# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l22, l1, l13, l18, l17, l21, l9, l14, l25, l8, l27, l0, l12, l19, l26, l7, l24, l11, l3, l20, l28, l2, l23, l4, l10, l29, l15, l16
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _chkerrHAT0 ∧ x2 = _i9HAT0 ∧ x3 = _iHAT0 ∧ x4 = _j10HAT0 ∧ x5 = _jHAT0 ∧ x6 = _k11HAT0 ∧ x7 = _n8HAT0 ∧ x8 = _nHAT0 ∧ x9 = _nmax7HAT0 ∧ x10 = _nmaxHAT0 ∧ x11 = _ret_ludcmp14HAT0 ∧ x12 = _w12HAT0 ∧ x13 = _wHAT0 ∧ x1 = _chkerrHATpost ∧ x2 = _i9HATpost ∧ x3 = _iHATpost ∧ x4 = _j10HATpost ∧ x5 = _jHATpost ∧ x6 = _k11HATpost ∧ x7 = _n8HATpost ∧ x8 = _nHATpost ∧ x9 = _nmax7HATpost ∧ x10 = _nmaxHATpost ∧ x11 = _ret_ludcmp14HATpost ∧ x12 = _w12HATpost ∧ x13 = _wHATpost ∧ _w12HAT0 = _w12HATpost ∧ _wHAT0 = _wHATpost ∧ _ret_ludcmp14HAT0 = _ret_ludcmp14HATpost ∧ _nmax7HAT0 = _nmax7HATpost ∧ _nmaxHAT0 = _nmaxHATpost ∧ _n8HAT0 = _n8HATpost ∧ _nHAT0 = _nHATpost ∧ _k11HAT0 = _k11HATpost ∧ _j10HAT0 = _j10HATpost ∧ _jHAT0 = _jHATpost ∧ _i9HAT0 = _i9HATpost ∧ _iHAT0 = _iHATpost ∧ _chkerrHAT0 = _chkerrHATpost l2 2 l3: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x10 = _x9 ∧ x11 = _x10 ∧ x12 = _x11 ∧ x13 = _x12 ∧ x1 = _x13 ∧ x2 = _x14 ∧ x3 = _x15 ∧ x4 = _x16 ∧ x5 = _x17 ∧ x6 = _x18 ∧ x7 = _x19 ∧ x8 = _x20 ∧ x9 = _x21 ∧ x10 = _x22 ∧ x11 = _x23 ∧ x12 = _x24 ∧ x13 = _x25 ∧ _x11 = _x24 ∧ _x12 = _x25 ∧ _x10 = _x23 ∧ _x8 = _x21 ∧ _x9 = _x22 ∧ _x6 = _x19 ∧ _x7 = _x20 ∧ _x5 = _x18 ∧ _x3 = _x16 ∧ _x4 = _x17 ∧ _x2 = _x15 ∧ _x = _x13 ∧ _x14 = −1 + _x1 ∧ 1 + _x6 ≤ _x3 l2 3 l4: x1 = _x26 ∧ x2 = _x27 ∧ x3 = _x28 ∧ x4 = _x29 ∧ x5 = _x30 ∧ x6 = _x31 ∧ x7 = _x32 ∧ x8 = _x33 ∧ x9 = _x34 ∧ x10 = _x35 ∧ x11 = _x36 ∧ x12 = _x37 ∧ x13 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ x4 = _x42 ∧ x5 = _x43 ∧ x6 = _x44 ∧ x7 = _x45 ∧ x8 = _x46 ∧ x9 = _x47 ∧ x10 = _x48 ∧ x11 = _x49 ∧ x12 = _x50 ∧ x13 = _x51 ∧ _x38 = _x51 ∧ _x36 = _x49 ∧ _x34 = _x47 ∧ _x35 = _x48 ∧ _x32 = _x45 ∧ _x33 = _x46 ∧ _x31 = _x44 ∧ _x30 = _x43 ∧ _x27 = _x40 ∧ _x28 = _x41 ∧ _x26 = _x39 ∧ _x42 = 1 + _x29 ∧ _x50 = _x50 ∧ _x29 ≤ _x32 l5 4 l6: x1 = _x52 ∧ x2 = _x53 ∧ x3 = _x54 ∧ x4 = _x55 ∧ x5 = _x56 ∧ x6 = _x57 ∧ x7 = _x58 ∧ x8 = _x59 ∧ x9 = _x60 ∧ x10 = _x61 ∧ x11 = _x62 ∧ x12 = _x63 ∧ x13 = _x64 ∧ x1 = _x65 ∧ x2 = _x66 ∧ x3 = _x67 ∧ x4 = _x68 ∧ x5 = _x69 ∧ x6 = _x70 ∧ x7 = _x71 ∧ x8 = _x72 ∧ x9 = _x73 ∧ x10 = _x74 ∧ x11 = _x75 ∧ x12 = _x76 ∧ x13 = _x77 ∧ _x63 = _x76 ∧ _x64 = _x77 ∧ _x60 = _x73 ∧ _x61 = _x74 ∧ _x58 = _x71 ∧ _x59 = _x72 ∧ _x57 = _x70 ∧ _x55 = _x68 ∧ _x56 = _x69 ∧ _x53 = _x66 ∧ _x54 = _x67 ∧ _x65 = _x75 ∧ _x75 = 0 ∧ 1 + _x53 ≤ 0 l5 5 l4: x1 = _x78 ∧ x2 = _x79 ∧ x3 = _x80 ∧ x4 = _x81 ∧ x5 = _x82 ∧ x6 = _x83 ∧ x7 = _x84 ∧ x8 = _x85 ∧ x9 = _x86 ∧ x10 = _x87 ∧ x11 = _x88 ∧ x12 = _x89 ∧ x13 = _x90 ∧ x1 = _x91 ∧ x2 = _x92 ∧ x3 = _x93 ∧ x4 = _x94 ∧ x5 = _x95 ∧ x6 = _x96 ∧ x7 = _x97 ∧ x8 = _x98 ∧ x9 = _x99 ∧ x10 = _x100 ∧ x11 = _x101 ∧ x12 = _x102 ∧ x13 = _x103 ∧ _x90 = _x103 ∧ _x88 = _x101 ∧ _x86 = _x99 ∧ _x87 = _x100 ∧ _x84 = _x97 ∧ _x85 = _x98 ∧ _x83 = _x96 ∧ _x82 = _x95 ∧ _x79 = _x92 ∧ _x80 = _x93 ∧ _x78 = _x91 ∧ _x94 = 1 + _x79 ∧ _x102 = _x102 ∧ 0 ≤ _x79 l7 6 l8: x1 = _x104 ∧ x2 = _x105 ∧ x3 = _x106 ∧ x4 = _x107 ∧ x5 = _x108 ∧ x6 = _x109 ∧ x7 = _x110 ∧ x8 = _x111 ∧ x9 = _x112 ∧ x10 = _x113 ∧ x11 = _x114 ∧ x12 = _x115 ∧ x13 = _x116 ∧ x1 = _x117 ∧ x2 = _x118 ∧ x3 = _x119 ∧ x4 = _x120 ∧ x5 = _x121 ∧ x6 = _x122 ∧ x7 = _x123 ∧ x8 = _x124 ∧ x9 = _x125 ∧ x10 = _x126 ∧ x11 = _x127 ∧ x12 = _x128 ∧ x13 = _x129 ∧ _x115 = _x128 ∧ _x116 = _x129 ∧ _x114 = _x127 ∧ _x112 = _x125 ∧ _x113 = _x126 ∧ _x110 = _x123 ∧ _x111 = _x124 ∧ _x109 = _x122 ∧ _x107 = _x120 ∧ _x108 = _x121 ∧ _x105 = _x118 ∧ _x106 = _x119 ∧ _x104 = _x117 l9 7 l10: x1 = _x130 ∧ x2 = _x131 ∧ x3 = _x132 ∧ x4 = _x133 ∧ x5 = _x134 ∧ x6 = _x135 ∧ x7 = _x136 ∧ x8 = _x137 ∧ x9 = _x138 ∧ x10 = _x139 ∧ x11 = _x140 ∧ x12 = _x141 ∧ x13 = _x142 ∧ x1 = _x143 ∧ x2 = _x144 ∧ x3 = _x145 ∧ x4 = _x146 ∧ x5 = _x147 ∧ x6 = _x148 ∧ x7 = _x149 ∧ x8 = _x150 ∧ x9 = _x151 ∧ x10 = _x152 ∧ x11 = _x153 ∧ x12 = _x154 ∧ x13 = _x155 ∧ _x141 = _x154 ∧ _x142 = _x155 ∧ _x140 = _x153 ∧ _x138 = _x151 ∧ _x139 = _x152 ∧ _x136 = _x149 ∧ _x137 = _x150 ∧ _x135 = _x148 ∧ _x133 = _x146 ∧ _x134 = _x147 ∧ _x132 = _x145 ∧ _x130 = _x143 ∧ _x144 = 1 + _x131 ∧ _x131 ≤ _x133 l9 8 l11: x1 = _x156 ∧ x2 = _x157 ∧ x3 = _x158 ∧ x4 = _x159 ∧ x5 = _x160 ∧ x6 = _x161 ∧ x7 = _x162 ∧ x8 = _x163 ∧ x9 = _x164 ∧ x10 = _x165 ∧ x11 = _x166 ∧ x12 = _x167 ∧ x13 = _x168 ∧ x1 = _x169 ∧ x2 = _x170 ∧ x3 = _x171 ∧ x4 = _x172 ∧ x5 = _x173 ∧ x6 = _x174 ∧ x7 = _x175 ∧ x8 = _x176 ∧ x9 = _x177 ∧ x10 = _x178 ∧ x11 = _x179 ∧ x12 = _x180 ∧ x13 = _x181 ∧ _x168 = _x181 ∧ _x166 = _x179 ∧ _x164 = _x177 ∧ _x165 = _x178 ∧ _x162 = _x175 ∧ _x163 = _x176 ∧ _x161 = _x174 ∧ _x160 = _x173 ∧ _x157 = _x170 ∧ _x158 = _x171 ∧ _x156 = _x169 ∧ _x172 = 1 + _x159 ∧ _x180 = _x180 ∧ 1 + _x159 ≤ _x157 l12 9 l13: x1 = _x182 ∧ x2 = _x183 ∧ x3 = _x184 ∧ x4 = _x185 ∧ x5 = _x186 ∧ x6 = _x187 ∧ x7 = _x188 ∧ x8 = _x189 ∧ x9 = _x190 ∧ x10 = _x191 ∧ x11 = _x192 ∧ x12 = _x193 ∧ x13 = _x194 ∧ x1 = _x195 ∧ x2 = _x196 ∧ x3 = _x197 ∧ x4 = _x198 ∧ x5 = _x199 ∧ x6 = _x200 ∧ x7 = _x201 ∧ x8 = _x202 ∧ x9 = _x203 ∧ x10 = _x204 ∧ x11 = _x205 ∧ x12 = _x206 ∧ x13 = _x207 ∧ _x193 = _x206 ∧ _x194 = _x207 ∧ _x192 = _x205 ∧ _x190 = _x203 ∧ _x191 = _x204 ∧ _x188 = _x201 ∧ _x189 = _x202 ∧ _x187 = _x200 ∧ _x185 = _x198 ∧ _x186 = _x199 ∧ _x183 = _x196 ∧ _x184 = _x197 ∧ _x182 = _x195 l14 10 l3: x1 = _x208 ∧ x2 = _x209 ∧ x3 = _x210 ∧ x4 = _x211 ∧ x5 = _x212 ∧ x6 = _x213 ∧ x7 = _x214 ∧ x8 = _x215 ∧ x9 = _x216 ∧ x10 = _x217 ∧ x11 = _x218 ∧ x12 = _x219 ∧ x13 = _x220 ∧ x1 = _x221 ∧ x2 = _x222 ∧ x3 = _x223 ∧ x4 = _x224 ∧ x5 = _x225 ∧ x6 = _x226 ∧ x7 = _x227 ∧ x8 = _x228 ∧ x9 = _x229 ∧ x10 = _x230 ∧ x11 = _x231 ∧ x12 = _x232 ∧ x13 = _x233 ∧ _x219 = _x232 ∧ _x220 = _x233 ∧ _x218 = _x231 ∧ _x216 = _x229 ∧ _x217 = _x230 ∧ _x214 = _x227 ∧ _x215 = _x228 ∧ _x213 = _x226 ∧ _x211 = _x224 ∧ _x212 = _x225 ∧ _x210 = _x223 ∧ _x208 = _x221 ∧ _x222 = −1 + _x214 ∧ 1 + _x214 ≤ _x209 l14 11 l11: x1 = _x234 ∧ x2 = _x235 ∧ x3 = _x236 ∧ x4 = _x237 ∧ x5 = _x238 ∧ x6 = _x239 ∧ x7 = _x240 ∧ x8 = _x241 ∧ x9 = _x242 ∧ x10 = _x243 ∧ x11 = _x244 ∧ x12 = _x245 ∧ x13 = _x246 ∧ x1 = _x247 ∧ x2 = _x248 ∧ x3 = _x249 ∧ x4 = _x250 ∧ x5 = _x251 ∧ x6 = _x252 ∧ x7 = _x253 ∧ x8 = _x254 ∧ x9 = _x255 ∧ x10 = _x256 ∧ x11 = _x257 ∧ x12 = _x258 ∧ x13 = _x259 ∧ _x246 = _x259 ∧ _x244 = _x257 ∧ _x242 = _x255 ∧ _x243 = _x256 ∧ _x240 = _x253 ∧ _x241 = _x254 ∧ _x239 = _x252 ∧ _x238 = _x251 ∧ _x235 = _x248 ∧ _x236 = _x249 ∧ _x234 = _x247 ∧ _x250 = 0 ∧ _x258 = _x258 ∧ _x235 ≤ _x240 l15 12 l16: x1 = _x260 ∧ x2 = _x261 ∧ x3 = _x262 ∧ x4 = _x263 ∧ x5 = _x264 ∧ x6 = _x265 ∧ x7 = _x266 ∧ x8 = _x267 ∧ x9 = _x268 ∧ x10 = _x269 ∧ x11 = _x270 ∧ x12 = _x271 ∧ x13 = _x272 ∧ x1 = _x273 ∧ x2 = _x274 ∧ x3 = _x275 ∧ x4 = _x276 ∧ x5 = _x277 ∧ x6 = _x278 ∧ x7 = _x279 ∧ x8 = _x280 ∧ x9 = _x281 ∧ x10 = _x282 ∧ x11 = _x283 ∧ x12 = _x284 ∧ x13 = _x285 ∧ _x271 = _x284 ∧ _x272 = _x285 ∧ _x270 = _x283 ∧ _x268 = _x281 ∧ _x269 = _x282 ∧ _x266 = _x279 ∧ _x267 = _x280 ∧ _x265 = _x278 ∧ _x263 = _x276 ∧ _x264 = _x277 ∧ _x261 = _x274 ∧ _x262 = _x275 ∧ _x260 = _x273 l16 13 l12: x1 = _x286 ∧ x2 = _x287 ∧ x3 = _x288 ∧ x4 = _x289 ∧ x5 = _x290 ∧ x6 = _x291 ∧ x7 = _x292 ∧ x8 = _x293 ∧ x9 = _x294 ∧ x10 = _x295 ∧ x11 = _x296 ∧ x12 = _x297 ∧ x13 = _x298 ∧ x1 = _x299 ∧ x2 = _x300 ∧ x3 = _x301 ∧ x4 = _x302 ∧ x5 = _x303 ∧ x6 = _x304 ∧ x7 = _x305 ∧ x8 = _x306 ∧ x9 = _x307 ∧ x10 = _x308 ∧ x11 = _x309 ∧ x12 = _x310 ∧ x13 = _x311 ∧ _x297 = _x310 ∧ _x298 = _x311 ∧ _x296 = _x309 ∧ _x294 = _x307 ∧ _x295 = _x308 ∧ _x292 = _x305 ∧ _x293 = _x306 ∧ _x291 = _x304 ∧ _x290 = _x303 ∧ _x287 = _x300 ∧ _x288 = _x301 ∧ _x286 = _x299 ∧ _x302 = 1 + _x289 ∧ 1 + _x287 ≤ _x291 l16 14 l15: x1 = _x312 ∧ x2 = _x313 ∧ x3 = _x314 ∧ x4 = _x315 ∧ x5 = _x316 ∧ x6 = _x317 ∧ x7 = _x318 ∧ x8 = _x319 ∧ x9 = _x320 ∧ x10 = _x321 ∧ x11 = _x322 ∧ x12 = _x323 ∧ x13 = _x324 ∧ x1 = _x325 ∧ x2 = _x326 ∧ x3 = _x327 ∧ x4 = _x328 ∧ x5 = _x329 ∧ x6 = _x330 ∧ x7 = _x331 ∧ x8 = _x332 ∧ x9 = _x333 ∧ x10 = _x334 ∧ x11 = _x335 ∧ x12 = _x336 ∧ x13 = _x337 ∧ _x324 = _x337 ∧ _x322 = _x335 ∧ _x320 = _x333 ∧ _x321 = _x334 ∧ _x318 = _x331 ∧ _x319 = _x332 ∧ _x315 = _x328 ∧ _x316 = _x329 ∧ _x313 = _x326 ∧ _x314 = _x327 ∧ _x312 = _x325 ∧ _x330 = 1 + _x317 ∧ _x336 = _x336 ∧ _x317 ≤ _x313 l13 15 l17: x1 = _x338 ∧ x2 = _x339 ∧ x3 = _x340 ∧ x4 = _x341 ∧ x5 = _x342 ∧ x6 = _x343 ∧ x7 = _x344 ∧ x8 = _x345 ∧ x9 = _x346 ∧ x10 = _x347 ∧ x11 = _x348 ∧ x12 = _x349 ∧ x13 = _x350 ∧ x1 = _x351 ∧ x2 = _x352 ∧ x3 = _x353 ∧ x4 = _x354 ∧ x5 = _x355 ∧ x6 = _x356 ∧ x7 = _x357 ∧ x8 = _x358 ∧ x9 = _x359 ∧ x10 = _x360 ∧ x11 = _x361 ∧ x12 = _x362 ∧ x13 = _x363 ∧ _x349 = _x362 ∧ _x350 = _x363 ∧ _x348 = _x361 ∧ _x346 = _x359 ∧ _x347 = _x360 ∧ _x344 = _x357 ∧ _x345 = _x358 ∧ _x343 = _x356 ∧ _x341 = _x354 ∧ _x342 = _x355 ∧ _x340 = _x353 ∧ _x338 = _x351 ∧ _x352 = 1 + _x339 ∧ 1 + _x344 ≤ _x341 l13 16 l15: x1 = _x364 ∧ x2 = _x365 ∧ x3 = _x366 ∧ x4 = _x367 ∧ x5 = _x368 ∧ x6 = _x369 ∧ x7 = _x370 ∧ x8 = _x371 ∧ x9 = _x372 ∧ x10 = _x373 ∧ x11 = _x374 ∧ x12 = _x375 ∧ x13 = _x376 ∧ x1 = _x377 ∧ x2 = _x378 ∧ x3 = _x379 ∧ x4 = _x380 ∧ x5 = _x381 ∧ x6 = _x382 ∧ x7 = _x383 ∧ x8 = _x384 ∧ x9 = _x385 ∧ x10 = _x386 ∧ x11 = _x387 ∧ x12 = _x388 ∧ x13 = _x389 ∧ _x376 = _x389 ∧ _x374 = _x387 ∧ _x372 = _x385 ∧ _x373 = _x386 ∧ _x370 = _x383 ∧ _x371 = _x384 ∧ _x367 = _x380 ∧ _x368 = _x381 ∧ _x365 = _x378 ∧ _x366 = _x379 ∧ _x364 = _x377 ∧ _x382 = 0 ∧ _x388 = _x388 ∧ _x367 ≤ _x370 l10 17 l14: x1 = _x390 ∧ x2 = _x391 ∧ x3 = _x392 ∧ x4 = _x393 ∧ x5 = _x394 ∧ x6 = _x395 ∧ x7 = _x396 ∧ x8 = _x397 ∧ x9 = _x398 ∧ x10 = _x399 ∧ x11 = _x400 ∧ x12 = _x401 ∧ x13 = _x402 ∧ x1 = _x403 ∧ x2 = _x404 ∧ x3 = _x405 ∧ x4 = _x406 ∧ x5 = _x407 ∧ x6 = _x408 ∧ x7 = _x409 ∧ x8 = _x410 ∧ x9 = _x411 ∧ x10 = _x412 ∧ x11 = _x413 ∧ x12 = _x414 ∧ x13 = _x415 ∧ _x401 = _x414 ∧ _x402 = _x415 ∧ _x400 = _x413 ∧ _x398 = _x411 ∧ _x399 = _x412 ∧ _x396 = _x409 ∧ _x397 = _x410 ∧ _x395 = _x408 ∧ _x393 = _x406 ∧ _x394 = _x407 ∧ _x391 = _x404 ∧ _x392 = _x405 ∧ _x390 = _x403 l18 18 l0: x1 = _x416 ∧ x2 = _x417 ∧ x3 = _x418 ∧ x4 = _x419 ∧ x5 = _x420 ∧ x6 = _x421 ∧ x7 = _x422 ∧ x8 = _x423 ∧ x9 = _x424 ∧ x10 = _x425 ∧ x11 = _x426 ∧ x12 = _x427 ∧ x13 = _x428 ∧ x1 = _x429 ∧ x2 = _x430 ∧ x3 = _x431 ∧ x4 = _x432 ∧ x5 = _x433 ∧ x6 = _x434 ∧ x7 = _x435 ∧ x8 = _x436 ∧ x9 = _x437 ∧ x10 = _x438 ∧ x11 = _x439 ∧ x12 = _x440 ∧ x13 = _x441 ∧ _x427 = _x440 ∧ _x428 = _x441 ∧ _x426 = _x439 ∧ _x424 = _x437 ∧ _x425 = _x438 ∧ _x422 = _x435 ∧ _x423 = _x436 ∧ _x421 = _x434 ∧ _x420 = _x433 ∧ _x417 = _x430 ∧ _x418 = _x431 ∧ _x416 = _x429 ∧ _x432 = 1 + _x419 l8 19 l18: x1 = _x442 ∧ x2 = _x443 ∧ x3 = _x444 ∧ x4 = _x445 ∧ x5 = _x446 ∧ x6 = _x447 ∧ x7 = _x448 ∧ x8 = _x449 ∧ x9 = _x450 ∧ x10 = _x451 ∧ x11 = _x452 ∧ x12 = _x453 ∧ x13 = _x454 ∧ x1 = _x455 ∧ x2 = _x456 ∧ x3 = _x457 ∧ x4 = _x458 ∧ x5 = _x459 ∧ x6 = _x460 ∧ x7 = _x461 ∧ x8 = _x462 ∧ x9 = _x463 ∧ x10 = _x464 ∧ x11 = _x465 ∧ x12 = _x466 ∧ x13 = _x467 ∧ _x453 = _x466 ∧ _x454 = _x467 ∧ _x452 = _x465 ∧ _x450 = _x463 ∧ _x451 = _x464 ∧ _x448 = _x461 ∧ _x449 = _x462 ∧ _x447 = _x460 ∧ _x445 = _x458 ∧ _x446 = _x459 ∧ _x443 = _x456 ∧ _x444 = _x457 ∧ _x442 = _x455 ∧ _x443 ≤ _x447 l8 20 l7: x1 = _x468 ∧ x2 = _x469 ∧ x3 = _x470 ∧ x4 = _x471 ∧ x5 = _x472 ∧ x6 = _x473 ∧ x7 = _x474 ∧ x8 = _x475 ∧ x9 = _x476 ∧ x10 = _x477 ∧ x11 = _x478 ∧ x12 = _x479 ∧ x13 = _x480 ∧ x1 = _x481 ∧ x2 = _x482 ∧ x3 = _x483 ∧ x4 = _x484 ∧ x5 = _x485 ∧ x6 = _x486 ∧ x7 = _x487 ∧ x8 = _x488 ∧ x9 = _x489 ∧ x10 = _x490 ∧ x11 = _x491 ∧ x12 = _x492 ∧ x13 = _x493 ∧ _x480 = _x493 ∧ _x478 = _x491 ∧ _x476 = _x489 ∧ _x477 = _x490 ∧ _x474 = _x487 ∧ _x475 = _x488 ∧ _x471 = _x484 ∧ _x472 = _x485 ∧ _x469 = _x482 ∧ _x470 = _x483 ∧ _x468 = _x481 ∧ _x486 = 1 + _x473 ∧ _x492 = _x492 ∧ 1 + _x473 ≤ _x469 l19 21 l7: x1 = _x494 ∧ x2 = _x495 ∧ x3 = _x496 ∧ x4 = _x497 ∧ x5 = _x498 ∧ x6 = _x499 ∧ x7 = _x500 ∧ x8 = _x501 ∧ x9 = _x502 ∧ x10 = _x503 ∧ x11 = _x504 ∧ x12 = _x505 ∧ x13 = _x506 ∧ x1 = _x507 ∧ x2 = _x508 ∧ x3 = _x509 ∧ x4 = _x510 ∧ x5 = _x511 ∧ x6 = _x512 ∧ x7 = _x513 ∧ x8 = _x514 ∧ x9 = _x515 ∧ x10 = _x516 ∧ x11 = _x517 ∧ x12 = _x518 ∧ x13 = _x519 ∧ _x505 = _x518 ∧ _x506 = _x519 ∧ _x504 = _x517 ∧ _x502 = _x515 ∧ _x503 = _x516 ∧ _x500 = _x513 ∧ _x501 = _x514 ∧ _x497 = _x510 ∧ _x498 = _x511 ∧ _x495 = _x508 ∧ _x496 = _x509 ∧ _x494 = _x507 ∧ _x512 = 0 l11 22 l9: x1 = _x520 ∧ x2 = _x521 ∧ x3 = _x522 ∧ x4 = _x523 ∧ x5 = _x524 ∧ x6 = _x525 ∧ x7 = _x526 ∧ x8 = _x527 ∧ x9 = _x528 ∧ x10 = _x529 ∧ x11 = _x530 ∧ x12 = _x531 ∧ x13 = _x532 ∧ x1 = _x533 ∧ x2 = _x534 ∧ x3 = _x535 ∧ x4 = _x536 ∧ x5 = _x537 ∧ x6 = _x538 ∧ x7 = _x539 ∧ x8 = _x540 ∧ x9 = _x541 ∧ x10 = _x542 ∧ x11 = _x543 ∧ x12 = _x544 ∧ x13 = _x545 ∧ _x531 = _x544 ∧ _x532 = _x545 ∧ _x530 = _x543 ∧ _x528 = _x541 ∧ _x529 = _x542 ∧ _x526 = _x539 ∧ _x527 = _x540 ∧ _x525 = _x538 ∧ _x523 = _x536 ∧ _x524 = _x537 ∧ _x521 = _x534 ∧ _x522 = _x535 ∧ _x520 = _x533 l20 23 l18: x1 = _x546 ∧ x2 = _x547 ∧ x3 = _x548 ∧ x4 = _x549 ∧ x5 = _x550 ∧ x6 = _x551 ∧ x7 = _x552 ∧ x8 = _x553 ∧ x9 = _x554 ∧ x10 = _x555 ∧ x11 = _x556 ∧ x12 = _x557 ∧ x13 = _x558 ∧ x1 = _x559 ∧ x2 = _x560 ∧ x3 = _x561 ∧ x4 = _x562 ∧ x5 = _x563 ∧ x6 = _x564 ∧ x7 = _x565 ∧ x8 = _x566 ∧ x9 = _x567 ∧ x10 = _x568 ∧ x11 = _x569 ∧ x12 = _x570 ∧ x13 = _x571 ∧ _x557 = _x570 ∧ _x558 = _x571 ∧ _x556 = _x569 ∧ _x554 = _x567 ∧ _x555 = _x568 ∧ _x552 = _x565 ∧ _x553 = _x566 ∧ _x551 = _x564 ∧ _x549 = _x562 ∧ _x550 = _x563 ∧ _x547 = _x560 ∧ _x548 = _x561 ∧ _x546 = _x559 ∧ 0 ≤ _x547 ∧ _x547 ≤ 0 l20 24 l19: x1 = _x572 ∧ x2 = _x573 ∧ x3 = _x574 ∧ x4 = _x575 ∧ x5 = _x576 ∧ x6 = _x577 ∧ x7 = _x578 ∧ x8 = _x579 ∧ x9 = _x580 ∧ x10 = _x581 ∧ x11 = _x582 ∧ x12 = _x583 ∧ x13 = _x584 ∧ x1 = _x585 ∧ x2 = _x586 ∧ x3 = _x587 ∧ x4 = _x588 ∧ x5 = _x589 ∧ x6 = _x590 ∧ x7 = _x591 ∧ x8 = _x592 ∧ x9 = _x593 ∧ x10 = _x594 ∧ x11 = _x595 ∧ x12 = _x596 ∧ x13 = _x597 ∧ _x583 = _x596 ∧ _x584 = _x597 ∧ _x582 = _x595 ∧ _x580 = _x593 ∧ _x581 = _x594 ∧ _x578 = _x591 ∧ _x579 = _x592 ∧ _x577 = _x590 ∧ _x575 = _x588 ∧ _x576 = _x589 ∧ _x573 = _x586 ∧ _x574 = _x587 ∧ _x572 = _x585 ∧ 1 ≤ _x573 l20 25 l19: x1 = _x598 ∧ x2 = _x599 ∧ x3 = _x600 ∧ x4 = _x601 ∧ x5 = _x602 ∧ x6 = _x603 ∧ x7 = _x604 ∧ x8 = _x605 ∧ x9 = _x606 ∧ x10 = _x607 ∧ x11 = _x608 ∧ x12 = _x609 ∧ x13 = _x610 ∧ x1 = _x611 ∧ x2 = _x612 ∧ x3 = _x613 ∧ x4 = _x614 ∧ x5 = _x615 ∧ x6 = _x616 ∧ x7 = _x617 ∧ x8 = _x618 ∧ x9 = _x619 ∧ x10 = _x620 ∧ x11 = _x621 ∧ x12 = _x622 ∧ x13 = _x623 ∧ _x609 = _x622 ∧ _x610 = _x623 ∧ _x608 = _x621 ∧ _x606 = _x619 ∧ _x607 = _x620 ∧ _x604 = _x617 ∧ _x605 = _x618 ∧ _x603 = _x616 ∧ _x601 = _x614 ∧ _x602 = _x615 ∧ _x599 = _x612 ∧ _x600 = _x613 ∧ _x598 = _x611 ∧ 1 + _x599 ≤ 0 l1 26 l12: x1 = _x624 ∧ x2 = _x625 ∧ x3 = _x626 ∧ x4 = _x627 ∧ x5 = _x628 ∧ x6 = _x629 ∧ x7 = _x630 ∧ x8 = _x631 ∧ x9 = _x632 ∧ x10 = _x633 ∧ x11 = _x634 ∧ x12 = _x635 ∧ x13 = _x636 ∧ x1 = _x637 ∧ x2 = _x638 ∧ x3 = _x639 ∧ x4 = _x640 ∧ x5 = _x641 ∧ x6 = _x642 ∧ x7 = _x643 ∧ x8 = _x644 ∧ x9 = _x645 ∧ x10 = _x646 ∧ x11 = _x647 ∧ x12 = _x648 ∧ x13 = _x649 ∧ _x635 = _x648 ∧ _x636 = _x649 ∧ _x634 = _x647 ∧ _x632 = _x645 ∧ _x633 = _x646 ∧ _x630 = _x643 ∧ _x631 = _x644 ∧ _x629 = _x642 ∧ _x628 = _x641 ∧ _x625 = _x638 ∧ _x626 = _x639 ∧ _x624 = _x637 ∧ _x640 = 1 + _x625 ∧ 1 + _x630 ≤ _x627 l1 27 l20: x1 = _x650 ∧ x2 = _x651 ∧ x3 = _x652 ∧ x4 = _x653 ∧ x5 = _x654 ∧ x6 = _x655 ∧ x7 = _x656 ∧ x8 = _x657 ∧ x9 = _x658 ∧ x10 = _x659 ∧ x11 = _x660 ∧ x12 = _x661 ∧ x13 = _x662 ∧ x1 = _x663 ∧ x2 = _x664 ∧ x3 = _x665 ∧ x4 = _x666 ∧ x5 = _x667 ∧ x6 = _x668 ∧ x7 = _x669 ∧ x8 = _x670 ∧ x9 = _x671 ∧ x10 = _x672 ∧ x11 = _x673 ∧ x12 = _x674 ∧ x13 = _x675 ∧ _x662 = _x675 ∧ _x660 = _x673 ∧ _x658 = _x671 ∧ _x659 = _x672 ∧ _x656 = _x669 ∧ _x657 = _x670 ∧ _x655 = _x668 ∧ _x653 = _x666 ∧ _x654 = _x667 ∧ _x651 = _x664 ∧ _x652 = _x665 ∧ _x650 = _x663 ∧ _x674 = _x674 ∧ _x653 ≤ _x656 l21 28 l10: x1 = _x676 ∧ x2 = _x677 ∧ x3 = _x678 ∧ x4 = _x679 ∧ x5 = _x680 ∧ x6 = _x681 ∧ x7 = _x682 ∧ x8 = _x683 ∧ x9 = _x684 ∧ x10 = _x685 ∧ x11 = _x686 ∧ x12 = _x687 ∧ x13 = _x688 ∧ x1 = _x689 ∧ x2 = _x690 ∧ x3 = _x691 ∧ x4 = _x692 ∧ x5 = _x693 ∧ x6 = _x694 ∧ x7 = _x695 ∧ x8 = _x696 ∧ x9 = _x697 ∧ x10 = _x698 ∧ x11 = _x699 ∧ x12 = _x700 ∧ x13 = _x701 ∧ _x687 = _x700 ∧ _x688 = _x701 ∧ _x686 = _x699 ∧ _x684 = _x697 ∧ _x685 = _x698 ∧ _x682 = _x695 ∧ _x683 = _x696 ∧ _x681 = _x694 ∧ _x679 = _x692 ∧ _x680 = _x693 ∧ _x678 = _x691 ∧ _x676 = _x689 ∧ _x690 = 1 ∧ _x682 ≤ _x677 l21 29 l0: x1 = _x702 ∧ x2 = _x703 ∧ x3 = _x704 ∧ x4 = _x705 ∧ x5 = _x706 ∧ x6 = _x707 ∧ x7 = _x708 ∧ x8 = _x709 ∧ x9 = _x710 ∧ x10 = _x711 ∧ x11 = _x712 ∧ x12 = _x713 ∧ x13 = _x714 ∧ x1 = _x715 ∧ x2 = _x716 ∧ x3 = _x717 ∧ x4 = _x718 ∧ x5 = _x719 ∧ x6 = _x720 ∧ x7 = _x721 ∧ x8 = _x722 ∧ x9 = _x723 ∧ x10 = _x724 ∧ x11 = _x725 ∧ x12 = _x726 ∧ x13 = _x727 ∧ _x713 = _x726 ∧ _x714 = _x727 ∧ _x712 = _x725 ∧ _x710 = _x723 ∧ _x711 = _x724 ∧ _x708 = _x721 ∧ _x709 = _x722 ∧ _x707 = _x720 ∧ _x706 = _x719 ∧ _x703 = _x716 ∧ _x704 = _x717 ∧ _x702 = _x715 ∧ _x718 = 1 + _x703 ∧ 1 + _x703 ≤ _x708 l3 30 l5: x1 = _x728 ∧ x2 = _x729 ∧ x3 = _x730 ∧ x4 = _x731 ∧ x5 = _x732 ∧ x6 = _x733 ∧ x7 = _x734 ∧ x8 = _x735 ∧ x9 = _x736 ∧ x10 = _x737 ∧ x11 = _x738 ∧ x12 = _x739 ∧ x13 = _x740 ∧ x1 = _x741 ∧ x2 = _x742 ∧ x3 = _x743 ∧ x4 = _x744 ∧ x5 = _x745 ∧ x6 = _x746 ∧ x7 = _x747 ∧ x8 = _x748 ∧ x9 = _x749 ∧ x10 = _x750 ∧ x11 = _x751 ∧ x12 = _x752 ∧ x13 = _x753 ∧ _x739 = _x752 ∧ _x740 = _x753 ∧ _x738 = _x751 ∧ _x736 = _x749 ∧ _x737 = _x750 ∧ _x734 = _x747 ∧ _x735 = _x748 ∧ _x733 = _x746 ∧ _x731 = _x744 ∧ _x732 = _x745 ∧ _x729 = _x742 ∧ _x730 = _x743 ∧ _x728 = _x741 l22 31 l23: x1 = _x754 ∧ x2 = _x755 ∧ x3 = _x756 ∧ x4 = _x757 ∧ x5 = _x758 ∧ x6 = _x759 ∧ x7 = _x760 ∧ x8 = _x761 ∧ x9 = _x762 ∧ x10 = _x763 ∧ x11 = _x764 ∧ x12 = _x765 ∧ x13 = _x766 ∧ x1 = _x767 ∧ x2 = _x768 ∧ x3 = _x769 ∧ x4 = _x770 ∧ x5 = _x771 ∧ x6 = _x772 ∧ x7 = _x773 ∧ x8 = _x774 ∧ x9 = _x775 ∧ x10 = _x776 ∧ x11 = _x777 ∧ x12 = _x778 ∧ x13 = _x779 ∧ _x765 = _x778 ∧ _x764 = _x777 ∧ _x762 = _x775 ∧ _x763 = _x776 ∧ _x760 = _x773 ∧ _x761 = _x774 ∧ _x759 = _x772 ∧ _x757 = _x770 ∧ _x755 = _x768 ∧ _x756 = _x769 ∧ _x754 = _x767 ∧ _x771 = 1 + _x758 ∧ _x779 = _x779 l24 32 l22: x1 = _x780 ∧ x2 = _x781 ∧ x3 = _x782 ∧ x4 = _x783 ∧ x5 = _x784 ∧ x6 = _x785 ∧ x7 = _x786 ∧ x8 = _x787 ∧ x9 = _x788 ∧ x10 = _x789 ∧ x11 = _x790 ∧ x12 = _x791 ∧ x13 = _x792 ∧ x1 = _x793 ∧ x2 = _x794 ∧ x3 = _x795 ∧ x4 = _x796 ∧ x5 = _x797 ∧ x6 = _x798 ∧ x7 = _x799 ∧ x8 = _x800 ∧ x9 = _x801 ∧ x10 = _x802 ∧ x11 = _x803 ∧ x12 = _x804 ∧ x13 = _x805 ∧ _x791 = _x804 ∧ _x792 = _x805 ∧ _x790 = _x803 ∧ _x788 = _x801 ∧ _x789 = _x802 ∧ _x786 = _x799 ∧ _x787 = _x800 ∧ _x785 = _x798 ∧ _x783 = _x796 ∧ _x784 = _x797 ∧ _x781 = _x794 ∧ _x782 = _x795 ∧ _x780 = _x793 ∧ 1 + _x784 ≤ _x782 l24 33 l22: x1 = _x806 ∧ x2 = _x807 ∧ x3 = _x808 ∧ x4 = _x809 ∧ x5 = _x810 ∧ x6 = _x811 ∧ x7 = _x812 ∧ x8 = _x813 ∧ x9 = _x814 ∧ x10 = _x815 ∧ x11 = _x816 ∧ x12 = _x817 ∧ x13 = _x818 ∧ x1 = _x819 ∧ x2 = _x820 ∧ x3 = _x821 ∧ x4 = _x822 ∧ x5 = _x823 ∧ x6 = _x824 ∧ x7 = _x825 ∧ x8 = _x826 ∧ x9 = _x827 ∧ x10 = _x828 ∧ x11 = _x829 ∧ x12 = _x830 ∧ x13 = _x831 ∧ _x817 = _x830 ∧ _x818 = _x831 ∧ _x816 = _x829 ∧ _x814 = _x827 ∧ _x815 = _x828 ∧ _x812 = _x825 ∧ _x813 = _x826 ∧ _x811 = _x824 ∧ _x809 = _x822 ∧ _x810 = _x823 ∧ _x807 = _x820 ∧ _x808 = _x821 ∧ _x806 = _x819 ∧ 1 + _x808 ≤ _x810 l24 34 l22: x1 = _x832 ∧ x2 = _x833 ∧ x3 = _x834 ∧ x4 = _x835 ∧ x5 = _x836 ∧ x6 = _x837 ∧ x7 = _x838 ∧ x8 = _x839 ∧ x9 = _x840 ∧ x10 = _x841 ∧ x11 = _x842 ∧ x12 = _x843 ∧ x13 = _x844 ∧ x1 = _x845 ∧ x2 = _x846 ∧ x3 = _x847 ∧ x4 = _x848 ∧ x5 = _x849 ∧ x6 = _x850 ∧ x7 = _x851 ∧ x8 = _x852 ∧ x9 = _x853 ∧ x10 = _x854 ∧ x11 = _x855 ∧ x12 = _x856 ∧ x13 = _x857 ∧ _x843 = _x856 ∧ _x844 = _x857 ∧ _x842 = _x855 ∧ _x840 = _x853 ∧ _x841 = _x854 ∧ _x838 = _x851 ∧ _x839 = _x852 ∧ _x837 = _x850 ∧ _x835 = _x848 ∧ _x836 = _x849 ∧ _x833 = _x846 ∧ _x834 = _x847 ∧ _x832 = _x845 ∧ _x836 ≤ _x834 ∧ _x834 ≤ _x836 l4 35 l2: x1 = _x858 ∧ x2 = _x859 ∧ x3 = _x860 ∧ x4 = _x861 ∧ x5 = _x862 ∧ x6 = _x863 ∧ x7 = _x864 ∧ x8 = _x865 ∧ x9 = _x866 ∧ x10 = _x867 ∧ x11 = _x868 ∧ x12 = _x869 ∧ x13 = _x870 ∧ x1 = _x871 ∧ x2 = _x872 ∧ x3 = _x873 ∧ x4 = _x874 ∧ x5 = _x875 ∧ x6 = _x876 ∧ x7 = _x877 ∧ x8 = _x878 ∧ x9 = _x879 ∧ x10 = _x880 ∧ x11 = _x881 ∧ x12 = _x882 ∧ x13 = _x883 ∧ _x869 = _x882 ∧ _x870 = _x883 ∧ _x868 = _x881 ∧ _x866 = _x879 ∧ _x867 = _x880 ∧ _x864 = _x877 ∧ _x865 = _x878 ∧ _x863 = _x876 ∧ _x861 = _x874 ∧ _x862 = _x875 ∧ _x859 = _x872 ∧ _x860 = _x873 ∧ _x858 = _x871 l25 36 l26: x1 = _x884 ∧ x2 = _x885 ∧ x3 = _x886 ∧ x4 = _x887 ∧ x5 = _x888 ∧ x6 = _x889 ∧ x7 = _x890 ∧ x8 = _x891 ∧ x9 = _x892 ∧ x10 = _x893 ∧ x11 = _x894 ∧ x12 = _x895 ∧ x13 = _x896 ∧ x1 = _x897 ∧ x2 = _x898 ∧ x3 = _x899 ∧ x4 = _x900 ∧ x5 = _x901 ∧ x6 = _x902 ∧ x7 = _x903 ∧ x8 = _x904 ∧ x9 = _x905 ∧ x10 = _x906 ∧ x11 = _x907 ∧ x12 = _x908 ∧ x13 = _x909 ∧ _x895 = _x908 ∧ _x896 = _x909 ∧ _x894 = _x907 ∧ _x892 = _x905 ∧ _x893 = _x906 ∧ _x890 = _x903 ∧ _x891 = _x904 ∧ _x889 = _x902 ∧ _x887 = _x900 ∧ _x888 = _x901 ∧ _x885 = _x898 ∧ _x884 = _x897 ∧ _x899 = 1 + _x886 ∧ 1 + _x891 ≤ _x888 l25 37 l24: x1 = _x910 ∧ x2 = _x911 ∧ x3 = _x912 ∧ x4 = _x913 ∧ x5 = _x914 ∧ x6 = _x915 ∧ x7 = _x916 ∧ x8 = _x917 ∧ x9 = _x918 ∧ x10 = _x919 ∧ x11 = _x920 ∧ x12 = _x921 ∧ x13 = _x922 ∧ x1 = _x923 ∧ x2 = _x924 ∧ x3 = _x925 ∧ x4 = _x926 ∧ x5 = _x927 ∧ x6 = _x928 ∧ x7 = _x929 ∧ x8 = _x930 ∧ x9 = _x931 ∧ x10 = _x932 ∧ x11 = _x933 ∧ x12 = _x934 ∧ x13 = _x935 ∧ _x921 = _x934 ∧ _x922 = _x935 ∧ _x920 = _x933 ∧ _x918 = _x931 ∧ _x919 = _x932 ∧ _x916 = _x929 ∧ _x917 = _x930 ∧ _x915 = _x928 ∧ _x913 = _x926 ∧ _x914 = _x927 ∧ _x911 = _x924 ∧ _x912 = _x925 ∧ _x910 = _x923 ∧ _x914 ≤ _x917 l27 38 l17: x1 = _x936 ∧ x2 = _x937 ∧ x3 = _x938 ∧ x4 = _x939 ∧ x5 = _x940 ∧ x6 = _x941 ∧ x7 = _x942 ∧ x8 = _x943 ∧ x9 = _x944 ∧ x10 = _x945 ∧ x11 = _x946 ∧ x12 = _x947 ∧ x13 = _x948 ∧ x1 = _x949 ∧ x2 = _x950 ∧ x3 = _x951 ∧ x4 = _x952 ∧ x5 = _x953 ∧ x6 = _x954 ∧ x7 = _x955 ∧ x8 = _x956 ∧ x9 = _x957 ∧ x10 = _x958 ∧ x11 = _x959 ∧ x12 = _x960 ∧ x13 = _x961 ∧ _x947 = _x960 ∧ _x948 = _x961 ∧ _x946 = _x959 ∧ _x945 = _x958 ∧ _x943 = _x956 ∧ _x941 = _x954 ∧ _x939 = _x952 ∧ _x940 = _x953 ∧ _x938 = _x951 ∧ _x936 = _x949 ∧ _x950 = 0 ∧ _x955 = _x943 ∧ _x957 = _x945 ∧ 1 + _x943 ≤ _x938 l27 39 l23: x1 = _x962 ∧ x2 = _x963 ∧ x3 = _x964 ∧ x4 = _x965 ∧ x5 = _x966 ∧ x6 = _x967 ∧ x7 = _x968 ∧ x8 = _x969 ∧ x9 = _x970 ∧ x10 = _x971 ∧ x11 = _x972 ∧ x12 = _x973 ∧ x13 = _x974 ∧ x1 = _x975 ∧ x2 = _x976 ∧ x3 = _x977 ∧ x4 = _x978 ∧ x5 = _x979 ∧ x6 = _x980 ∧ x7 = _x981 ∧ x8 = _x982 ∧ x9 = _x983 ∧ x10 = _x984 ∧ x11 = _x985 ∧ x12 = _x986 ∧ x13 = _x987 ∧ _x973 = _x986 ∧ _x972 = _x985 ∧ _x970 = _x983 ∧ _x971 = _x984 ∧ _x968 = _x981 ∧ _x969 = _x982 ∧ _x967 = _x980 ∧ _x965 = _x978 ∧ _x963 = _x976 ∧ _x964 = _x977 ∧ _x962 = _x975 ∧ _x979 = 0 ∧ _x987 = 0 ∧ _x964 ≤ _x969 l26 40 l27: x1 = _x988 ∧ x2 = _x989 ∧ x3 = _x990 ∧ x4 = _x991 ∧ x5 = _x992 ∧ x6 = _x993 ∧ x7 = _x994 ∧ x8 = _x995 ∧ x9 = _x996 ∧ x10 = _x997 ∧ x11 = _x998 ∧ x12 = _x999 ∧ x13 = _x1000 ∧ x1 = _x1001 ∧ x2 = _x1002 ∧ x3 = _x1003 ∧ x4 = _x1004 ∧ x5 = _x1005 ∧ x6 = _x1006 ∧ x7 = _x1007 ∧ x8 = _x1008 ∧ x9 = _x1009 ∧ x10 = _x1010 ∧ x11 = _x1011 ∧ x12 = _x1012 ∧ x13 = _x1013 ∧ _x999 = _x1012 ∧ _x1000 = _x1013 ∧ _x998 = _x1011 ∧ _x996 = _x1009 ∧ _x997 = _x1010 ∧ _x994 = _x1007 ∧ _x995 = _x1008 ∧ _x993 = _x1006 ∧ _x991 = _x1004 ∧ _x992 = _x1005 ∧ _x989 = _x1002 ∧ _x990 = _x1003 ∧ _x988 = _x1001 l23 41 l25: x1 = _x1014 ∧ x2 = _x1015 ∧ x3 = _x1016 ∧ x4 = _x1017 ∧ x5 = _x1018 ∧ x6 = _x1019 ∧ x7 = _x1020 ∧ x8 = _x1021 ∧ x9 = _x1022 ∧ x10 = _x1023 ∧ x11 = _x1024 ∧ x12 = _x1025 ∧ x13 = _x1026 ∧ x1 = _x1027 ∧ x2 = _x1028 ∧ x3 = _x1029 ∧ x4 = _x1030 ∧ x5 = _x1031 ∧ x6 = _x1032 ∧ x7 = _x1033 ∧ x8 = _x1034 ∧ x9 = _x1035 ∧ x10 = _x1036 ∧ x11 = _x1037 ∧ x12 = _x1038 ∧ x13 = _x1039 ∧ _x1025 = _x1038 ∧ _x1026 = _x1039 ∧ _x1024 = _x1037 ∧ _x1022 = _x1035 ∧ _x1023 = _x1036 ∧ _x1020 = _x1033 ∧ _x1021 = _x1034 ∧ _x1019 = _x1032 ∧ _x1017 = _x1030 ∧ _x1018 = _x1031 ∧ _x1015 = _x1028 ∧ _x1016 = _x1029 ∧ _x1014 = _x1027 l17 42 l21: x1 = _x1040 ∧ x2 = _x1041 ∧ x3 = _x1042 ∧ x4 = _x1043 ∧ x5 = _x1044 ∧ x6 = _x1045 ∧ x7 = _x1046 ∧ x8 = _x1047 ∧ x9 = _x1048 ∧ x10 = _x1049 ∧ x11 = _x1050 ∧ x12 = _x1051 ∧ x13 = _x1052 ∧ x1 = _x1053 ∧ x2 = _x1054 ∧ x3 = _x1055 ∧ x4 = _x1056 ∧ x5 = _x1057 ∧ x6 = _x1058 ∧ x7 = _x1059 ∧ x8 = _x1060 ∧ x9 = _x1061 ∧ x10 = _x1062 ∧ x11 = _x1063 ∧ x12 = _x1064 ∧ x13 = _x1065 ∧ _x1051 = _x1064 ∧ _x1052 = _x1065 ∧ _x1050 = _x1063 ∧ _x1048 = _x1061 ∧ _x1049 = _x1062 ∧ _x1046 = _x1059 ∧ _x1047 = _x1060 ∧ _x1045 = _x1058 ∧ _x1043 = _x1056 ∧ _x1044 = _x1057 ∧ _x1041 = _x1054 ∧ _x1042 = _x1055 ∧ _x1040 = _x1053 l28 43 l26: x1 = _x1066 ∧ x2 = _x1067 ∧ x3 = _x1068 ∧ x4 = _x1069 ∧ x5 = _x1070 ∧ x6 = _x1071 ∧ x7 = _x1072 ∧ x8 = _x1073 ∧ x9 = _x1074 ∧ x10 = _x1075 ∧ x11 = _x1076 ∧ x12 = _x1077 ∧ x13 = _x1078 ∧ x1 = _x1079 ∧ x2 = _x1080 ∧ x3 = _x1081 ∧ x4 = _x1082 ∧ x5 = _x1083 ∧ x6 = _x1084 ∧ x7 = _x1085 ∧ x8 = _x1086 ∧ x9 = _x1087 ∧ x10 = _x1088 ∧ x11 = _x1089 ∧ x12 = _x1090 ∧ x13 = _x1091 ∧ _x1077 = _x1090 ∧ _x1078 = _x1091 ∧ _x1076 = _x1089 ∧ _x1074 = _x1087 ∧ _x1072 = _x1085 ∧ _x1071 = _x1084 ∧ _x1069 = _x1082 ∧ _x1070 = _x1083 ∧ _x1067 = _x1080 ∧ _x1066 = _x1079 ∧ _x1081 = 0 ∧ _x1086 = 5 ∧ _x1088 = 50 l29 44 l28: x1 = _x1092 ∧ x2 = _x1093 ∧ x3 = _x1094 ∧ x4 = _x1095 ∧ x5 = _x1096 ∧ x6 = _x1097 ∧ x7 = _x1098 ∧ x8 = _x1099 ∧ x9 = _x1100 ∧ x10 = _x1101 ∧ x11 = _x1102 ∧ x12 = _x1103 ∧ x13 = _x1104 ∧ x1 = _x1105 ∧ x2 = _x1106 ∧ x3 = _x1107 ∧ x4 = _x1108 ∧ x5 = _x1109 ∧ x6 = _x1110 ∧ x7 = _x1111 ∧ x8 = _x1112 ∧ x9 = _x1113 ∧ x10 = _x1114 ∧ x11 = _x1115 ∧ x12 = _x1116 ∧ x13 = _x1117 ∧ _x1103 = _x1116 ∧ _x1104 = _x1117 ∧ _x1102 = _x1115 ∧ _x1100 = _x1113 ∧ _x1101 = _x1114 ∧ _x1098 = _x1111 ∧ _x1099 = _x1112 ∧ _x1097 = _x1110 ∧ _x1095 = _x1108 ∧ _x1096 = _x1109 ∧ _x1093 = _x1106 ∧ _x1094 = _x1107 ∧ _x1092 = _x1105

## 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 l28 l28 l28: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13 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 ∧ x12 = x12 ∧ x13 = x13
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 4 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/4

Here we consider the SCC { l23, l22, l25, l24, l27, l26 }.

### 2.1.1 Transition Removal

We remove transition 39 using the following ranking functions, which are bounded by 0.

 l22: −1 − x3 + x8 l23: −1 − x3 + x8 l24: −1 − x3 + x8 l25: −1 − x3 + x8 l27: − x3 + x8 l26: − x3 + x8

### 2.1.2 Transition Removal

We remove transitions 40, 36 using the following ranking functions, which are bounded by 0.

 l22: 1 l23: 1 l24: 1 l25: 1 l26: 0 l27: −1

### 2.1.3 Transition Removal

We remove transition 37 using the following ranking functions, which are bounded by 0.

 l22: −4⋅x5 + 4⋅x8 l23: −4⋅x5 + 4⋅x8 + 3 l24: −4⋅x5 + 4⋅x8 + 1 l25: −4⋅x5 + 4⋅x8 + 2

### 2.1.4 Transition Removal

We remove transitions 31, 34, 33, 32, 41 using the following ranking functions, which are bounded by −2.

 l22: −1 l23: −2 l24: 0 l25: −3

### 2.1.5 Trivial Cooperation Program

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

### 2.2 SCC Subproblem 2/4

Here we consider the SCC { l7, l1, l13, l20, l18, l17, l21, l8, l16, l15, l0, l12, l19 }.

### 2.2.1 Transition Removal

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

 l0: −2 − x2 + x7 l1: −2 − x2 + x7 l21: −1 − x2 + x7 l17: −1 − x2 + x7 l13: −2 − x2 + x7 l12: −2 − x2 + x7 l16: −2 − x2 + x7 l15: −2 − x2 + x7 l18: −2 − x2 + x7 l20: −2 − x2 + x7 l8: −2 − x2 + x7 l7: −2 − x2 + x7 l19: −2 − x2 + x7

### 2.2.2 Transition Removal

We remove transitions 42, 15, 26 using the following ranking functions, which are bounded by 0.

 l0: 2 l1: 2 l17: 0 l21: −1 l13: 1 l12: 1 l16: 1 l15: 1 l18: 2 l20: 2 l8: 2 l7: 2 l19: 2

### 2.2.3 Transition Removal

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

 l0: −1 + 2⋅x1 + x2 + 3⋅x3 − x4 + 4⋅x5 − x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l1: −2 + 2⋅x1 + x2 + 3⋅x3 − x4 + 4⋅x5 − x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l12: − x4 + x7 l13: − x4 + x7 l16: −1 − x4 + x7 l15: −1 − x4 + x7 l18: −2 + 2⋅x1 + x2 + 3⋅x3 − x4 + 4⋅x5 − x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l20: −2 + 2⋅x1 + x2 + 3⋅x3 − x4 + 4⋅x5 − x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l8: −2 + 2⋅x1 + x2 + 3⋅x3 − x4 + 4⋅x5 − x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l7: −2 + 2⋅x1 + x2 + 3⋅x3 − x4 + 4⋅x5 − x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l19: −2 + 2⋅x1 + x2 + 3⋅x3 − x4 + 4⋅x5 − x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13

### 2.2.4 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by 0.

 l0: −1 + 2⋅x1 + x2 + 3⋅x3 − 2⋅x4 + 4⋅x5 + x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l1: −3 + 2⋅x1 + x2 + 3⋅x3 − 2⋅x4 + 4⋅x5 + x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l12: x2 − x6 l13: x2 − x6 l16: x2 − x6 l15: x2 − x6 l18: −3 + 2⋅x1 + x2 + 3⋅x3 − 2⋅x4 + 4⋅x5 + x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l20: −3 + 2⋅x1 + x2 + 3⋅x3 − 2⋅x4 + 4⋅x5 + x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l8: −3 + 2⋅x1 + x2 + 3⋅x3 − 2⋅x4 + 4⋅x5 + x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l7: −3 + 2⋅x1 + x2 + 3⋅x3 − 2⋅x4 + 4⋅x5 + x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13 l19: −3 + 2⋅x1 + x2 + 3⋅x3 − 2⋅x4 + 4⋅x5 + x7 + 5⋅x8 + 6⋅x9 + 7⋅x10 + 8⋅x11 + 9⋅x13

### 2.2.5 Transition Removal

We remove transitions 9, 13, 12 using the following ranking functions, which are bounded by 0.

 l0: −1 + 3⋅x1 − x2 + 4⋅x3 − x4 + 5⋅x5 − x7 + 6⋅x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x13 l1: −2 + 3⋅x1 − x2 + 4⋅x3 − x4 + 5⋅x5 − x7 + 6⋅x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x13 l12: 0 l13: −1 l16: 1 l15: 2 l18: −2 + 3⋅x1 − x2 + 4⋅x3 − x4 + 5⋅x5 − x7 + 6⋅x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x13 l20: −2 + 3⋅x1 − x2 + 4⋅x3 − x4 + 5⋅x5 − x7 + 6⋅x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x13 l8: −2 + 3⋅x1 − x2 + 4⋅x3 − x4 + 5⋅x5 − x7 + 6⋅x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x13 l7: −2 + 3⋅x1 − x2 + 4⋅x3 − x4 + 5⋅x5 − x7 + 6⋅x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x13 l19: −2 + 3⋅x1 − x2 + 4⋅x3 − x4 + 5⋅x5 − x7 + 6⋅x8 + 7⋅x9 + 8⋅x10 + 9⋅x11 + 10⋅x13

### 2.2.6 Transition Removal

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

 l0: − x4 + x7 l1: − x4 + x7 l18: −1 − x4 + x7 l20: −1 − x4 + x7 l8: −1 − x4 + x7 l7: −1 − x4 + x7 l19: −1 − x4 + x7

### 2.2.7 Transition Removal

We remove transitions 23, 24 using the following ranking functions, which are bounded by 0.

 l0: −1 + x2 l1: −1 + x2 l18: −1 + x2 l20: x2 l8: −1 + x2 l7: −1 + x2 l19: −1 + x2

### 2.2.8 Transition Removal

We remove transition 20 using the following ranking functions, which are bounded by 0.

 l0: −1 + x2 − x6 l1: −1 + x2 − x6 l18: −1 + x2 − x6 l8: −1 + x2 − x6 l7: −1 + x2 − x6 l19: −1 + x2 l20: −1 + x2

### 2.2.9 Transition Removal

We remove transitions 1, 18, 19, 6, 21, 25 using the following ranking functions, which are bounded by 0.

 l0: 0 l1: −1 l18: 1 l8: 2 l7: 3 l19: 4 l20: 5

### 2.2.10 Trivial Cooperation Program

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

### 2.3 SCC Subproblem 3/4

Here we consider the SCC { l10, l11, l9, l14 }.

### 2.3.1 Transition Removal

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

 l10: − x2 + x7 l14: − x2 + x7 l9: −1 − x2 + x7 l11: −1 − x2 + x7

### 2.3.2 Transition Removal

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

 l10: −1 l14: −1 l9: 0 l11: 0

### 2.3.3 Transition Removal

We remove transitions 17, 8 using the following ranking functions, which are bounded by 0.

 l10: 0 l14: −1 l11: 2⋅x2 − 2⋅x4 + 1 l9: 2⋅x2 − 2⋅x4

### 2.3.4 Transition Removal

We remove transition 22 using the following ranking functions, which are bounded by 0.

 l11: 0 l9: −1

### 2.3.5 Trivial Cooperation Program

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

### 2.4 SCC Subproblem 4/4

Here we consider the SCC { l5, l4, l3, l2 }.

### 2.4.1 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by 0.

 l3: 3⋅x2 + 2 l5: 3⋅x2 + 1 l2: 3⋅x2 l4: 3⋅x2

### 2.4.2 Transition Removal

We remove transitions 30, 2 using the following ranking functions, which are bounded by 0.

 l3: 0 l5: −1 l2: 1 l4: 1

### 2.4.3 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

 l4: − x4 + x7 l2: − x4 + x7

### 2.4.4 Transition Removal

We remove transition 35 using the following ranking functions, which are bounded by 0.

 l4: 0 l2: −1

### 2.4.5 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 % (31 real / 0 unknown / 0 assumptions / 31 total proof steps)