# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l22, l1, l13, l31, l18, l17, l21, l9, l14, l25, l6, l8, l27, l0, l12, l19, l26, l7, l24, l11, l3, l20, l32, l2, l23, l4, l10, l29, l15, l16, l30
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _bigHAT0 ∧ x2 = _dumHAT0 ∧ x3 = _iHAT0 ∧ x4 = _imaxHAT0 ∧ x5 = _jHAT0 ∧ x6 = _kHAT0 ∧ x7 = _nHAT0 ∧ x8 = _sumHAT0 ∧ x9 = _tempHAT0 ∧ x10 = _tmpHAT0 ∧ x11 = _tmp___0HAT0 ∧ x1 = _bigHATpost ∧ x2 = _dumHATpost ∧ x3 = _iHATpost ∧ x4 = _imaxHATpost ∧ x5 = _jHATpost ∧ x6 = _kHATpost ∧ x7 = _nHATpost ∧ x8 = _sumHATpost ∧ x9 = _tempHATpost ∧ x10 = _tmpHATpost ∧ x11 = _tmp___0HATpost ∧ _tmp___0HAT0 = _tmp___0HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _tempHAT0 = _tempHATpost ∧ _sumHAT0 = _sumHATpost ∧ _nHAT0 = _nHATpost ∧ _kHAT0 = _kHATpost ∧ _jHAT0 = _jHATpost ∧ _imaxHAT0 = _imaxHATpost ∧ _iHAT0 = _iHATpost ∧ _dumHAT0 = _dumHATpost ∧ _bigHAT0 = _bigHATpost ∧ 1 + _nHAT0 ≤ _jHAT0 l0 2 l2: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x10 = _x9 ∧ x11 = _x10 ∧ x1 = _x11 ∧ x2 = _x12 ∧ x3 = _x13 ∧ x4 = _x14 ∧ x5 = _x15 ∧ x6 = _x16 ∧ x7 = _x17 ∧ x8 = _x18 ∧ x9 = _x19 ∧ x10 = _x20 ∧ x11 = _x21 ∧ _x10 = _x21 ∧ _x7 = _x18 ∧ _x6 = _x17 ∧ _x5 = _x16 ∧ _x4 = _x15 ∧ _x3 = _x14 ∧ _x2 = _x13 ∧ _x1 = _x12 ∧ _x = _x11 ∧ _x19 = _x20 ∧ _x20 = _x20 ∧ _x4 ≤ _x6 l3 3 l0: x1 = _x22 ∧ x2 = _x23 ∧ x3 = _x24 ∧ x4 = _x25 ∧ x5 = _x26 ∧ x6 = _x27 ∧ x7 = _x28 ∧ x8 = _x29 ∧ x9 = _x30 ∧ x10 = _x31 ∧ x11 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ x4 = _x36 ∧ x5 = _x37 ∧ x6 = _x38 ∧ x7 = _x39 ∧ x8 = _x40 ∧ x9 = _x41 ∧ x10 = _x42 ∧ x11 = _x43 ∧ _x32 = _x43 ∧ _x31 = _x42 ∧ _x30 = _x41 ∧ _x29 = _x40 ∧ _x28 = _x39 ∧ _x27 = _x38 ∧ _x26 = _x37 ∧ _x25 = _x36 ∧ _x24 = _x35 ∧ _x23 = _x34 ∧ _x22 = _x33 l4 4 l5: x1 = _x44 ∧ x2 = _x45 ∧ x3 = _x46 ∧ x4 = _x47 ∧ x5 = _x48 ∧ x6 = _x49 ∧ x7 = _x50 ∧ x8 = _x51 ∧ x9 = _x52 ∧ x10 = _x53 ∧ x11 = _x54 ∧ x1 = _x55 ∧ x2 = _x56 ∧ x3 = _x57 ∧ x4 = _x58 ∧ x5 = _x59 ∧ x6 = _x60 ∧ x7 = _x61 ∧ x8 = _x62 ∧ x9 = _x63 ∧ x10 = _x64 ∧ x11 = _x65 ∧ _x54 = _x65 ∧ _x53 = _x64 ∧ _x52 = _x63 ∧ _x51 = _x62 ∧ _x50 = _x61 ∧ _x49 = _x60 ∧ _x47 = _x58 ∧ _x46 = _x57 ∧ _x45 = _x56 ∧ _x44 = _x55 ∧ _x59 = 1 + _x48 l6 5 l4: x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x4 = _x69 ∧ x5 = _x70 ∧ x6 = _x71 ∧ x7 = _x72 ∧ x8 = _x73 ∧ x9 = _x74 ∧ x10 = _x75 ∧ x11 = _x76 ∧ x1 = _x77 ∧ x2 = _x78 ∧ x3 = _x79 ∧ x4 = _x80 ∧ x5 = _x81 ∧ x6 = _x82 ∧ x7 = _x83 ∧ x8 = _x84 ∧ x9 = _x85 ∧ x10 = _x86 ∧ x11 = _x87 ∧ _x76 = _x87 ∧ _x75 = _x86 ∧ _x74 = _x85 ∧ _x73 = _x84 ∧ _x72 = _x83 ∧ _x71 = _x82 ∧ _x70 = _x81 ∧ _x69 = _x80 ∧ _x68 = _x79 ∧ _x67 = _x78 ∧ _x66 = _x77 ∧ 1 + _x72 ≤ _x68 l6 6 l7: x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x90 ∧ x4 = _x91 ∧ x5 = _x92 ∧ x6 = _x93 ∧ x7 = _x94 ∧ x8 = _x95 ∧ x9 = _x96 ∧ x10 = _x97 ∧ x11 = _x98 ∧ x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x101 ∧ x4 = _x102 ∧ x5 = _x103 ∧ x6 = _x104 ∧ x7 = _x105 ∧ x8 = _x106 ∧ x9 = _x107 ∧ x10 = _x108 ∧ x11 = _x109 ∧ _x98 = _x109 ∧ _x97 = _x108 ∧ _x96 = _x107 ∧ _x95 = _x106 ∧ _x94 = _x105 ∧ _x93 = _x104 ∧ _x92 = _x103 ∧ _x91 = _x102 ∧ _x89 = _x100 ∧ _x88 = _x99 ∧ _x101 = 1 + _x90 ∧ _x90 ≤ _x94 l7 7 l6: x1 = _x110 ∧ x2 = _x111 ∧ x3 = _x112 ∧ x4 = _x113 ∧ x5 = _x114 ∧ x6 = _x115 ∧ x7 = _x116 ∧ x8 = _x117 ∧ x9 = _x118 ∧ x10 = _x119 ∧ x11 = _x120 ∧ x1 = _x121 ∧ x2 = _x122 ∧ x3 = _x123 ∧ x4 = _x124 ∧ x5 = _x125 ∧ x6 = _x126 ∧ x7 = _x127 ∧ x8 = _x128 ∧ x9 = _x129 ∧ x10 = _x130 ∧ x11 = _x131 ∧ _x120 = _x131 ∧ _x119 = _x130 ∧ _x118 = _x129 ∧ _x117 = _x128 ∧ _x116 = _x127 ∧ _x115 = _x126 ∧ _x114 = _x125 ∧ _x113 = _x124 ∧ _x112 = _x123 ∧ _x111 = _x122 ∧ _x110 = _x121 l8 8 l7: x1 = _x132 ∧ x2 = _x133 ∧ x3 = _x134 ∧ x4 = _x135 ∧ x5 = _x136 ∧ x6 = _x137 ∧ x7 = _x138 ∧ x8 = _x139 ∧ x9 = _x140 ∧ x10 = _x141 ∧ x11 = _x142 ∧ x1 = _x143 ∧ x2 = _x144 ∧ x3 = _x145 ∧ x4 = _x146 ∧ x5 = _x147 ∧ x6 = _x148 ∧ x7 = _x149 ∧ x8 = _x150 ∧ x9 = _x151 ∧ x10 = _x152 ∧ x11 = _x153 ∧ _x142 = _x153 ∧ _x141 = _x152 ∧ _x140 = _x151 ∧ _x139 = _x150 ∧ _x138 = _x149 ∧ _x137 = _x148 ∧ _x136 = _x147 ∧ _x135 = _x146 ∧ _x134 = _x145 ∧ _x132 = _x143 ∧ _x144 = _x144 l9 9 l4: x1 = _x154 ∧ x2 = _x155 ∧ x3 = _x156 ∧ x4 = _x157 ∧ x5 = _x158 ∧ x6 = _x159 ∧ x7 = _x160 ∧ x8 = _x161 ∧ x9 = _x162 ∧ x10 = _x163 ∧ x11 = _x164 ∧ x1 = _x165 ∧ x2 = _x166 ∧ x3 = _x167 ∧ x4 = _x168 ∧ x5 = _x169 ∧ x6 = _x170 ∧ x7 = _x171 ∧ x8 = _x172 ∧ x9 = _x173 ∧ x10 = _x174 ∧ x11 = _x175 ∧ _x164 = _x175 ∧ _x163 = _x174 ∧ _x162 = _x173 ∧ _x161 = _x172 ∧ _x160 = _x171 ∧ _x159 = _x170 ∧ _x158 = _x169 ∧ _x157 = _x168 ∧ _x156 = _x167 ∧ _x155 = _x166 ∧ _x154 = _x165 ∧ _x160 ≤ _x158 ∧ _x158 ≤ _x160 l9 10 l8: x1 = _x176 ∧ x2 = _x177 ∧ x3 = _x178 ∧ x4 = _x179 ∧ x5 = _x180 ∧ x6 = _x181 ∧ x7 = _x182 ∧ x8 = _x183 ∧ x9 = _x184 ∧ x10 = _x185 ∧ x11 = _x186 ∧ x1 = _x187 ∧ x2 = _x188 ∧ x3 = _x189 ∧ x4 = _x190 ∧ x5 = _x191 ∧ x6 = _x192 ∧ x7 = _x193 ∧ x8 = _x194 ∧ x9 = _x195 ∧ x10 = _x196 ∧ x11 = _x197 ∧ _x186 = _x197 ∧ _x185 = _x196 ∧ _x184 = _x195 ∧ _x183 = _x194 ∧ _x182 = _x193 ∧ _x181 = _x192 ∧ _x180 = _x191 ∧ _x179 = _x190 ∧ _x178 = _x189 ∧ _x177 = _x188 ∧ _x176 = _x187 ∧ 1 + _x182 ≤ _x180 l9 11 l8: x1 = _x198 ∧ x2 = _x199 ∧ x3 = _x200 ∧ x4 = _x201 ∧ x5 = _x202 ∧ x6 = _x203 ∧ x7 = _x204 ∧ x8 = _x205 ∧ x9 = _x206 ∧ x10 = _x207 ∧ x11 = _x208 ∧ x1 = _x209 ∧ x2 = _x210 ∧ x3 = _x211 ∧ x4 = _x212 ∧ x5 = _x213 ∧ x6 = _x214 ∧ x7 = _x215 ∧ x8 = _x216 ∧ x9 = _x217 ∧ x10 = _x218 ∧ x11 = _x219 ∧ _x208 = _x219 ∧ _x207 = _x218 ∧ _x206 = _x217 ∧ _x205 = _x216 ∧ _x204 = _x215 ∧ _x203 = _x214 ∧ _x202 = _x213 ∧ _x201 = _x212 ∧ _x200 = _x211 ∧ _x199 = _x210 ∧ _x198 = _x209 ∧ 1 + _x202 ≤ _x204 l10 12 l9: x1 = _x220 ∧ x2 = _x221 ∧ x3 = _x222 ∧ x4 = _x223 ∧ x5 = _x224 ∧ x6 = _x225 ∧ x7 = _x226 ∧ x8 = _x227 ∧ x9 = _x228 ∧ x10 = _x229 ∧ x11 = _x230 ∧ x1 = _x231 ∧ x2 = _x232 ∧ x3 = _x233 ∧ x4 = _x234 ∧ x5 = _x235 ∧ x6 = _x236 ∧ x7 = _x237 ∧ x8 = _x238 ∧ x9 = _x239 ∧ x10 = _x240 ∧ x11 = _x241 ∧ _x230 = _x241 ∧ _x229 = _x240 ∧ _x228 = _x239 ∧ _x227 = _x238 ∧ _x226 = _x237 ∧ _x225 = _x236 ∧ _x224 = _x235 ∧ _x223 = _x234 ∧ _x222 = _x233 ∧ _x221 = _x232 ∧ _x220 = _x231 l11 13 l10: x1 = _x242 ∧ x2 = _x243 ∧ x3 = _x244 ∧ x4 = _x245 ∧ x5 = _x246 ∧ x6 = _x247 ∧ x7 = _x248 ∧ x8 = _x249 ∧ x9 = _x250 ∧ x10 = _x251 ∧ x11 = _x252 ∧ x1 = _x253 ∧ x2 = _x254 ∧ x3 = _x255 ∧ x4 = _x256 ∧ x5 = _x257 ∧ x6 = _x258 ∧ x7 = _x259 ∧ x8 = _x260 ∧ x9 = _x261 ∧ x10 = _x262 ∧ x11 = _x263 ∧ _x252 = _x263 ∧ _x251 = _x262 ∧ _x250 = _x261 ∧ _x249 = _x260 ∧ _x248 = _x259 ∧ _x247 = _x258 ∧ _x246 = _x257 ∧ _x245 = _x256 ∧ _x244 = _x255 ∧ _x243 = _x254 ∧ _x242 = _x253 l12 14 l11: x1 = _x264 ∧ x2 = _x265 ∧ x3 = _x266 ∧ x4 = _x267 ∧ x5 = _x268 ∧ x6 = _x269 ∧ x7 = _x270 ∧ x8 = _x271 ∧ x9 = _x272 ∧ x10 = _x273 ∧ x11 = _x274 ∧ x1 = _x275 ∧ x2 = _x276 ∧ x3 = _x277 ∧ x4 = _x278 ∧ x5 = _x279 ∧ x6 = _x280 ∧ x7 = _x281 ∧ x8 = _x282 ∧ x9 = _x283 ∧ x10 = _x284 ∧ x11 = _x285 ∧ _x274 = _x285 ∧ _x273 = _x284 ∧ _x272 = _x283 ∧ _x271 = _x282 ∧ _x270 = _x281 ∧ _x269 = _x280 ∧ _x268 = _x279 ∧ _x267 = _x278 ∧ _x266 = _x277 ∧ _x265 = _x276 ∧ _x264 = _x275 ∧ 1 + _x270 ≤ _x269 l12 15 l13: x1 = _x286 ∧ x2 = _x287 ∧ x3 = _x288 ∧ x4 = _x289 ∧ x5 = _x290 ∧ x6 = _x291 ∧ x7 = _x292 ∧ x8 = _x293 ∧ x9 = _x294 ∧ x10 = _x295 ∧ x11 = _x296 ∧ x1 = _x297 ∧ x2 = _x298 ∧ x3 = _x299 ∧ x4 = _x300 ∧ x5 = _x301 ∧ x6 = _x302 ∧ x7 = _x303 ∧ x8 = _x304 ∧ x9 = _x305 ∧ x10 = _x306 ∧ x11 = _x307 ∧ _x296 = _x307 ∧ _x295 = _x306 ∧ _x294 = _x305 ∧ _x293 = _x304 ∧ _x292 = _x303 ∧ _x290 = _x301 ∧ _x289 = _x300 ∧ _x288 = _x299 ∧ _x286 = _x297 ∧ _x302 = 1 + _x291 ∧ _x298 = _x298 ∧ _x291 ≤ _x292 l13 16 l12: x1 = _x308 ∧ x2 = _x309 ∧ x3 = _x310 ∧ x4 = _x311 ∧ x5 = _x312 ∧ x6 = _x313 ∧ x7 = _x314 ∧ x8 = _x315 ∧ x9 = _x316 ∧ x10 = _x317 ∧ x11 = _x318 ∧ x1 = _x319 ∧ x2 = _x320 ∧ x3 = _x321 ∧ x4 = _x322 ∧ x5 = _x323 ∧ x6 = _x324 ∧ x7 = _x325 ∧ x8 = _x326 ∧ x9 = _x327 ∧ x10 = _x328 ∧ x11 = _x329 ∧ _x318 = _x329 ∧ _x317 = _x328 ∧ _x316 = _x327 ∧ _x315 = _x326 ∧ _x314 = _x325 ∧ _x313 = _x324 ∧ _x312 = _x323 ∧ _x311 = _x322 ∧ _x310 = _x321 ∧ _x309 = _x320 ∧ _x308 = _x319 l14 17 l11: x1 = _x330 ∧ x2 = _x331 ∧ x3 = _x332 ∧ x4 = _x333 ∧ x5 = _x334 ∧ x6 = _x335 ∧ x7 = _x336 ∧ x8 = _x337 ∧ x9 = _x338 ∧ x10 = _x339 ∧ x11 = _x340 ∧ x1 = _x341 ∧ x2 = _x342 ∧ x3 = _x343 ∧ x4 = _x344 ∧ x5 = _x345 ∧ x6 = _x346 ∧ x7 = _x347 ∧ x8 = _x348 ∧ x9 = _x349 ∧ x10 = _x350 ∧ x11 = _x351 ∧ _x340 = _x351 ∧ _x339 = _x350 ∧ _x338 = _x349 ∧ _x337 = _x348 ∧ _x336 = _x347 ∧ _x335 = _x346 ∧ _x334 = _x345 ∧ _x333 = _x344 ∧ _x332 = _x343 ∧ _x331 = _x342 ∧ _x330 = _x341 ∧ _x333 ≤ _x334 ∧ _x334 ≤ _x333 l14 18 l13: x1 = _x352 ∧ x2 = _x353 ∧ x3 = _x354 ∧ x4 = _x355 ∧ x5 = _x356 ∧ x6 = _x357 ∧ x7 = _x358 ∧ x8 = _x359 ∧ x9 = _x360 ∧ x10 = _x361 ∧ x11 = _x362 ∧ x1 = _x363 ∧ x2 = _x364 ∧ x3 = _x365 ∧ x4 = _x366 ∧ x5 = _x367 ∧ x6 = _x368 ∧ x7 = _x369 ∧ x8 = _x370 ∧ x9 = _x371 ∧ x10 = _x372 ∧ x11 = _x373 ∧ _x362 = _x373 ∧ _x361 = _x372 ∧ _x360 = _x371 ∧ _x359 = _x370 ∧ _x358 = _x369 ∧ _x357 = _x368 ∧ _x356 = _x367 ∧ _x355 = _x366 ∧ _x354 = _x365 ∧ _x353 = _x364 ∧ _x352 = _x363 ∧ 1 + _x355 ≤ _x356 l14 19 l13: x1 = _x374 ∧ x2 = _x375 ∧ x3 = _x376 ∧ x4 = _x377 ∧ x5 = _x378 ∧ x6 = _x379 ∧ x7 = _x380 ∧ x8 = _x381 ∧ x9 = _x382 ∧ x10 = _x383 ∧ x11 = _x384 ∧ x1 = _x385 ∧ x2 = _x386 ∧ x3 = _x387 ∧ x4 = _x388 ∧ x5 = _x389 ∧ x6 = _x390 ∧ x7 = _x391 ∧ x8 = _x392 ∧ x9 = _x393 ∧ x10 = _x394 ∧ x11 = _x395 ∧ _x384 = _x395 ∧ _x383 = _x394 ∧ _x382 = _x393 ∧ _x381 = _x392 ∧ _x380 = _x391 ∧ _x379 = _x390 ∧ _x378 = _x389 ∧ _x377 = _x388 ∧ _x376 = _x387 ∧ _x375 = _x386 ∧ _x374 = _x385 ∧ 1 + _x378 ≤ _x377 l15 20 l16: x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x5 = _x400 ∧ x6 = _x401 ∧ x7 = _x402 ∧ x8 = _x403 ∧ x9 = _x404 ∧ x10 = _x405 ∧ x11 = _x406 ∧ x1 = _x407 ∧ x2 = _x408 ∧ x3 = _x409 ∧ x4 = _x410 ∧ x5 = _x411 ∧ x6 = _x412 ∧ x7 = _x413 ∧ x8 = _x414 ∧ x9 = _x415 ∧ x10 = _x416 ∧ x11 = _x417 ∧ _x406 = _x417 ∧ _x405 = _x416 ∧ _x404 = _x415 ∧ _x403 = _x414 ∧ _x402 = _x413 ∧ _x401 = _x412 ∧ _x400 = _x411 ∧ _x399 = _x410 ∧ _x397 = _x408 ∧ _x396 = _x407 ∧ _x409 = 1 + _x398 l17 21 l15: x1 = _x418 ∧ x2 = _x419 ∧ x3 = _x420 ∧ x4 = _x421 ∧ x5 = _x422 ∧ x6 = _x423 ∧ x7 = _x424 ∧ x8 = _x425 ∧ x9 = _x426 ∧ x10 = _x427 ∧ x11 = _x428 ∧ x1 = _x429 ∧ x2 = _x430 ∧ x3 = _x431 ∧ x4 = _x432 ∧ x5 = _x433 ∧ x6 = _x434 ∧ x7 = _x435 ∧ x8 = _x436 ∧ x9 = _x437 ∧ x10 = _x438 ∧ x11 = _x439 ∧ _x428 = _x439 ∧ _x427 = _x438 ∧ _x426 = _x437 ∧ _x425 = _x436 ∧ _x424 = _x435 ∧ _x423 = _x434 ∧ _x422 = _x433 ∧ _x421 = _x432 ∧ _x420 = _x431 ∧ _x419 = _x430 ∧ _x418 = _x429 ∧ 1 + _x419 ≤ _x418 l17 22 l15: x1 = _x440 ∧ x2 = _x441 ∧ x3 = _x442 ∧ x4 = _x443 ∧ x5 = _x444 ∧ x6 = _x445 ∧ x7 = _x446 ∧ x8 = _x447 ∧ x9 = _x448 ∧ x10 = _x449 ∧ x11 = _x450 ∧ x1 = _x451 ∧ x2 = _x452 ∧ x3 = _x453 ∧ x4 = _x454 ∧ x5 = _x455 ∧ x6 = _x456 ∧ x7 = _x457 ∧ x8 = _x458 ∧ x9 = _x459 ∧ x10 = _x460 ∧ x11 = _x461 ∧ _x450 = _x461 ∧ _x449 = _x460 ∧ _x448 = _x459 ∧ _x447 = _x458 ∧ _x446 = _x457 ∧ _x445 = _x456 ∧ _x444 = _x455 ∧ _x442 = _x453 ∧ _x441 = _x452 ∧ _x454 = _x442 ∧ _x451 = _x441 ∧ _x440 ≤ _x441 l18 23 l5: x1 = _x462 ∧ x2 = _x463 ∧ x3 = _x464 ∧ x4 = _x465 ∧ x5 = _x466 ∧ x6 = _x467 ∧ x7 = _x468 ∧ x8 = _x469 ∧ x9 = _x470 ∧ x10 = _x471 ∧ x11 = _x472 ∧ x1 = _x473 ∧ x2 = _x474 ∧ x3 = _x475 ∧ x4 = _x476 ∧ x5 = _x477 ∧ x6 = _x478 ∧ x7 = _x479 ∧ x8 = _x480 ∧ x9 = _x481 ∧ x10 = _x482 ∧ x11 = _x483 ∧ _x472 = _x483 ∧ _x471 = _x482 ∧ _x470 = _x481 ∧ _x469 = _x480 ∧ _x468 = _x479 ∧ _x467 = _x478 ∧ _x466 = _x477 ∧ _x465 = _x476 ∧ _x464 = _x475 ∧ _x463 = _x474 ∧ _x462 = _x473 ∧ 1 + _x468 ≤ _x464 l18 24 l3: x1 = _x484 ∧ x2 = _x485 ∧ x3 = _x486 ∧ x4 = _x487 ∧ x5 = _x488 ∧ x6 = _x489 ∧ x7 = _x490 ∧ x8 = _x491 ∧ x9 = _x492 ∧ x10 = _x493 ∧ x11 = _x494 ∧ x1 = _x495 ∧ x2 = _x496 ∧ x3 = _x497 ∧ x4 = _x498 ∧ x5 = _x499 ∧ x6 = _x500 ∧ x7 = _x501 ∧ x8 = _x502 ∧ x9 = _x503 ∧ x10 = _x504 ∧ x11 = _x505 ∧ _x494 = _x505 ∧ _x493 = _x504 ∧ _x492 = _x503 ∧ _x491 = _x502 ∧ _x490 = _x501 ∧ _x489 = _x500 ∧ _x488 = _x499 ∧ _x487 = _x498 ∧ _x486 = _x497 ∧ _x485 = _x496 ∧ _x495 = 0 ∧ _x486 ≤ _x490 l19 25 l17: x1 = _x506 ∧ x2 = _x507 ∧ x3 = _x508 ∧ x4 = _x509 ∧ x5 = _x510 ∧ x6 = _x511 ∧ x7 = _x512 ∧ x8 = _x513 ∧ x9 = _x514 ∧ x10 = _x515 ∧ x11 = _x516 ∧ x1 = _x517 ∧ x2 = _x518 ∧ x3 = _x519 ∧ x4 = _x520 ∧ x5 = _x521 ∧ x6 = _x522 ∧ x7 = _x523 ∧ x8 = _x524 ∧ x9 = _x525 ∧ x10 = _x526 ∧ x11 = _x527 ∧ _x515 = _x526 ∧ _x514 = _x525 ∧ _x513 = _x524 ∧ _x512 = _x523 ∧ _x511 = _x522 ∧ _x510 = _x521 ∧ _x509 = _x520 ∧ _x508 = _x519 ∧ _x506 = _x517 ∧ _x518 = _x518 ∧ _x527 = _x527 ∧ _x510 ≤ _x511 l19 26 l20: x1 = _x528 ∧ x2 = _x529 ∧ x3 = _x530 ∧ x4 = _x531 ∧ x5 = _x532 ∧ x6 = _x533 ∧ x7 = _x534 ∧ x8 = _x535 ∧ x9 = _x536 ∧ x10 = _x537 ∧ x11 = _x538 ∧ x1 = _x539 ∧ x2 = _x540 ∧ x3 = _x541 ∧ x4 = _x542 ∧ x5 = _x543 ∧ x6 = _x544 ∧ x7 = _x545 ∧ x8 = _x546 ∧ x9 = _x547 ∧ x10 = _x548 ∧ x11 = _x549 ∧ _x538 = _x549 ∧ _x537 = _x548 ∧ _x536 = _x547 ∧ _x534 = _x545 ∧ _x532 = _x543 ∧ _x531 = _x542 ∧ _x530 = _x541 ∧ _x529 = _x540 ∧ _x528 = _x539 ∧ _x544 = 1 + _x533 ∧ _x546 = _x546 ∧ 1 + _x533 ≤ _x532 l20 27 l19: x1 = _x550 ∧ x2 = _x551 ∧ x3 = _x552 ∧ x4 = _x553 ∧ x5 = _x554 ∧ x6 = _x555 ∧ x7 = _x556 ∧ x8 = _x557 ∧ x9 = _x558 ∧ x10 = _x559 ∧ x11 = _x560 ∧ x1 = _x561 ∧ x2 = _x562 ∧ x3 = _x563 ∧ x4 = _x564 ∧ x5 = _x565 ∧ x6 = _x566 ∧ x7 = _x567 ∧ x8 = _x568 ∧ x9 = _x569 ∧ x10 = _x570 ∧ x11 = _x571 ∧ _x560 = _x571 ∧ _x559 = _x570 ∧ _x558 = _x569 ∧ _x557 = _x568 ∧ _x556 = _x567 ∧ _x555 = _x566 ∧ _x554 = _x565 ∧ _x553 = _x564 ∧ _x552 = _x563 ∧ _x551 = _x562 ∧ _x550 = _x561 l21 28 l14: x1 = _x572 ∧ x2 = _x573 ∧ x3 = _x574 ∧ x4 = _x575 ∧ x5 = _x576 ∧ x6 = _x577 ∧ x7 = _x578 ∧ x8 = _x579 ∧ x9 = _x580 ∧ x10 = _x581 ∧ x11 = _x582 ∧ x1 = _x583 ∧ x2 = _x584 ∧ x3 = _x585 ∧ x4 = _x586 ∧ x5 = _x587 ∧ x6 = _x588 ∧ x7 = _x589 ∧ x8 = _x590 ∧ x9 = _x591 ∧ x10 = _x592 ∧ x11 = _x593 ∧ _x582 = _x593 ∧ _x581 = _x592 ∧ _x580 = _x591 ∧ _x579 = _x590 ∧ _x578 = _x589 ∧ _x577 = _x588 ∧ _x576 = _x587 ∧ _x575 = _x586 ∧ _x574 = _x585 ∧ _x573 = _x584 ∧ _x572 = _x583 ∧ 1 + _x578 ≤ _x574 l21 29 l20: x1 = _x594 ∧ x2 = _x595 ∧ x3 = _x596 ∧ x4 = _x597 ∧ x5 = _x598 ∧ x6 = _x599 ∧ x7 = _x600 ∧ x8 = _x601 ∧ x9 = _x602 ∧ x10 = _x603 ∧ x11 = _x604 ∧ x1 = _x605 ∧ x2 = _x606 ∧ x3 = _x607 ∧ x4 = _x608 ∧ x5 = _x609 ∧ x6 = _x610 ∧ x7 = _x611 ∧ x8 = _x612 ∧ x9 = _x613 ∧ x10 = _x614 ∧ x11 = _x615 ∧ _x604 = _x615 ∧ _x603 = _x614 ∧ _x602 = _x613 ∧ _x600 = _x611 ∧ _x599 = _x610 ∧ _x598 = _x609 ∧ _x597 = _x608 ∧ _x596 = _x607 ∧ _x595 = _x606 ∧ _x594 = _x605 ∧ _x612 = _x612 ∧ _x596 ≤ _x600 l22 30 l18: x1 = _x616 ∧ x2 = _x617 ∧ x3 = _x618 ∧ x4 = _x619 ∧ x5 = _x620 ∧ x6 = _x621 ∧ x7 = _x622 ∧ x8 = _x623 ∧ x9 = _x624 ∧ x10 = _x625 ∧ x11 = _x626 ∧ x1 = _x627 ∧ x2 = _x628 ∧ x3 = _x629 ∧ x4 = _x630 ∧ x5 = _x631 ∧ x6 = _x632 ∧ x7 = _x633 ∧ x8 = _x634 ∧ x9 = _x635 ∧ x10 = _x636 ∧ x11 = _x637 ∧ _x626 = _x637 ∧ _x625 = _x636 ∧ _x624 = _x635 ∧ _x623 = _x634 ∧ _x622 = _x633 ∧ _x621 = _x632 ∧ _x620 = _x631 ∧ _x619 = _x630 ∧ _x618 = _x629 ∧ _x617 = _x628 ∧ _x616 = _x627 l16 31 l21: x1 = _x638 ∧ x2 = _x639 ∧ x3 = _x640 ∧ x4 = _x641 ∧ x5 = _x642 ∧ x6 = _x643 ∧ x7 = _x644 ∧ x8 = _x645 ∧ x9 = _x646 ∧ x10 = _x647 ∧ x11 = _x648 ∧ x1 = _x649 ∧ x2 = _x650 ∧ x3 = _x651 ∧ x4 = _x652 ∧ x5 = _x653 ∧ x6 = _x654 ∧ x7 = _x655 ∧ x8 = _x656 ∧ x9 = _x657 ∧ x10 = _x658 ∧ x11 = _x659 ∧ _x648 = _x659 ∧ _x647 = _x658 ∧ _x646 = _x657 ∧ _x645 = _x656 ∧ _x644 = _x655 ∧ _x643 = _x654 ∧ _x642 = _x653 ∧ _x641 = _x652 ∧ _x640 = _x651 ∧ _x639 = _x650 ∧ _x638 = _x649 l23 32 l24: x1 = _x660 ∧ x2 = _x661 ∧ x3 = _x662 ∧ x4 = _x663 ∧ x5 = _x664 ∧ x6 = _x665 ∧ x7 = _x666 ∧ x8 = _x667 ∧ x9 = _x668 ∧ x10 = _x669 ∧ x11 = _x670 ∧ x1 = _x671 ∧ x2 = _x672 ∧ x3 = _x673 ∧ x4 = _x674 ∧ x5 = _x675 ∧ x6 = _x676 ∧ x7 = _x677 ∧ x8 = _x678 ∧ x9 = _x679 ∧ x10 = _x680 ∧ x11 = _x681 ∧ _x670 = _x681 ∧ _x669 = _x680 ∧ _x668 = _x679 ∧ _x667 = _x678 ∧ _x666 = _x677 ∧ _x665 = _x676 ∧ _x664 = _x675 ∧ _x663 = _x674 ∧ _x661 = _x672 ∧ _x660 = _x671 ∧ _x673 = 1 + _x662 ∧ _x662 ≤ _x665 l23 33 l25: x1 = _x682 ∧ x2 = _x683 ∧ x3 = _x684 ∧ x4 = _x685 ∧ x5 = _x686 ∧ x6 = _x687 ∧ x7 = _x688 ∧ x8 = _x689 ∧ x9 = _x690 ∧ x10 = _x691 ∧ x11 = _x692 ∧ x1 = _x693 ∧ x2 = _x694 ∧ x3 = _x695 ∧ x4 = _x696 ∧ x5 = _x697 ∧ x6 = _x698 ∧ x7 = _x699 ∧ x8 = _x700 ∧ x9 = _x701 ∧ x10 = _x702 ∧ x11 = _x703 ∧ _x692 = _x703 ∧ _x691 = _x702 ∧ _x690 = _x701 ∧ _x688 = _x699 ∧ _x686 = _x697 ∧ _x685 = _x696 ∧ _x684 = _x695 ∧ _x683 = _x694 ∧ _x682 = _x693 ∧ _x698 = 1 + _x687 ∧ _x700 = _x700 ∧ 1 + _x687 ≤ _x684 l25 34 l23: x1 = _x704 ∧ x2 = _x705 ∧ x3 = _x706 ∧ x4 = _x707 ∧ x5 = _x708 ∧ x6 = _x709 ∧ x7 = _x710 ∧ x8 = _x711 ∧ x9 = _x712 ∧ x10 = _x713 ∧ x11 = _x714 ∧ x1 = _x715 ∧ x2 = _x716 ∧ x3 = _x717 ∧ x4 = _x718 ∧ x5 = _x719 ∧ x6 = _x720 ∧ x7 = _x721 ∧ x8 = _x722 ∧ x9 = _x723 ∧ x10 = _x724 ∧ x11 = _x725 ∧ _x714 = _x725 ∧ _x713 = _x724 ∧ _x712 = _x723 ∧ _x711 = _x722 ∧ _x710 = _x721 ∧ _x709 = _x720 ∧ _x708 = _x719 ∧ _x707 = _x718 ∧ _x706 = _x717 ∧ _x705 = _x716 ∧ _x704 = _x715 l26 35 l16: x1 = _x726 ∧ x2 = _x727 ∧ x3 = _x728 ∧ x4 = _x729 ∧ x5 = _x730 ∧ x6 = _x731 ∧ x7 = _x732 ∧ x8 = _x733 ∧ x9 = _x734 ∧ x10 = _x735 ∧ x11 = _x736 ∧ x1 = _x737 ∧ x2 = _x738 ∧ x3 = _x739 ∧ x4 = _x740 ∧ x5 = _x741 ∧ x6 = _x742 ∧ x7 = _x743 ∧ x8 = _x744 ∧ x9 = _x745 ∧ x10 = _x746 ∧ x11 = _x747 ∧ _x736 = _x747 ∧ _x735 = _x746 ∧ _x734 = _x745 ∧ _x733 = _x744 ∧ _x732 = _x743 ∧ _x731 = _x742 ∧ _x730 = _x741 ∧ _x729 = _x740 ∧ _x728 = _x739 ∧ _x727 = _x738 ∧ _x737 = 0 ∧ _x730 ≤ _x728 l26 36 l25: x1 = _x748 ∧ x2 = _x749 ∧ x3 = _x750 ∧ x4 = _x751 ∧ x5 = _x752 ∧ x6 = _x753 ∧ x7 = _x754 ∧ x8 = _x755 ∧ x9 = _x756 ∧ x10 = _x757 ∧ x11 = _x758 ∧ x1 = _x759 ∧ x2 = _x760 ∧ x3 = _x761 ∧ x4 = _x762 ∧ x5 = _x763 ∧ x6 = _x764 ∧ x7 = _x765 ∧ x8 = _x766 ∧ x9 = _x767 ∧ x10 = _x768 ∧ x11 = _x769 ∧ _x758 = _x769 ∧ _x757 = _x768 ∧ _x756 = _x767 ∧ _x754 = _x765 ∧ _x753 = _x764 ∧ _x752 = _x763 ∧ _x751 = _x762 ∧ _x750 = _x761 ∧ _x749 = _x760 ∧ _x748 = _x759 ∧ _x766 = _x766 ∧ 1 + _x750 ≤ _x752 l24 37 l26: x1 = _x770 ∧ x2 = _x771 ∧ x3 = _x772 ∧ x4 = _x773 ∧ x5 = _x774 ∧ x6 = _x775 ∧ x7 = _x776 ∧ x8 = _x777 ∧ x9 = _x778 ∧ x10 = _x779 ∧ x11 = _x780 ∧ x1 = _x781 ∧ x2 = _x782 ∧ x3 = _x783 ∧ x4 = _x784 ∧ x5 = _x785 ∧ x6 = _x786 ∧ x7 = _x787 ∧ x8 = _x788 ∧ x9 = _x789 ∧ x10 = _x790 ∧ x11 = _x791 ∧ _x780 = _x791 ∧ _x779 = _x790 ∧ _x778 = _x789 ∧ _x777 = _x788 ∧ _x776 = _x787 ∧ _x775 = _x786 ∧ _x774 = _x785 ∧ _x773 = _x784 ∧ _x772 = _x783 ∧ _x771 = _x782 ∧ _x770 = _x781 l27 38 l28: x1 = _x792 ∧ x2 = _x793 ∧ x3 = _x794 ∧ x4 = _x795 ∧ x5 = _x796 ∧ x6 = _x797 ∧ x7 = _x798 ∧ x8 = _x799 ∧ x9 = _x800 ∧ x10 = _x801 ∧ x11 = _x802 ∧ x1 = _x803 ∧ x2 = _x804 ∧ x3 = _x805 ∧ x4 = _x806 ∧ x5 = _x807 ∧ x6 = _x808 ∧ x7 = _x809 ∧ x8 = _x810 ∧ x9 = _x811 ∧ x10 = _x812 ∧ x11 = _x813 ∧ _x802 = _x813 ∧ _x801 = _x812 ∧ _x800 = _x811 ∧ _x799 = _x810 ∧ _x798 = _x809 ∧ _x797 = _x808 ∧ _x796 = _x807 ∧ _x795 = _x806 ∧ _x794 = _x805 ∧ _x793 = _x804 ∧ _x792 = _x803 ∧ 1 + _x798 ≤ _x796 l27 39 l24: x1 = _x814 ∧ x2 = _x815 ∧ x3 = _x816 ∧ x4 = _x817 ∧ x5 = _x818 ∧ x6 = _x819 ∧ x7 = _x820 ∧ x8 = _x821 ∧ x9 = _x822 ∧ x10 = _x823 ∧ x11 = _x824 ∧ x1 = _x825 ∧ x2 = _x826 ∧ x3 = _x827 ∧ x4 = _x828 ∧ x5 = _x829 ∧ x6 = _x830 ∧ x7 = _x831 ∧ x8 = _x832 ∧ x9 = _x833 ∧ x10 = _x834 ∧ x11 = _x835 ∧ _x824 = _x835 ∧ _x823 = _x834 ∧ _x822 = _x833 ∧ _x821 = _x832 ∧ _x820 = _x831 ∧ _x819 = _x830 ∧ _x818 = _x829 ∧ _x817 = _x828 ∧ _x816 = _x827 ∧ _x815 = _x826 ∧ _x814 = _x825 ∧ _x818 ≤ _x820 l5 40 l27: x1 = _x836 ∧ x2 = _x837 ∧ x3 = _x838 ∧ x4 = _x839 ∧ x5 = _x840 ∧ x6 = _x841 ∧ x7 = _x842 ∧ x8 = _x843 ∧ x9 = _x844 ∧ x10 = _x845 ∧ x11 = _x846 ∧ x1 = _x847 ∧ x2 = _x848 ∧ x3 = _x849 ∧ x4 = _x850 ∧ x5 = _x851 ∧ x6 = _x852 ∧ x7 = _x853 ∧ x8 = _x854 ∧ x9 = _x855 ∧ x10 = _x856 ∧ x11 = _x857 ∧ _x846 = _x857 ∧ _x845 = _x856 ∧ _x844 = _x855 ∧ _x843 = _x854 ∧ _x842 = _x853 ∧ _x841 = _x852 ∧ _x840 = _x851 ∧ _x839 = _x850 ∧ _x838 = _x849 ∧ _x837 = _x848 ∧ _x836 = _x847 l29 41 l22: x1 = _x858 ∧ x2 = _x859 ∧ x3 = _x860 ∧ x4 = _x861 ∧ x5 = _x862 ∧ x6 = _x863 ∧ x7 = _x864 ∧ x8 = _x865 ∧ x9 = _x866 ∧ x10 = _x867 ∧ x11 = _x868 ∧ x1 = _x869 ∧ x2 = _x870 ∧ x3 = _x871 ∧ x4 = _x872 ∧ x5 = _x873 ∧ x6 = _x874 ∧ x7 = _x875 ∧ x8 = _x876 ∧ x9 = _x877 ∧ x10 = _x878 ∧ x11 = _x879 ∧ _x868 = _x879 ∧ _x867 = _x878 ∧ _x866 = _x877 ∧ _x865 = _x876 ∧ _x864 = _x875 ∧ _x863 = _x874 ∧ _x862 = _x873 ∧ _x861 = _x872 ∧ _x860 = _x871 ∧ _x859 = _x870 ∧ _x858 = _x869 l30 42 l22: x1 = _x880 ∧ x2 = _x881 ∧ x3 = _x882 ∧ x4 = _x883 ∧ x5 = _x884 ∧ x6 = _x885 ∧ x7 = _x886 ∧ x8 = _x887 ∧ x9 = _x888 ∧ x10 = _x889 ∧ x11 = _x890 ∧ x1 = _x891 ∧ x2 = _x892 ∧ x3 = _x893 ∧ x4 = _x894 ∧ x5 = _x895 ∧ x6 = _x896 ∧ x7 = _x897 ∧ x8 = _x898 ∧ x9 = _x899 ∧ x10 = _x900 ∧ x11 = _x901 ∧ _x890 = _x901 ∧ _x889 = _x900 ∧ _x888 = _x899 ∧ _x887 = _x898 ∧ _x886 = _x897 ∧ _x885 = _x896 ∧ _x884 = _x895 ∧ _x883 = _x894 ∧ _x881 = _x892 ∧ _x880 = _x891 ∧ _x893 = 1 + _x882 l1 43 l30: x1 = _x902 ∧ x2 = _x903 ∧ x3 = _x904 ∧ x4 = _x905 ∧ x5 = _x906 ∧ x6 = _x907 ∧ x7 = _x908 ∧ x8 = _x909 ∧ x9 = _x910 ∧ x10 = _x911 ∧ x11 = _x912 ∧ x1 = _x913 ∧ x2 = _x914 ∧ x3 = _x915 ∧ x4 = _x916 ∧ x5 = _x917 ∧ x6 = _x918 ∧ x7 = _x919 ∧ x8 = _x920 ∧ x9 = _x921 ∧ x10 = _x922 ∧ x11 = _x923 ∧ _x912 = _x923 ∧ _x911 = _x922 ∧ _x910 = _x921 ∧ _x909 = _x920 ∧ _x908 = _x919 ∧ _x907 = _x918 ∧ _x906 = _x917 ∧ _x905 = _x916 ∧ _x904 = _x915 ∧ _x903 = _x914 ∧ _x902 = _x913 ∧ 1 ≤ _x902 l1 44 l30: x1 = _x924 ∧ x2 = _x925 ∧ x3 = _x926 ∧ x4 = _x927 ∧ x5 = _x928 ∧ x6 = _x929 ∧ x7 = _x930 ∧ x8 = _x931 ∧ x9 = _x932 ∧ x10 = _x933 ∧ x11 = _x934 ∧ x1 = _x935 ∧ x2 = _x936 ∧ x3 = _x937 ∧ x4 = _x938 ∧ x5 = _x939 ∧ x6 = _x940 ∧ x7 = _x941 ∧ x8 = _x942 ∧ x9 = _x943 ∧ x10 = _x944 ∧ x11 = _x945 ∧ _x934 = _x945 ∧ _x933 = _x944 ∧ _x932 = _x943 ∧ _x931 = _x942 ∧ _x930 = _x941 ∧ _x929 = _x940 ∧ _x928 = _x939 ∧ _x927 = _x938 ∧ _x926 = _x937 ∧ _x925 = _x936 ∧ _x924 = _x935 ∧ 1 + _x924 ≤ 0 l1 45 l30: x1 = _x946 ∧ x2 = _x947 ∧ x3 = _x948 ∧ x4 = _x949 ∧ x5 = _x950 ∧ x6 = _x951 ∧ x7 = _x952 ∧ x8 = _x953 ∧ x9 = _x954 ∧ x10 = _x955 ∧ x11 = _x956 ∧ x1 = _x957 ∧ x2 = _x958 ∧ x3 = _x959 ∧ x4 = _x960 ∧ x5 = _x961 ∧ x6 = _x962 ∧ x7 = _x963 ∧ x8 = _x964 ∧ x9 = _x965 ∧ x10 = _x966 ∧ x11 = _x967 ∧ _x956 = _x967 ∧ _x955 = _x966 ∧ _x954 = _x965 ∧ _x953 = _x964 ∧ _x952 = _x963 ∧ _x951 = _x962 ∧ _x950 = _x961 ∧ _x949 = _x960 ∧ _x948 = _x959 ∧ _x947 = _x958 ∧ _x946 = _x957 ∧ 0 ≤ _x946 ∧ _x946 ≤ 0 l31 46 l3: x1 = _x968 ∧ x2 = _x969 ∧ x3 = _x970 ∧ x4 = _x971 ∧ x5 = _x972 ∧ x6 = _x973 ∧ x7 = _x974 ∧ x8 = _x975 ∧ x9 = _x976 ∧ x10 = _x977 ∧ x11 = _x978 ∧ x1 = _x979 ∧ x2 = _x980 ∧ x3 = _x981 ∧ x4 = _x982 ∧ x5 = _x983 ∧ x6 = _x984 ∧ x7 = _x985 ∧ x8 = _x986 ∧ x9 = _x987 ∧ x10 = _x988 ∧ x11 = _x989 ∧ _x978 = _x989 ∧ _x977 = _x988 ∧ _x976 = _x987 ∧ _x975 = _x986 ∧ _x974 = _x985 ∧ _x973 = _x984 ∧ _x971 = _x982 ∧ _x970 = _x981 ∧ _x969 = _x980 ∧ _x968 = _x979 ∧ _x983 = 1 + _x972 l2 47 l31: x1 = _x990 ∧ x2 = _x991 ∧ x3 = _x992 ∧ x4 = _x993 ∧ x5 = _x994 ∧ x6 = _x995 ∧ x7 = _x996 ∧ x8 = _x997 ∧ x9 = _x998 ∧ x10 = _x999 ∧ x11 = _x1000 ∧ x1 = _x1001 ∧ x2 = _x1002 ∧ x3 = _x1003 ∧ x4 = _x1004 ∧ x5 = _x1005 ∧ x6 = _x1006 ∧ x7 = _x1007 ∧ x8 = _x1008 ∧ x9 = _x1009 ∧ x10 = _x1010 ∧ x11 = _x1011 ∧ _x1000 = _x1011 ∧ _x999 = _x1010 ∧ _x998 = _x1009 ∧ _x997 = _x1008 ∧ _x996 = _x1007 ∧ _x995 = _x1006 ∧ _x994 = _x1005 ∧ _x993 = _x1004 ∧ _x992 = _x1003 ∧ _x991 = _x1002 ∧ _x990 = _x1001 ∧ _x998 ≤ _x990 l2 48 l31: x1 = _x1012 ∧ x2 = _x1013 ∧ x3 = _x1014 ∧ x4 = _x1015 ∧ x5 = _x1016 ∧ x6 = _x1017 ∧ x7 = _x1018 ∧ x8 = _x1019 ∧ x9 = _x1020 ∧ x10 = _x1021 ∧ x11 = _x1022 ∧ x1 = _x1023 ∧ x2 = _x1024 ∧ x3 = _x1025 ∧ x4 = _x1026 ∧ x5 = _x1027 ∧ x6 = _x1028 ∧ x7 = _x1029 ∧ x8 = _x1030 ∧ x9 = _x1031 ∧ x10 = _x1032 ∧ x11 = _x1033 ∧ _x1022 = _x1033 ∧ _x1021 = _x1032 ∧ _x1020 = _x1031 ∧ _x1019 = _x1030 ∧ _x1018 = _x1029 ∧ _x1017 = _x1028 ∧ _x1016 = _x1027 ∧ _x1015 = _x1026 ∧ _x1014 = _x1025 ∧ _x1013 = _x1024 ∧ _x1023 = _x1020 ∧ 1 + _x1012 ≤ _x1020 l32 49 l29: x1 = _x1034 ∧ x2 = _x1035 ∧ x3 = _x1036 ∧ x4 = _x1037 ∧ x5 = _x1038 ∧ x6 = _x1039 ∧ x7 = _x1040 ∧ x8 = _x1041 ∧ x9 = _x1042 ∧ x10 = _x1043 ∧ x11 = _x1044 ∧ x1 = _x1045 ∧ x2 = _x1046 ∧ x3 = _x1047 ∧ x4 = _x1048 ∧ x5 = _x1049 ∧ x6 = _x1050 ∧ x7 = _x1051 ∧ x8 = _x1052 ∧ x9 = _x1053 ∧ x10 = _x1054 ∧ x11 = _x1055 ∧ _x1044 = _x1055 ∧ _x1043 = _x1054 ∧ _x1042 = _x1053 ∧ _x1041 = _x1052 ∧ _x1040 = _x1051 ∧ _x1039 = _x1050 ∧ _x1038 = _x1049 ∧ _x1037 = _x1048 ∧ _x1036 = _x1047 ∧ _x1035 = _x1046 ∧ _x1034 = _x1045

## 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 ∧ x11 = x11 l22 l22 l22: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l1 l1 l1: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l13 l13 l13: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l31 l31 l31: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l18 l18 l18: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l17 l17 l17: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l21 l21 l21: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l9 l9 l9: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l14 l14 l14: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l25 l25 l25: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l6 l6 l6: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l8 l8 l8: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l27 l27 l27: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l0 l0 l0: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l12 l12 l12: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l19 l19 l19: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l26 l26 l26: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l7 l7 l7: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l24 l24 l24: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l11 l11 l11: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l3 l3 l3: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l20 l20 l20: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l32 l32 l32: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l2 l2 l2: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l23 l23 l23: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l4 l4 l4: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l10 l10 l10: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l29 l29 l29: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l15 l15 l15: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l16 l16 l16: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l30 l30 l30: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11
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 { l22, l1, l3, l31, l18, l30, l0, l2 }.

### 2.1.1 Transition Removal

We remove transition 24 using the following ranking functions, which are bounded by 0.

 l0: −1 − x3 + x7 l1: −1 − x3 + x7 l3: −1 − x3 + x7 l31: −1 − x3 + x7 l2: −1 − x3 + x7 l18: − x3 + x7 l22: − x3 + x7 l30: −1 − x3 + x7

### 2.1.2 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 0.

 l0: 0 l1: −1 − x5 + x7 l3: 0 l31: 0 l2: 0 l22: −1 − x5 + x7 l18: −1 − x5 + x7 l30: −1 − x5 + x7

### 2.1.3 Transition Removal

We remove transitions 30, 42, 45, 44, 43 using the following ranking functions, which are bounded by 0.

 l3: −1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x11 l0: −1 + 3⋅x2 + 4⋅x3 + 5⋅x4 − x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x11 l31: −2 + 3⋅x2 + 4⋅x3 + 5⋅x4 − x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x11 l2: −2 + 3⋅x2 + 4⋅x3 + 5⋅x4 − x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x11 l22: 0 l18: −1 l30: 1 l1: 2

### 2.1.4 Transition Removal

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

 l3: −4⋅x5 + 4⋅x7 + 3 l0: −4⋅x5 + 4⋅x7 + 2 l31: −4⋅x5 + 4⋅x7 l2: −4⋅x5 + 4⋅x7 + 1

### 2.1.5 Transition Removal

We remove transitions 3, 46, 48, 47 using the following ranking functions, which are bounded by 0.

 l3: 0 l0: −1 l31: 1 l2: 2

### 2.1.6 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, l7, l24, l11, l13, l20, l17, l21, l9, l14, l23, l4, l25, l6, l10, l8, l27, l16, l15, l12, l19, l26 }.

### 2.2.1 Transition Removal

We remove transition 29 using the following ranking functions, which are bounded by 0.

 l5: − x3 + x7 l27: − x3 + x7 l4: − x3 + x7 l9: − x3 + x7 l6: − x3 + x7 l7: − x3 + x7 l8: − x3 + x7 l10: − x3 + x7 l11: − x3 + x7 l14: − x3 + x7 l12: − x3 + x7 l13: − x3 + x7 l21: − x3 + x7 l16: − x3 + x7 l26: − x3 + x7 l24: − x3 + x7 l23: − x3 + x7 l25: − x3 + x7 l15: −1 − x3 + x7 l17: −1 − x3 + x7 l19: −1 − x3 + x7 l20: −1 − x3 + x7

### 2.2.2 Transition Removal

We remove transitions 9, 11, 39 using the following ranking functions, which are bounded by 0.

 l5: 1 − 2⋅x5 + 2⋅x7 l27: 1 − 2⋅x5 + 2⋅x7 l4: −1 − 2⋅x5 + 2⋅x7 l9: −2⋅x5 + 2⋅x7 l6: −1 − 2⋅x5 + 2⋅x7 l7: −1 − 2⋅x5 + 2⋅x7 l8: −1 − 2⋅x5 + 2⋅x7 l10: −2⋅x5 + 2⋅x7 l11: −2⋅x5 + 2⋅x7 l14: −2⋅x5 + 2⋅x7 l12: −2⋅x5 + 2⋅x7 l13: −2⋅x5 + 2⋅x7 l21: −2⋅x5 + 2⋅x7 l16: −2⋅x5 + 2⋅x7 l26: −2⋅x5 + 2⋅x7 l24: −2⋅x5 + 2⋅x7 l23: −2⋅x5 + 2⋅x7 l25: −2⋅x5 + 2⋅x7 l15: −2⋅x5 + 2⋅x7 l17: −2⋅x5 + 2⋅x7 l19: −2⋅x5 + 2⋅x7 l20: −2⋅x5 + 2⋅x7

### 2.2.3 Transition Removal

We remove transition 25 using the following ranking functions, which are bounded by 0.

 l5: −1 − x3 − x5 − 2⋅x6 + 4⋅x7 l27: −1 − x3 − x5 − 2⋅x6 + 4⋅x7 l4: −2 − x3 − x5 − 2⋅x6 + 4⋅x7 l6: −2 − x3 − x5 − 2⋅x6 + 4⋅x7 l7: −2 − x3 − x5 − 2⋅x6 + 4⋅x7 l8: −2 − x3 − x5 − 2⋅x6 + 4⋅x7 l9: −5 − x3 + 2⋅x5 − 2⋅x6 + x7 l10: −5 − x3 + 2⋅x5 − 2⋅x6 + x7 l11: −5 − x3 + 2⋅x5 − 2⋅x6 + x7 l14: −3 − x3 + 2⋅x5 − 2⋅x6 + x7 l12: −5 − x3 + 2⋅x5 − 2⋅x6 + x7 l13: −3 − x3 + 2⋅x5 − 2⋅x6 + x7 l21: −4 + 2⋅x5 − 2⋅x6 l16: −4 + 2⋅x5 − 2⋅x6 l26: −4 + 2⋅x5 − 2⋅x6 l24: −4 + 2⋅x5 − 2⋅x6 l23: −4 + 2⋅x5 − 2⋅x6 l25: −4 + 2⋅x5 − 2⋅x6 l15: −4 + 2⋅x5 − 2⋅x6 l17: −4 + 2⋅x5 − 2⋅x6 l19: 11 l20: 11

### 2.2.4 Transition Removal

We remove transition 26 using the following ranking functions, which are bounded by 0.

 l5: −4 − x1 − 5⋅x3 − 2⋅x5 − x6 + x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l27: −4 − x1 − 5⋅x3 − 2⋅x5 − x6 + x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l4: −6 − x1 − 5⋅x3 − 2⋅x5 − x6 + x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l6: −6 − x1 − 5⋅x3 − 2⋅x5 − x6 + x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l7: −1 − x1 − 5⋅x3 − 2⋅x5 − x6 + x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l8: −1 − x1 − 5⋅x3 − 2⋅x5 − x6 + x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l9: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l10: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l11: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l14: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l12: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l13: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l21: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l16: −4 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l26: −4 − x3 − 3⋅x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l24: −4 − x3 − 3⋅x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l23: −5 − x3 − 3⋅x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l25: −4 − x3 − 3⋅x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l15: −9 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l17: −9 − x1 − 5⋅x3 + x5 − x6 − 2⋅x7 + 2⋅x9 + 3⋅x10 + 4⋅x11 l20: −1 + x5 − x6 l19: −1 + x5 − x6

### 2.2.5 Transition Removal

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

 l5: −2 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l27: −2 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l4: −5 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l6: −5 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l7: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l8: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l9: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l10: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l11: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l14: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l12: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l13: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l21: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l16: −4 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l26: −4 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l24: −3 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l23: −4 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l25: −4 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l15: −5 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l17: −5 − x1 − x3 − 3⋅x5 − 3⋅x6 + 2⋅x7 + 3⋅x9 + 4⋅x10 + 5⋅x11 l20: 0 l19: −1

### 2.2.6 Transition Removal

We remove transitions 40, 4, 5, 8, 10 using the following ranking functions, which are bounded by 0.

 l5: 0 l27: −1 l4: 1 l6: 2 l7: 2 l8: 3 l9: −1 + 5⋅x5 − 5⋅x7 l10: −1 + 5⋅x5 − 5⋅x7 l11: −1 + 5⋅x5 − 5⋅x7 l14: −1 + 5⋅x5 − 5⋅x7 l12: −1 + 5⋅x5 − 5⋅x7 l13: −1 + 5⋅x5 − 5⋅x7 l21: −1 + 5⋅x5 − 5⋅x7 l16: −1 + 5⋅x5 − 5⋅x7 l26: −1 + 5⋅x5 − 5⋅x7 l24: −1 + 5⋅x5 − 5⋅x7 l23: −1 + 5⋅x5 − 5⋅x7 l25: −1 + 5⋅x5 − 5⋅x7 l15: −1 + 5⋅x5 − 5⋅x7 l17: −1 + 5⋅x5 − 5⋅x7

### 2.2.7 Transition Removal

We remove transitions 12, 13, 17, 14, 19, 18, 28, 31, 35, 20, 22, 21 using the following ranking functions, which are bounded by 0.

 l7: −1 + 8⋅x1 + 9⋅x2 − x3 + 10⋅x4 + 11⋅x5 + 12⋅x6 + 13⋅x7 + 14⋅x8 + 15⋅x9 + 16⋅x10 + 17⋅x11 l6: −1 + 8⋅x1 + 9⋅x2 − x3 + 10⋅x4 + 11⋅x5 + 12⋅x6 + 13⋅x7 + 14⋅x8 + 15⋅x9 + 16⋅x10 + 17⋅x11 l10: 0 l9: −1 l11: 1 l14: 3 l12: 2 l13: 2 l21: 4 l16: 5 l26: 6 l24: 6 l23: 6 l25: 6 l15: 6 l17: 7

### 2.2.8 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by 0.

 l7: −1 + 2⋅x1 + 3⋅x2 − x3 + 4⋅x4 + 5⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 11⋅x11 l6: −1 + 2⋅x1 + 3⋅x2 − x3 + 4⋅x4 + 5⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 11⋅x11 l13: − x6 + x7 l12: − x6 + x7 l24: −1 + 12⋅x1 + 13⋅x2 − 2⋅x3 + 14⋅x4 + x5 + 15⋅x7 + 16⋅x9 + 17⋅x10 + 18⋅x11 l26: −3 + 12⋅x1 + 13⋅x2 − 2⋅x3 + 14⋅x4 + x5 + 15⋅x7 + 16⋅x9 + 17⋅x10 + 18⋅x11 l23: −3 + 12⋅x1 + 13⋅x2 − 2⋅x3 + 14⋅x4 + x5 + 15⋅x7 + 16⋅x9 + 17⋅x10 + 18⋅x11 l25: −3 + 12⋅x1 + 13⋅x2 − 2⋅x3 + 14⋅x4 + x5 + 15⋅x7 + 16⋅x9 + 17⋅x10 + 18⋅x11

### 2.2.9 Transition Removal

We remove transitions 16, 36 using the following ranking functions, which are bounded by 0.

 l7: −1 + 2⋅x1 + 3⋅x2 − x3 + 4⋅x4 + 5⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 11⋅x11 l6: −2 + 2⋅x1 + 3⋅x2 − x3 + 4⋅x4 + 5⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 11⋅x11 l13: 1 l12: 0 l24: −1 − x3 + x5 l26: −1 − x3 + x5 l23: −2 − x3 + x5 l25: −2 − x3 + x5

### 2.2.10 Transition Removal

We remove transition 33 using the following ranking functions, which are bounded by 0.

 l7: −1 + 2⋅x1 + 3⋅x2 − x3 + 4⋅x4 + 5⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 11⋅x11 l6: −2 + 2⋅x1 + 3⋅x2 − x3 + 4⋅x4 + 5⋅x5 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9 + 10⋅x10 + 11⋅x11 l24: −2 + x3 − x6 l26: −2 + x3 − x6 l23: −1 + x3 − x6 l25: −1 + x3 − x6

### 2.2.11 Transition Removal

We remove transitions 37, 32, 34 using the following ranking functions, which are bounded by 0.

 l7: −1 + 3⋅x1 + 4⋅x2 − x3 + 5⋅x4 + 6⋅x5 + 7⋅x6 + 8⋅x7 + 9⋅x8 + 10⋅x9 + 11⋅x10 + 12⋅x11 l6: −2 + 3⋅x1 + 4⋅x2 − x3 + 5⋅x4 + 6⋅x5 + 7⋅x6 + 8⋅x7 + 9⋅x8 + 10⋅x9 + 11⋅x10 + 12⋅x11 l24: 0 l26: −1 l23: 1 l25: 2

### 2.2.12 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by 0.

 l7: −2⋅x3 + 2⋅x7 + 1 l6: −2⋅x3 + 2⋅x7

### 2.2.13 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 0.

 l7: 0 l6: −1

### 2.2.14 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 % (24 real / 0 unknown / 0 assumptions / 24 total proof steps)