNoCaptureHATpost ∧ x3 = _nDimHATpost ∧ x4 = _niHATpost ∧ x5 = _njHATpost ∧ x6 = _tmpHATpost ∧ x7 = _tmp___0HATpost ∧ x8 = _tmp___1HATpost ∧ x9 = _tmp___2HATpost ∧ x10 = _tmp___3HATpost ∧ _tmp___3HAT0 = _tmp___3HATpost ∧ _tmp___2HAT0 = _tmp___2HATpost ∧ _tmp___1HAT0 = _tmp___1HATpost ∧ _tmp___0HAT0 = _tmp___0HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _njHAT0 = _njHATpost ∧ _niHAT0 = _niHATpost ∧ _nDimHAT0 = _nDimHATpost ∧ _bNoCaptureHAT0 = _bNoCaptureHATpost ∧ _bDomainHAT0 = _bDomainHATpost l2 2 l0: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x10 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ x3 = _x12 ∧ x4 = _x13 ∧ x5 = _x14 ∧ x6 = _x15 ∧ x7 = _x16 ∧ x8 = _x17 ∧ x9 = _x18 ∧ x10 = _x19 ∧ _x8 = _x18 ∧ _x7 = _x17 ∧ _x6 = _x16 ∧ _x5 = _x15 ∧ _x4 = _x14 ∧ _x3 = _x13 ∧ _x2 = _x12 ∧ _x1 = _x11 ∧ _x = _x10 ∧ _x19 = 0 l3 3 l0: x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x23 ∧ x5 = _x24 ∧ x6 = _x25 ∧ x7 = _x26 ∧ x8 = _x27 ∧ x9 = _x28 ∧ x10 = _x29 ∧ x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x4 = _x33 ∧ x5 = _x34 ∧ x6 = _x35 ∧ x7 = _x36 ∧ x8 = _x37 ∧ x9 = _x38 ∧ x10 = _x39 ∧ _x28 = _x38 ∧ _x27 = _x37 ∧ _x26 = _x36 ∧ _x25 = _x35 ∧ _x24 = _x34 ∧ _x23 = _x33 ∧ _x22 = _x32 ∧ _x21 = _x31 ∧ _x20 = _x30 ∧ _x39 = 1 ∧ 0 ≤ _x21 ∧ _x21 ≤ 0 l3 4 l2: x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x7 = _x46 ∧ x8 = _x47 ∧ x9 = _x48 ∧ x10 = _x49 ∧ x1 = _x50 ∧ x2 = _x51 ∧ x3 = _x52 ∧ x4 = _x53 ∧ x5 = _x54 ∧ x6 = _x55 ∧ x7 = _x56 ∧ x8 = _x57 ∧ x9 = _x58 ∧ x10 = _x59 ∧ _x49 = _x59 ∧ _x48 = _x58 ∧ _x47 = _x57 ∧ _x46 = _x56 ∧ _x45 = _x55 ∧ _x44 = _x54 ∧ _x43 = _x53 ∧ _x42 = _x52 ∧ _x41 = _x51 ∧ _x40 = _x50 ∧ 1 ≤ _x41 l3 5 l2: x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x63 ∧ x5 = _x64 ∧ x6 = _x65 ∧ x7 = _x66 ∧ x8 = _x67 ∧ x9 = _x68 ∧ x10 = _x69 ∧ x1 = _x70 ∧ x2 = _x71 ∧ x3 = _x72 ∧ x4 = _x73 ∧ x5 = _x74 ∧ x6 = _x75 ∧ x7 = _x76 ∧ x8 = _x77 ∧ x9 = _x78 ∧ x10 = _x79 ∧ _x69 = _x79 ∧ _x68 = _x78 ∧ _x67 = _x77 ∧ _x66 = _x76 ∧ _x65 = _x75 ∧ _x64 = _x74 ∧ _x63 = _x73 ∧ _x62 = _x72 ∧ _x61 = _x71 ∧ _x60 = _x70 ∧ 1 + _x61 ≤ 0 l4 6 l0: x1 = _x80 ∧ x2 = _x81 ∧ x3 = _x82 ∧ x4 = _x83 ∧ x5 = _x84 ∧ x6 = _x85 ∧ x7 = _x86 ∧ x8 = _x87 ∧ x9 = _x88 ∧ x10 = _x89 ∧ x1 = _x90 ∧ x2 = _x91 ∧ x3 = _x92 ∧ x4 = _x93 ∧ x5 = _x94 ∧ x6 = _x95 ∧ x7 = _x96 ∧ x8 = _x97 ∧ x9 = _x98 ∧ x10 = _x99 ∧ _x88 = _x98 ∧ _x87 = _x97 ∧ _x86 = _x96 ∧ _x85 = _x95 ∧ _x84 = _x94 ∧ _x83 = _x93 ∧ _x82 = _x92 ∧ _x81 = _x91 ∧ _x80 = _x90 ∧ _x99 = 1 ∧ 0 ≤ _x80 ∧ _x80 ≤ 0 l4 7 l3: x1 = _x100 ∧ x2 = _x101 ∧ x3 = _x102 ∧ x4 = _x103 ∧ x5 = _x104 ∧ x6 = _x105 ∧ x7 = _x106 ∧ x8 = _x107 ∧ x9 = _x108 ∧ x10 = _x109 ∧ x1 = _x110 ∧ x2 = _x111 ∧ x3 = _x112 ∧ x4 = _x113 ∧ x5 = _x114 ∧ x6 = _x115 ∧ x7 = _x116 ∧ x8 = _x117 ∧ x9 = _x118 ∧ x10 = _x119 ∧ _x109 = _x119 ∧ _x108 = _x118 ∧ _x107 = _x117 ∧ _x106 = _x116 ∧ _x105 = _x115 ∧ _x104 = _x114 ∧ _x103 = _x113 ∧ _x102 = _x112 ∧ _x101 = _x111 ∧ _x100 = _x110 ∧ 1 ≤ _x100 l4 8 l3: x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x4 = _x123 ∧ x5 = _x124 ∧ x6 = _x125 ∧ x7 = _x126 ∧ x8 = _x127 ∧ x9 = _x128 ∧ x10 = _x129 ∧ x1 = _x130 ∧ x2 = _x131 ∧ x3 = _x132 ∧ x4 = _x133 ∧ x5 = _x134 ∧ x6 = _x135 ∧ x7 = _x136 ∧ x8 = _x137 ∧ x9 = _x138 ∧ x10 = _x139 ∧ _x129 = _x139 ∧ _x128 = _x138 ∧ _x127 = _x137 ∧ _x126 = _x136 ∧ _x125 = _x135 ∧ _x124 = _x134 ∧ _x123 = _x133 ∧ _x122 = _x132 ∧ _x121 = _x131 ∧ _x120 = _x130 ∧ 1 + _x120 ≤ 0 l5 9 l6: x1 = _x140 ∧ x2 = _x141 ∧ x3 = _x142 ∧ x4 = _x143 ∧ x5 = _x144 ∧ x6 = _x145 ∧ x7 = _x146 ∧ x8 = _x147 ∧ x9 = _x148 ∧ x10 = _x149 ∧ x1 = _x150 ∧ x2 = _x151 ∧ x3 = _x152 ∧ x4 = _x153 ∧ x5 = _x154 ∧ x6 = _x155 ∧ x7 = _x156 ∧ x8 = _x157 ∧ x9 = _x158 ∧ x10 = _x159 ∧ _x149 = _x159 ∧ _x148 = _x158 ∧ _x147 = _x157 ∧ _x146 = _x156 ∧ _x145 = _x155 ∧ _x143 = _x153 ∧ _x142 = _x152 ∧ _x141 = _x151 ∧ _x140 = _x150 ∧ _x154 = 1 + _x144 l7 10 l5: x1 = _x160 ∧ x2 = _x161 ∧ x3 = _x162 ∧ x4 = _x163 ∧ x5 = _x164 ∧ x6 = _x165 ∧ x7 = _x166 ∧ x8 = _x167 ∧ x9 = _x168 ∧ x10 = _x169 ∧ x1 = _x170 ∧ x2 = _x171 ∧ x3 = _x172 ∧ x4 = _x173 ∧ x5 = _x174 ∧ x6 = _x175 ∧ x7 = _x176 ∧ x8 = _x177 ∧ x9 = _x178 ∧ x10 = _x179 ∧ _x169 = _x179 ∧ _x168 = _x178 ∧ _x167 = _x177 ∧ _x166 = _x176 ∧ _x165 = _x175 ∧ _x164 = _x174 ∧ _x163 = _x173 ∧ _x162 = _x172 ∧ _x160 = _x170 ∧ _x171 = _x168 l8 11 l9: x1 = _x180 ∧ x2 = _x181 ∧ x3 = _x182 ∧ x4 = _x183 ∧ x5 = _x184 ∧ x6 = _x185 ∧ x7 = _x186 ∧ x8 = _x187 ∧ x9 = _x188 ∧ x10 = _x189 ∧ x1 = _x190 ∧ x2 = _x191 ∧ x3 = _x192 ∧ x4 = _x193 ∧ x5 = _x194 ∧ x6 = _x195 ∧ x7 = _x196 ∧ x8 = _x197 ∧ x9 = _x198 ∧ x10 = _x199 ∧ _x189 = _x199 ∧ _x188 = _x198 ∧ _x187 = _x197 ∧ _x186 = _x196 ∧ _x185 = _x195 ∧ _x184 = _x194 ∧ _x183 = _x193 ∧ _x182 = _x192 ∧ _x181 = _x191 ∧ _x180 = _x190 l10 12 l7: x1 = _x200 ∧ x2 = _x201 ∧ x3 = _x202 ∧ x4 = _x203 ∧ x5 = _x204 ∧ x6 = _x205 ∧ x7 = _x206 ∧ x8 = _x207 ∧ x9 = _x208 ∧ x10 = _x209 ∧ x1 = _x210 ∧ x2 = _x211 ∧ x3 = _x212 ∧ x4 = _x213 ∧ x5 = _x214 ∧ x6 = _x215 ∧ x7 = _x216 ∧ x8 = _x217 ∧ x9 = _x218 ∧ x10 = _x219 ∧ _x209 = _x219 ∧ _x207 = _x217 ∧ _x206 = _x216 ∧ _x205 = _x215 ∧ _x204 = _x214 ∧ _x203 = _x213 ∧ _x202 = _x212 ∧ _x201 = _x211 ∧ _x200 = _x210 ∧ _x218 = 1 l11 13 l7: x1 = _x220 ∧ x2 = _x221 ∧ x3 = _x222 ∧ x4 = _x223 ∧ x5 = _x224 ∧ x6 = _x225 ∧ x7 = _x226 ∧ x8 = _x227 ∧ x9 = _x228 ∧ x10 = _x229 ∧ x1 = _x230 ∧ x2 = _x231 ∧ x3 = _x232 ∧ x4 = _x233 ∧ x5 = _x234 ∧ x6 = _x235 ∧ x7 = _x236 ∧ x8 = _x237 ∧ x9 = _x238 ∧ x10 = _x239 ∧ _x229 = _x239 ∧ _x227 = _x237 ∧ _x226 = _x236 ∧ _x225 = _x235 ∧ _x224 = _x234 ∧ _x223 = _x233 ∧ _x222 = _x232 ∧ _x221 = _x231 ∧ _x220 = _x230 ∧ _x238 = 0 l11 14 l10: x1 = _x240 ∧ x2 = _x241 ∧ x3 = _x242 ∧ x4 = _x243 ∧ x5 = _x244 ∧ x6 = _x245 ∧ x7 = _x246 ∧ x8 = _x247 ∧ x9 = _x248 ∧ x10 = _x249 ∧ x1 = _x250 ∧ x2 = _x251 ∧ x3 = _x252 ∧ x4 = _x253 ∧ x5 = _x254 ∧ x6 = _x255 ∧ x7 = _x256 ∧ x8 = _x257 ∧ x9 = _x258 ∧ x10 = _x259 ∧ _x249 = _x259 ∧ _x248 = _x258 ∧ _x247 = _x257 ∧ _x246 = _x256 ∧ _x245 = _x255 ∧ _x244 = _x254 ∧ _x243 = _x253 ∧ _x242 = _x252 ∧ _x241 = _x251 ∧ _x240 = _x250 l12 15 l7: x1 = _x260 ∧ x2 = _x261 ∧ x3 = _x262 ∧ x4 = _x263 ∧ x5 = _x264 ∧ x6 = _x265 ∧ x7 = _x266 ∧ x8 = _x267 ∧ x9 = _x268 ∧ x10 = _x269 ∧ x1 = _x270 ∧ x2 = _x271 ∧ x3 = _x272 ∧ x4 = _x273 ∧ x5 = _x274 ∧ x6 = _x275 ∧ x7 = _x276 ∧ x8 = _x277 ∧ x9 = _x278 ∧ x10 = _x279 ∧ _x269 = _x279 ∧ _x267 = _x277 ∧ _x266 = _x276 ∧ _x265 = _x275 ∧ _x264 = _x274 ∧ _x263 = _x273 ∧ _x262 = _x272 ∧ _x261 = _x271 ∧ _x260 = _x270 ∧ _x278 = 0 l12 16 l11: x1 = _x280 ∧ x2 = _x281 ∧ x3 = _x282 ∧ x4 = _x283 ∧ x5 = _x284 ∧ x6 = _x285 ∧ x7 = _x286 ∧ x8 = _x287 ∧ x9 = _x288 ∧ x10 = _x289 ∧ x1 = _x290 ∧ x2 = _x291 ∧ x3 = _x292 ∧ x4 = _x293 ∧ x5 = _x294 ∧ x6 = _x295 ∧ x7 = _x296 ∧ x8 = _x297 ∧ x9 = _x298 ∧ x10 = _x299 ∧ _x289 = _x299 ∧ _x288 = _x298 ∧ _x287 = _x297 ∧ _x286 = _x296 ∧ _x285 = _x295 ∧ _x284 = _x294 ∧ _x283 = _x293 ∧ _x282 = _x292 ∧ _x281 = _x291 ∧ _x280 = _x290 l13 17 l7: x1 = _x300 ∧ x2 = _x301 ∧ x3 = _x302 ∧ x4 = _x303 ∧ x5 = _x304 ∧ x6 = _x305 ∧ x7 = _x306 ∧ x8 = _x307 ∧ x9 = _x308 ∧ x10 = _x309 ∧ x1 = _x310 ∧ x2 = _x311 ∧ x3 = _x312 ∧ x4 = _x313 ∧ x5 = _x314 ∧ x6 = _x315 ∧ x7 = _x316 ∧ x8 = _x317 ∧ x9 = _x318 ∧ x10 = _x319 ∧ _x309 = _x319 ∧ _x307 = _x317 ∧ _x306 = _x316 ∧ _x305 = _x315 ∧ _x304 = _x314 ∧ _x303 = _x313 ∧ _x302 = _x312 ∧ _x301 = _x311 ∧ _x300 = _x310 ∧ _x318 = 0 ∧ 0 ≤ _x301 ∧ _x301 ≤ 0 l13 18 l12: x1 = _x320 ∧ x2 = _x321 ∧ x3 = _x322 ∧ x4 = _x323 ∧ x5 = _x324 ∧ x6 = _x325 ∧ x7 = _x326 ∧ x8 = _x327 ∧ x9 = _x328 ∧ x10 = _x329 ∧ x1 = _x330 ∧ x2 = _x331 ∧ x3 = _x332 ∧ x4 = _x333 ∧ x5 = _x334 ∧ x6 = _x335 ∧ x7 = _x336 ∧ x8 = _x337 ∧ x9 = _x338 ∧ x10 = _x339 ∧ _x329 = _x339 ∧ _x328 = _x338 ∧ _x327 = _x337 ∧ _x326 = _x336 ∧ _x325 = _x335 ∧ _x324 = _x334 ∧ _x323 = _x333 ∧ _x322 = _x332 ∧ _x321 = _x331 ∧ _x320 = _x330 ∧ 1 ≤ _x321 l13 19 l12: x1 = _x340 ∧ x2 = _x341 ∧ x3 = _x342 ∧ x4 = _x343 ∧ x5 = _x344 ∧ x6 = _x345 ∧ x7 = _x346 ∧ x8 = _x347 ∧ x9 = _x348 ∧ x10 = _x349 ∧ x1 = _x350 ∧ x2 = _x351 ∧ x3 = _x352 ∧ x4 = _x353 ∧ x5 = _x354 ∧ x6 = _x355 ∧ x7 = _x356 ∧ x8 = _x357 ∧ x9 = _x358 ∧ x10 = _x359 ∧ _x349 = _x359 ∧ _x348 = _x358 ∧ _x347 = _x357 ∧ _x346 = _x356 ∧ _x345 = _x355 ∧ _x344 = _x354 ∧ _x343 = _x353 ∧ _x342 = _x352 ∧ _x341 = _x351 ∧ _x340 = _x350 ∧ 1 + _x341 ≤ 0 l14 20 l13: x1 = _x360 ∧ x2 = _x361 ∧ x3 = _x362 ∧ x4 = _x363 ∧ x5 = _x364 ∧ x6 = _x365 ∧ x7 = _x366 ∧ x8 = _x367 ∧ x9 = _x368 ∧ x10 = _x369 ∧ x1 = _x370 ∧ x2 = _x371 ∧ x3 = _x372 ∧ x4 = _x373 ∧ x5 = _x374 ∧ x6 = _x375 ∧ x7 = _x376 ∧ x8 = _x377 ∧ x9 = _x378 ∧ x10 = _x379 ∧ _x369 = _x379 ∧ _x368 = _x378 ∧ _x367 = _x377 ∧ _x366 = _x376 ∧ _x365 = _x375 ∧ _x364 = _x374 ∧ _x363 = _x373 ∧ _x362 = _x372 ∧ _x360 = _x370 ∧ _x371 = _x367 l15 21 l14: x1 = _x380 ∧ x2 = _x381 ∧ x3 = _x382 ∧ x4 = _x383 ∧ x5 = _x384 ∧ x6 = _x385 ∧ x7 = _x386 ∧ x8 = _x387 ∧ x9 = _x388 ∧ x10 = _x389 ∧ x1 = _x390 ∧ x2 = _x391 ∧ x3 = _x392 ∧ x4 = _x393 ∧ x5 = _x394 ∧ x6 = _x395 ∧ x7 = _x396 ∧ x8 = _x397 ∧ x9 = _x398 ∧ x10 = _x399 ∧ _x389 = _x399 ∧ _x388 = _x398 ∧ _x386 = _x396 ∧ _x385 = _x395 ∧ _x384 = _x394 ∧ _x383 = _x393 ∧ _x382 = _x392 ∧ _x381 = _x391 ∧ _x380 = _x390 ∧ _x397 = 1 l16 22 l15: x1 = _x400 ∧ x2 = _x401 ∧ x3 = _x402 ∧ x4 = _x403 ∧ x5 = _x404 ∧ x6 = _x405 ∧ x7 = _x406 ∧ x8 = _x407 ∧ x9 = _x408 ∧ x10 = _x409 ∧ x1 = _x410 ∧ x2 = _x411 ∧ x3 = _x412 ∧ x4 = _x413 ∧ x5 = _x414 ∧ x6 = _x415 ∧ x7 = _x416 ∧ x8 = _x417 ∧ x9 = _x418 ∧ x10 = _x419 ∧ _x409 = _x419 ∧ _x408 = _x418 ∧ _x407 = _x417 ∧ _x406 = _x416 ∧ _x405 = _x415 ∧ _x404 = _x414 ∧ _x403 = _x413 ∧ _x402 = _x412 ∧ _x401 = _x411 ∧ _x400 = _x410 l16 23 l14: x1 = _x420 ∧ x2 = _x421 ∧ x3 = _x422 ∧ x4 = _x423 ∧ x5 = _x424 ∧ x6 = _x425 ∧ x7 = _x426 ∧ x8 = _x427 ∧ x9 = _x428 ∧ x10 = _x429 ∧ x1 = _x430 ∧ x2 = _x431 ∧ x3 = _x432 ∧ x4 = _x433 ∧ x5 = _x434 ∧ x6 = _x435 ∧ x7 = _x436 ∧ x8 = _x437 ∧ x9 = _x438 ∧ x10 = _x439 ∧ _x429 = _x439 ∧ _x428 = _x438 ∧ _x426 = _x436 ∧ _x425 = _x435 ∧ _x424 = _x434 ∧ _x423 = _x433 ∧ _x422 = _x432 ∧ _x421 = _x431 ∧ _x420 = _x430 ∧ _x437 = 0 l17 24 l14: x1 = _x440 ∧ x2 = _x441 ∧ x3 = _x442 ∧ x4 = _x443 ∧ x5 = _x444 ∧ x6 = _x445 ∧ x7 = _x446 ∧ x8 = _x447 ∧ x9 = _x448 ∧ x10 = _x449 ∧ x1 = _x450 ∧ x2 = _x451 ∧ x3 = _x452 ∧ x4 = _x453 ∧ x5 = _x454 ∧ x6 = _x455 ∧ x7 = _x456 ∧ x8 = _x457 ∧ x9 = _x458 ∧ x10 = _x459 ∧ _x449 = _x459 ∧ _x448 = _x458 ∧ _x446 = _x456 ∧ _x445 = _x455 ∧ _x444 = _x454 ∧ _x443 = _x453 ∧ _x442 = _x452 ∧ _x441 = _x451 ∧ _x440 = _x450 ∧ _x457 = 0 ∧ 0 ≤ _x441 ∧ _x441 ≤ 0 l17 25 l16: x1 = _x460 ∧ x2 = _x461 ∧ x3 = _x462 ∧ x4 = _x463 ∧ x5 = _x464 ∧ x6 = _x465 ∧ x7 = _x466 ∧ x8 = _x467 ∧ x9 = _x468 ∧ x10 = _x469 ∧ x1 = _x470 ∧ x2 = _x471 ∧ x3 = _x472 ∧ x4 = _x473 ∧ x5 = _x474 ∧ x6 = _x475 ∧ x7 = _x476 ∧ x8 = _x477 ∧ x9 = _x478 ∧ x10 = _x479 ∧ _x469 = _x479 ∧ _x468 = _x478 ∧ _x467 = _x477 ∧ _x466 = _x476 ∧ _x465 = _x475 ∧ _x464 = _x474 ∧ _x463 = _x473 ∧ _x462 = _x472 ∧ _x461 = _x471 ∧ _x460 = _x470 ∧ 1 ≤ _x461 l17 26 l16: x1 = _x480 ∧ x2 = _x481 ∧ x3 = _x482 ∧ x4 = _x483 ∧ x5 = _x484 ∧ x6 = _x485 ∧ x7 = _x486 ∧ x8 = _x487 ∧ x9 = _x488 ∧ x10 = _x489 ∧ x1 = _x490 ∧ x2 = _x491 ∧ x3 = _x492 ∧ x4 = _x493 ∧ x5 = _x494 ∧ x6 = _x495 ∧ x7 = _x496 ∧ x8 = _x497 ∧ x9 = _x498 ∧ x10 = _x499 ∧ _x489 = _x499 ∧ _x488 = _x498 ∧ _x487 = _x497 ∧ _x486 = _x496 ∧ _x485 = _x495 ∧ _x484 = _x494 ∧ _x483 = _x493 ∧ _x482 = _x492 ∧ _x481 = _x491 ∧ _x480 = _x490 ∧ 1 + _x481 ≤ 0 l18 27 l19: x1 = _x500 ∧ x2 = _x501 ∧ x3 = _x502 ∧ x4 = _x503 ∧ x5 = _x504 ∧ x6 = _x505 ∧ x7 = _x506 ∧ x8 = _x507 ∧ x9 = _x508 ∧ x10 = _x509 ∧ x1 = _x510 ∧ x2 = _x511 ∧ x3 = _x512 ∧ x4 = _x513 ∧ x5 = _x514 ∧ x6 = _x515 ∧ x7 = _x516 ∧ x8 = _x517 ∧ x9 = _x518 ∧ x10 = _x519 ∧ _x509 = _x519 ∧ _x508 = _x518 ∧ _x507 = _x517 ∧ _x506 = _x516 ∧ _x505 = _x515 ∧ _x504 = _x514 ∧ _x503 = _x513 ∧ _x502 = _x512 ∧ _x501 = _x511 ∧ _x500 = _x510 l20 28 l5: x1 = _x520 ∧ x2 = _x521 ∧ x3 = _x522 ∧ x4 = _x523 ∧ x5 = _x524 ∧ x6 = _x525 ∧ x7 = _x526 ∧ x8 = _x527 ∧ x9 = _x528 ∧ x10 = _x529 ∧ x1 = _x530 ∧ x2 = _x531 ∧ x3 = _x532 ∧ x4 = _x533 ∧ x5 = _x534 ∧ x6 = _x535 ∧ x7 = _x536 ∧ x8 = _x537 ∧ x9 = _x538 ∧ x10 = _x539 ∧ _x529 = _x539 ∧ _x528 = _x538 ∧ _x527 = _x537 ∧ _x526 = _x536 ∧ _x525 = _x535 ∧ _x524 = _x534 ∧ _x523 = _x533 ∧ _x522 = _x532 ∧ _x521 = _x531 ∧ _x520 = _x530 ∧ _x524 ≤ _x523 ∧ _x523 ≤ _x524 l20 29 l17: x1 = _x540 ∧ x2 = _x541 ∧ x3 = _x542 ∧ x4 = _x543 ∧ x5 = _x544 ∧ x6 = _x545 ∧ x7 = _x546 ∧ x8 = _x547 ∧ x9 = _x548 ∧ x10 = _x549 ∧ x1 = _x550 ∧ x2 = _x551 ∧ x3 = _x552 ∧ x4 = _x553 ∧ x5 = _x554 ∧ x6 = _x555 ∧ x7 = _x556 ∧ x8 = _x557 ∧ x9 = _x558 ∧ x10 = _x559 ∧ _x549 = _x559 ∧ _x548 = _x558 ∧ _x547 = _x557 ∧ _x546 = _x556 ∧ _x545 = _x555 ∧ _x544 = _x554 ∧ _x543 = _x553 ∧ _x542 = _x552 ∧ _x541 = _x551 ∧ _x540 = _x550 ∧ 1 + _x544 ≤ _x543 l20 30 l17: x1 = _x560 ∧ x2 = _x561 ∧ x3 = _x562 ∧ x4 = _x563 ∧ x5 = _x564 ∧ x6 = _x565 ∧ x7 = _x566 ∧ x8 = _x567 ∧ x9 = _x568 ∧ x10 = _x569 ∧ x1 = _x570 ∧ x2 = _x571 ∧ x3 = _x572 ∧ x4 = _x573 ∧ x5 = _x574 ∧ x6 = _x575 ∧ x7 = _x576 ∧ x8 = _x577 ∧ x9 = _x578 ∧ x10 = _x579 ∧ _x569 = _x579 ∧ _x568 = _x578 ∧ _x567 = _x577 ∧ _x566 = _x576 ∧ _x565 = _x575 ∧ _x564 = _x574 ∧ _x563 = _x573 ∧ _x562 = _x572 ∧ _x561 = _x571 ∧ _x560 = _x570 ∧ 1 + _x563 ≤ _x564 l21 31 l18: x1 = _x580 ∧ x2 = _x581 ∧ x3 = _x582 ∧ x4 = _x583 ∧ x5 = _x584 ∧ x6 = _x585 ∧ x7 = _x586 ∧ x8 = _x587 ∧ x9 = _x588 ∧ x10 = _x589 ∧ x1 = _x590 ∧ x2 = _x591 ∧ x3 = _x592 ∧ x4 = _x593 ∧ x5 = _x594 ∧ x6 = _x595 ∧ x7 = _x596 ∧ x8 = _x597 ∧ x9 = _x598 ∧ x10 = _x599 ∧ _x589 = _x599 ∧ _x588 = _x598 ∧ _x587 = _x597 ∧ _x586 = _x596 ∧ _x585 = _x595 ∧ _x584 = _x594 ∧ _x582 = _x592 ∧ _x581 = _x591 ∧ _x580 = _x590 ∧ _x593 = 1 + _x583 ∧ _x582 ≤ _x584 l21 32 l20: x1 = _x600 ∧ x2 = _x601 ∧ x3 = _x602 ∧ x4 = _x603 ∧ x5 = _x604 ∧ x6 = _x605 ∧ x7 = _x606 ∧ x8 = _x607 ∧ x9 = _x608 ∧ x10 = _x609 ∧ x1 = _x610 ∧ x2 = _x611 ∧ x3 = _x612 ∧ x4 = _x613 ∧ x5 = _x614 ∧ x6 = _x615 ∧ x7 = _x616 ∧ x8 = _x617 ∧ x9 = _x618 ∧ x10 = _x619 ∧ _x609 = _x619 ∧ _x608 = _x618 ∧ _x607 = _x617 ∧ _x606 = _x616 ∧ _x605 = _x615 ∧ _x604 = _x614 ∧ _x603 = _x613 ∧ _x602 = _x612 ∧ _x601 = _x611 ∧ _x600 = _x610 ∧ 1 + _x604 ≤ _x602 l22 33 l6: x1 = _x620 ∧ x2 = _x621 ∧ x3 = _x622 ∧ x4 = _x623 ∧ x5 = _x624 ∧ x6 = _x625 ∧ x7 = _x626 ∧ x8 = _x627 ∧ x9 = _x628 ∧ x10 = _x629 ∧ x1 = _x630 ∧ x2 = _x631 ∧ x3 = _x632 ∧ x4 = _x633 ∧ x5 = _x634 ∧ x6 = _x635 ∧ x7 = _x636 ∧ x8 = _x637 ∧ x9 = _x638 ∧ x10 = _x639 ∧ _x629 = _x639 ∧ _x628 = _x638 ∧ _x627 = _x637 ∧ _x626 = _x636 ∧ _x625 = _x635 ∧ _x623 = _x633 ∧ _x622 = _x632 ∧ _x621 = _x631 ∧ _x634 = 0 ∧ _x630 = _x626 l23 34 l22: x1 = _x640 ∧ x2 = _x641 ∧ x3 = _x642 ∧ x4 = _x643 ∧ x5 = _x644 ∧ x6 = _x645 ∧ x7 = _x646 ∧ x8 = _x647 ∧ x9 = _x648 ∧ x10 = _x649 ∧ x1 = _x650 ∧ x2 = _x651 ∧ x3 = _x652 ∧ x4 = _x653 ∧ x5 = _x654 ∧ x6 = _x655 ∧ x7 = _x656 ∧ x8 = _x657 ∧ x9 = _x658 ∧ x10 = _x659 ∧ _x649 = _x659 ∧ _x648 = _x658 ∧ _x647 = _x657 ∧ _x645 = _x655 ∧ _x644 = _x654 ∧ _x643 = _x653 ∧ _x642 = _x652 ∧ _x641 = _x651 ∧ _x640 = _x650 ∧ _x656 = 1 l23 35 l22: x1 = _x660 ∧ x2 = _x661 ∧ x3 = _x662 ∧ x4 = _x663 ∧ x5 = _x664 ∧ x6 = _x665 ∧ x7 = _x666 ∧ x8 = _x667 ∧ x9 = _x668 ∧ x10 = _x669 ∧ x1 = _x670 ∧ x2 = _x671 ∧ x3 = _x672 ∧ x4 = _x673 ∧ x5 = _x674 ∧ x6 = _x675 ∧ x7 = _x676 ∧ x8 = _x677 ∧ x9 = _x678 ∧ x10 = _x679 ∧ _x669 = _x679 ∧ _x668 = _x678 ∧ _x667 = _x677 ∧ _x665 = _x675 ∧ _x664 = _x674 ∧ _x663 = _x673 ∧ _x662 = _x672 ∧ _x661 = _x671 ∧ _x660 = _x670 ∧ _x676 = 0 l6 36 l21: x1 = _x680 ∧ x2 = _x681 ∧ x3 = _x682 ∧ x4 = _x683 ∧ x5 = _x684 ∧ x6 = _x685 ∧ x7 = _x686 ∧ x8 = _x687 ∧ x9 = _x688 ∧ x10 = _x689 ∧ x1 = _x690 ∧ x2 = _x691 ∧ x3 = _x692 ∧ x4 = _x693 ∧ x5 = _x694 ∧ x6 = _x695 ∧ x7 = _x696 ∧ x8 = _x697 ∧ x9 = _x698 ∧ x10 = _x699 ∧ _x689 = _x699 ∧ _x688 = _x698 ∧ _x687 = _x697 ∧ _x686 = _x696 ∧ _x685 = _x695 ∧ _x684 = _x694 ∧ _x683 = _x693 ∧ _x682 = _x692 ∧ _x681 = _x691 ∧ _x680 = _x690 l24 37 l22: x1 = _x700 ∧ x2 = _x701 ∧ x3 = _x702 ∧ x4 = _x703 ∧ x5 = _x704 ∧ x6 = _x705 ∧ x7 = _x706 ∧ x8 = _x707 ∧ x9 = _x708 ∧ x10 = _x709 ∧ x1 = _x710 ∧ x2 = _x711 ∧ x3 = _x712 ∧ x4 = _x713 ∧ x5 = _x714 ∧ x6 = _x715 ∧ x7 = _x716 ∧ x8 = _x717 ∧ x9 = _x718 ∧ x10 = _x719 ∧ _x709 = _x719 ∧ _x708 = _x718 ∧ _x707 = _x717 ∧ _x705 = _x715 ∧ _x704 = _x714 ∧ _x703 = _x713 ∧ _x702 = _x712 ∧ _x701 = _x711 ∧ _x700 = _x710 ∧ _x716 = 0 l24 38 l23: x1 = _x720 ∧ x2 = _x721 ∧ x3 = _x722 ∧ x4 = _x723 ∧ x5 = _x724 ∧ x6 = _x725 ∧ x7 = _x726 ∧ x8 = _x727 ∧ x9 = _x728 ∧ x10 = _x729 ∧ x1 = _x730 ∧ x2 = _x731 ∧ x3 = _x732 ∧ x4 = _x733 ∧ x5 = _x734 ∧ x6 = _x735 ∧ x7 = _x736 ∧ x8 = _x737 ∧ x9 = _x738 ∧ x10 = _x739 ∧ _x729 = _x739 ∧ _x728 = _x738 ∧ _x727 = _x737 ∧ _x726 = _x736 ∧ _x725 = _x735 ∧ _x724 = _x734 ∧ _x723 = _x733 ∧ _x722 = _x732 ∧ _x721 = _x731 ∧ _x720 = _x730 l25 39 l22: x1 = _x740 ∧ x2 = _x741 ∧ x3 = _x742 ∧ x4 = _x743 ∧ x5 = _x744 ∧ x6 = _x745 ∧ x7 = _x746 ∧ x8 = _x747 ∧ x9 = _x748 ∧ x10 = _x749 ∧ x1 = _x750 ∧ x2 = _x751 ∧ x3 = _x752 ∧ x4 = _x753 ∧ x5 = _x754 ∧ x6 = _x755 ∧ x7 = _x756 ∧ x8 = _x757 ∧ x9 = _x758 ∧ x10 = _x759 ∧ _x749 = _x759 ∧ _x748 = _x758 ∧ _x747 = _x757 ∧ _x745 = _x755 ∧ _x744 = _x754 ∧ _x743 = _x753 ∧ _x742 = _x752 ∧ _x741 = _x751 ∧ _x740 = _x750 ∧ _x756 = 0 ∧ 0 ≤ _x740 ∧ _x740 ≤ 0 l25 40 l24: x1 = _x760 ∧ x2 = _x761 ∧ x3 = _x762 ∧ x4 = _x763 ∧ x5 = _x764 ∧ x6 = _x765 ∧ x7 = _x766 ∧ x8 = _x767 ∧ x9 = _x768 ∧ x10 = _x769 ∧ x1 = _x770 ∧ x2 = _x771 ∧ x3 = _x772 ∧ x4 = _x773 ∧ x5 = _x774 ∧ x6 = _x775 ∧ x7 = _x776 ∧ x8 = _x777 ∧ x9 = _x778 ∧ x10 = _x779 ∧ _x769 = _x779 ∧ _x768 = _x778 ∧ _x767 = _x777 ∧ _x766 = _x776 ∧ _x765 = _x775 ∧ _x764 = _x774 ∧ _x763 = _x773 ∧ _x762 = _x772 ∧ _x761 = _x771 ∧ _x760 = _x770 ∧ 1 ≤ _x760 l25 41 l24: x1 = _x780 ∧ x2 = _x781 ∧ x3 = _x782 ∧ x4 = _x783 ∧ x5 = _x784 ∧ x6 = _x785 ∧ x7 = _x786 ∧ x8 = _x787 ∧ x9 = _x788 ∧ x10 = _x789 ∧ x1 = _x790 ∧ x2 = _x791 ∧ x3 = _x792 ∧ x4 = _x793 ∧ x5 = _x794 ∧ x6 = _x795 ∧ x7 = _x796 ∧ x8 = _x797 ∧ x9 = _x798 ∧ x10 = _x799 ∧ _x789 = _x799 ∧ _x788 = _x798 ∧ _x787 = _x797 ∧ _x786 = _x796 ∧ _x785 = _x795 ∧ _x784 = _x794 ∧ _x783 = _x793 ∧ _x782 = _x792 ∧ _x781 = _x791 ∧ _x780 = _x790 ∧ 1 + _x780 ≤ 0 l19 42 l4: x1 = _x800 ∧ x2 = _x801 ∧ x3 = _x802 ∧ x4 = _x803 ∧ x5 = _x804 ∧ x6 = _x805 ∧ x7 = _x806 ∧ x8 = _x807 ∧ x9 = _x808 ∧ x10 = _x809 ∧ x1 = _x810 ∧ x2 = _x811 ∧ x3 = _x812 ∧ x4 = _x813 ∧ x5 = _x814 ∧ x6 = _x815 ∧ x7 = _x816 ∧ x8 = _x817 ∧ x9 = _x818 ∧ x10 = _x819 ∧ _x809 = _x819 ∧ _x808 = _x818 ∧ _x807 = _x817 ∧ _x806 = _x816 ∧ _x805 = _x815 ∧ _x804 = _x814 ∧ _x803 = _x813 ∧ _x802 = _x812 ∧ _x801 = _x811 ∧ _x800 = _x810 ∧ _x802 ≤ _x803 l19 43 l25: x1 = _x820 ∧ x2 = _x821 ∧ x3 = _x822 ∧ x4 = _x823 ∧ x5 = _x824 ∧ x6 = _x825 ∧ x7 = _x826 ∧ x8 = _x827 ∧ x9 = _x828 ∧ x10 = _x829 ∧ x1 = _x830 ∧ x2 = _x831 ∧ x3 = _x832 ∧ x4 = _x833 ∧ x5 = _x834 ∧ x6 = _x835 ∧ x7 = _x836 ∧ x8 = _x837 ∧ x9 = _x838 ∧ x10 = _x839 ∧ _x829 = _x839 ∧ _x828 = _x838 ∧ _x827 = _x837 ∧ _x826 = _x836 ∧ _x825 = _x835 ∧ _x824 = _x834 ∧ _x823 = _x833 ∧ _x822 = _x832 ∧ _x821 = _x831 ∧ _x820 = _x830 ∧ 1 + _x823 ≤ _x822 l9 44 l18: x1 = _x840 ∧ x2 = _x841 ∧ x3 = _x842 ∧ x4 = _x843 ∧ x5 = _x844 ∧ x6 = _x845 ∧ x7 = _x846 ∧ x8 = _x847 ∧ x9 = _x848 ∧ x10 = _x849 ∧ x1 = _x850 ∧ x2 = _x851 ∧ x3 = _x852 ∧ x4 = _x853 ∧ x5 = _x854 ∧ x6 = _x855 ∧ x7 = _x856 ∧ x8 = _x857 ∧ x9 = _x858 ∧ x10 = _x859 ∧ _x849 = _x859 ∧ _x848 = _x858 ∧ _x847 = _x857 ∧ _x846 = _x856 ∧ _x845 = _x855 ∧ _x844 = _x854 ∧ _x842 = _x852 ∧ _x841 = _x851 ∧ _x840 = _x850 ∧ _x853 = 0 ∧ _x842 ≤ _x843 l9 45 l8: x1 = _x860 ∧ x2 = _x861 ∧ x3 = _x862 ∧ x4 = _x863 ∧ x5 = _x864 ∧ x6 = _x865 ∧ x7 = _x866 ∧ x8 = _x867 ∧ x9 = _x868 ∧ x10 = _x869 ∧ x1 = _x870 ∧ x2 = _x871 ∧ x3 = _x872 ∧ x4 = _x873 ∧ x5 = _x874 ∧ x6 = _x875 ∧ x7 = _x876 ∧ x8 = _x877 ∧ x9 = _x878 ∧ x10 = _x879 ∧ _x869 = _x879 ∧ _x868 = _x878 ∧ _x867 = _x877 ∧ _x866 = _x876 ∧ _x865 = _x875 ∧ _x864 = _x874 ∧ _x862 = _x872 ∧ _x861 = _x871 ∧ _x860 = _x870 ∧ _x873 = 1 + _x863 ∧ 1 + _x863 ≤ _x862 l26 46 l8: x1 = _x880 ∧ x2 = _x881 ∧ x3 = _x882 ∧ x4 = _x883 ∧ x5 = _x884 ∧ x6 = _x885 ∧ x7 = _x886 ∧ x8 = _x887 ∧ x9 = _x888 ∧ x10 = _x889 ∧ x1 = _x890 ∧ x2 = _x891 ∧ x3 = _x892 ∧ x4 = _x893 ∧ x5 = _x894 ∧ x6 = _x895 ∧ x7 = _x896 ∧ x8 = _x897 ∧ x9 = _x898 ∧ x10 = _x899 ∧ _x889 = _x899 ∧ _x888 = _x898 ∧ _x887 = _x897 ∧ _x886 = _x896 ∧ _x884 = _x894 ∧ _x893 = 0 ∧ _x895 = _x895 ∧ _x891 = 1 ∧ _x890 = 1 ∧ _x892 = 9 l27 47 l26: x1 = _x900 ∧ x2 = _x901 ∧ x3 = _x902 ∧ x4 = _x903 ∧ x5 = _x904 ∧ x6 = _x905 ∧ x7 = _x906 ∧ x8 = _x907 ∧ x9 = _x908 ∧ x10 = _x909 ∧ x1 = _x910 ∧ x2 = _x911 ∧ x3 = _x912 ∧ x4 = _x913 ∧ x5 = _x914 ∧ x6 = _x915 ∧ x7 = _x916 ∧ x8 = _x917 ∧ x9 = _x918 ∧ x10 = _x919 ∧ _x909 = _x919 ∧ _x908 = _x918 ∧ _x907 = _x917 ∧ _x906 = _x916 ∧ _x905 = _x915 ∧ _x904 = _x914 ∧ _x903 = _x913 ∧ _x902 = _x912 ∧ _x901 = _x911 ∧ _x900 = _x910

## 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 ∧ x9 = x9 ∧ x10 = x10 l22 l22 l22: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l13 l13 l13: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l18 l18 l18: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l17 l17 l17: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l21 l21 l21: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l14 l14 l14: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l9 l9 l9: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l25 l25 l25: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l6 l6 l6: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l8 l8 l8: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l27 l27 l27: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l0 l0 l0: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l12 l12 l12: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l19 l19 l19: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l26 l26 l26: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l7 l7 l7: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l24 l24 l24: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l11 l11 l11: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l3 l3 l3: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l20 l20 l20: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l2 l2 l2: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l23 l23 l23: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l4 l4 l4: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l10 l10 l10: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l15 l15 l15: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 l16 l16 l16: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/2

Here we consider the SCC { l8, l9 }.

### 2.1.1 Transition Removal

We remove transition 45 using the following ranking functions, which are bounded by 0.

 l8: −1 + x3 − x4 l9: −1 + x3 − x4

### 2.1.2 Transition Removal

We remove transition 11 using the following ranking functions, which are bounded by 0.

 l8: 0 l9: −1

### 2.1.3 Trivial Cooperation Program

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

### 2.2 SCC Subproblem 2/2

Here we consider the SCC { l5, l22, l7, l24, l11, l13, l20, l18, l17, l21, l14, l23, l25, l10, l6, l16, l15, l12, l19 }.

### 2.2.1 Transition Removal

We remove transition 43 using the following ranking functions, which are bounded by 0.

 l5: −2 + x3 − x4 l6: −2 + x3 − x4 l20: −2 + x3 − x4 l7: −2 + x3 − x4 l13: −2 + x3 − x4 l12: −2 + x3 − x4 l11: −2 + x3 − x4 l10: −2 + x3 − x4 l14: −2 + x3 − x4 l17: −2 + x3 − x4 l16: −2 + x3 − x4 l15: −2 + x3 − x4 l21: −2 + x3 − x4 l22: −2 + x3 − x4 l25: −2 + x3 − x4 l24: −2 + x3 − x4 l23: −2 + x3 − x4 l19: −1 + x3 − x4 l18: −1 + x3 − x4

### 2.2.2 Transition Removal

We remove transitions 33, 39, 37, 35, 34, 38, 41, 40 using the following ranking functions, which are bounded by 0.

 l5: −3 − x1 − x5 + x7 l6: −2 − x1 − x5 + x7 l20: −3 − x1 − x5 + x7 l7: −3 − x1 − x5 + x7 l13: −3 − x1 − x5 + x7 l12: −3 − x1 − x5 + x7 l11: −3 − x1 − x5 + x7 l10: −3 − x1 − x5 + x7 l14: −3 − x1 − x5 + x7 l17: −3 − x1 − x5 + x7 l16: −3 − x1 − x5 + x7 l15: −3 − x1 − x5 + x7 l21: −2 − x1 − x5 + x7 l22: 0 l25: 3 l24: 2 l23: 1 l18: −2 − x1 + x3 − 2⋅x5 + x7 l19: −2 − x1 + x3 − 2⋅x5 + x7

### 2.2.3 Transition Removal

We remove transitions 27, 31 using the following ranking functions, which are bounded by 0.

 l5: 1 l6: 1 l20: 1 l7: 1 l13: 1 l12: 1 l11: 1 l10: 1 l14: 1 l17: 1 l16: 1 l15: 1 l21: 1 l18: 0 l19: −1

### 2.2.4 Transition Removal

We remove transition 32 using the following ranking functions, which are bounded by 0.

 l5: −2 + x3 − x5 l6: −1 + x3 − x5 l20: −2 + x3 − x5 l7: −2 + x3 − x5 l13: −2 + x3 − x5 l12: −2 + x3 − x5 l11: −2 + x3 − x5 l10: −2 + x3 − x5 l14: −2 + x3 − x5 l17: −2 + x3 − x5 l16: −2 + x3 − x5 l15: −2 + x3 − x5 l21: −1 + x3 − x5

### 2.2.5 Transition Removal

We remove transitions 9, 28, 10, 17, 15, 13, 12, 14, 16, 19, 18, 20, 24, 23, 21, 22, 26, 25, 30, 29, 36 using the following ranking functions, which are bounded by 0.

 l5: 1 l6: 0 l20: 11 l7: 2 l13: 6 l12: 5 l11: 4 l10: 3 l14: 7 l17: 10 l16: 9 l15: 8 l21: −1

### 2.2.6 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 % (12 real / 0 unknown / 0 assumptions / 12 total proof steps)