# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l7, l11, l1, l13, l18, l17, l2, l9, l14, l4, l10, l6, l8, l15, l16, l0, l12
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = ___const_50HAT0 ∧ x2 = _i11HAT0 ∧ x3 = _i13HAT0 ∧ x4 = _i15HAT0 ∧ x5 = _i17HAT0 ∧ x6 = _i7HAT0 ∧ x7 = _i9HAT0 ∧ x8 = _iHAT0 ∧ x9 = _tmpHAT0 ∧ x10 = _tmp___0HAT0 ∧ x1 = ___const_50HATpost ∧ x2 = _i11HATpost ∧ x3 = _i13HATpost ∧ x4 = _i15HATpost ∧ x5 = _i17HATpost ∧ x6 = _i7HATpost ∧ x7 = _i9HATpost ∧ x8 = _iHATpost ∧ x9 = _tmpHATpost ∧ x10 = _tmp___0HATpost ∧ _tmp___0HAT0 = _tmp___0HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _i9HAT0 = _i9HATpost ∧ _i7HAT0 = _i7HATpost ∧ _i17HAT0 = _i17HATpost ∧ _i15HAT0 = _i15HATpost ∧ _i13HAT0 = _i13HATpost ∧ _i11HAT0 = _i11HATpost ∧ _iHAT0 = _iHATpost ∧ ___const_50HAT0 = ___const_50HATpost l2 2 l3: 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 ∧ _x9 = _x19 ∧ _x8 = _x18 ∧ _x6 = _x16 ∧ _x5 = _x15 ∧ _x4 = _x14 ∧ _x3 = _x13 ∧ _x2 = _x12 ∧ _x1 = _x11 ∧ _x7 = _x17 ∧ _x = _x10 ∧ _x ≤ _x7 l2 3 l4: 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 ∧ _x29 = _x39 ∧ _x28 = _x38 ∧ _x26 = _x36 ∧ _x25 = _x35 ∧ _x24 = _x34 ∧ _x23 = _x33 ∧ _x22 = _x32 ∧ _x21 = _x31 ∧ _x20 = _x30 ∧ _x37 = 1 + _x27 ∧ 1 + _x27 ≤ _x20 l5 4 l6: 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 ∧ _x46 = _x56 ∧ _x45 = _x55 ∧ _x44 = _x54 ∧ _x43 = _x53 ∧ _x42 = _x52 ∧ _x41 = _x51 ∧ _x47 = _x57 ∧ _x40 = _x50 l7 5 l4: 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 ∧ _x66 = _x76 ∧ _x65 = _x75 ∧ _x64 = _x74 ∧ _x63 = _x73 ∧ _x62 = _x72 ∧ _x61 = _x71 ∧ _x60 = _x70 ∧ _x77 = 0 ∧ _x60 ≤ _x64 l7 6 l8: 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 ∧ _x89 = _x99 ∧ _x88 = _x98 ∧ _x86 = _x96 ∧ _x85 = _x95 ∧ _x83 = _x93 ∧ _x82 = _x92 ∧ _x81 = _x91 ∧ _x87 = _x97 ∧ _x80 = _x90 ∧ _x94 = 1 + _x84 ∧ 1 + _x84 ≤ _x80 l9 7 l10: 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 ∧ _x106 = _x116 ∧ _x105 = _x115 ∧ _x104 = _x114 ∧ _x103 = _x113 ∧ _x102 = _x112 ∧ _x101 = _x111 ∧ _x107 = _x117 ∧ _x100 = _x110 l11 8 l8: 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 ∧ _x120 ≤ _x123 ∧ _x140 = 0 ∧ _x134 = 0 ∧ _x120 = _x130 ∧ _x127 = _x137 ∧ _x121 = _x131 ∧ _x122 = _x132 ∧ _x123 = _x133 ∧ _x125 = _x135 ∧ _x126 = _x136 ∧ _x128 = _x138 ∧ _x129 = _x139 l11 9 l12: x1 = _x141 ∧ x2 = _x142 ∧ x3 = _x143 ∧ x4 = _x144 ∧ x5 = _x145 ∧ x6 = _x146 ∧ x7 = _x147 ∧ x8 = _x148 ∧ x9 = _x149 ∧ x10 = _x150 ∧ x1 = _x151 ∧ x2 = _x152 ∧ x3 = _x153 ∧ x4 = _x154 ∧ x5 = _x155 ∧ x6 = _x156 ∧ x7 = _x157 ∧ x8 = _x158 ∧ x9 = _x159 ∧ x10 = _x160 ∧ _x150 = _x160 ∧ _x149 = _x159 ∧ _x147 = _x157 ∧ _x146 = _x156 ∧ _x145 = _x155 ∧ _x143 = _x153 ∧ _x142 = _x152 ∧ _x148 = _x158 ∧ _x141 = _x151 ∧ _x154 = 1 + _x144 ∧ 1 + _x144 ≤ _x141 l13 10 l14: x1 = _x161 ∧ x2 = _x162 ∧ x3 = _x163 ∧ x4 = _x164 ∧ x5 = _x165 ∧ x6 = _x166 ∧ x7 = _x167 ∧ x8 = _x168 ∧ x9 = _x169 ∧ x10 = _x170 ∧ x1 = _x171 ∧ x2 = _x172 ∧ x3 = _x173 ∧ x4 = _x174 ∧ x5 = _x175 ∧ x6 = _x176 ∧ x7 = _x177 ∧ x8 = _x178 ∧ x9 = _x179 ∧ x10 = _x180 ∧ _x170 = _x180 ∧ _x169 = _x179 ∧ _x167 = _x177 ∧ _x166 = _x176 ∧ _x165 = _x175 ∧ _x164 = _x174 ∧ _x163 = _x173 ∧ _x162 = _x172 ∧ _x168 = _x178 ∧ _x161 = _x171 l15 11 l12: x1 = _x181 ∧ x2 = _x182 ∧ x3 = _x183 ∧ x4 = _x184 ∧ x5 = _x185 ∧ x6 = _x186 ∧ x7 = _x187 ∧ x8 = _x188 ∧ x9 = _x189 ∧ x10 = _x190 ∧ x1 = _x191 ∧ x2 = _x192 ∧ x3 = _x193 ∧ x4 = _x194 ∧ x5 = _x195 ∧ x6 = _x196 ∧ x7 = _x197 ∧ x8 = _x198 ∧ x9 = _x199 ∧ x10 = _x200 ∧ _x181 ≤ _x183 ∧ _x201 = 0 ∧ _x194 = 0 ∧ _x181 = _x191 ∧ _x188 = _x198 ∧ _x182 = _x192 ∧ _x183 = _x193 ∧ _x185 = _x195 ∧ _x186 = _x196 ∧ _x187 = _x197 ∧ _x189 = _x199 ∧ _x190 = _x200 l15 12 l16: x1 = _x202 ∧ x2 = _x203 ∧ x3 = _x204 ∧ x4 = _x205 ∧ x5 = _x206 ∧ x6 = _x207 ∧ x7 = _x208 ∧ x8 = _x209 ∧ x9 = _x210 ∧ x10 = _x211 ∧ x1 = _x212 ∧ x2 = _x213 ∧ x3 = _x214 ∧ x4 = _x215 ∧ x5 = _x216 ∧ x6 = _x217 ∧ x7 = _x218 ∧ x8 = _x219 ∧ x9 = _x220 ∧ x10 = _x221 ∧ _x211 = _x221 ∧ _x210 = _x220 ∧ _x208 = _x218 ∧ _x207 = _x217 ∧ _x206 = _x216 ∧ _x205 = _x215 ∧ _x203 = _x213 ∧ _x209 = _x219 ∧ _x202 = _x212 ∧ _x214 = 1 + _x204 ∧ 1 + _x204 ≤ _x202 l16 13 l15: x1 = _x222 ∧ x2 = _x223 ∧ x3 = _x224 ∧ x4 = _x225 ∧ x5 = _x226 ∧ x6 = _x227 ∧ x7 = _x228 ∧ x8 = _x229 ∧ x9 = _x230 ∧ x10 = _x231 ∧ x1 = _x232 ∧ x2 = _x233 ∧ x3 = _x234 ∧ x4 = _x235 ∧ x5 = _x236 ∧ x6 = _x237 ∧ x7 = _x238 ∧ x8 = _x239 ∧ x9 = _x240 ∧ x10 = _x241 ∧ _x231 = _x241 ∧ _x230 = _x240 ∧ _x228 = _x238 ∧ _x227 = _x237 ∧ _x226 = _x236 ∧ _x225 = _x235 ∧ _x224 = _x234 ∧ _x223 = _x233 ∧ _x229 = _x239 ∧ _x222 = _x232 l14 14 l16: x1 = _x242 ∧ x2 = _x243 ∧ x3 = _x244 ∧ x4 = _x245 ∧ x5 = _x246 ∧ x6 = _x247 ∧ x7 = _x248 ∧ x8 = _x249 ∧ x9 = _x250 ∧ x10 = _x251 ∧ x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ x8 = _x259 ∧ x9 = _x260 ∧ x10 = _x261 ∧ _x242 ≤ _x249 ∧ _x262 = 0 ∧ _x254 = 0 ∧ _x242 = _x252 ∧ _x249 = _x259 ∧ _x243 = _x253 ∧ _x245 = _x255 ∧ _x246 = _x256 ∧ _x247 = _x257 ∧ _x248 = _x258 ∧ _x250 = _x260 ∧ _x251 = _x261 l14 15 l13: x1 = _x263 ∧ x2 = _x264 ∧ x3 = _x265 ∧ x4 = _x266 ∧ x5 = _x267 ∧ x6 = _x268 ∧ x7 = _x269 ∧ x8 = _x270 ∧ x9 = _x271 ∧ x10 = _x272 ∧ x1 = _x273 ∧ x2 = _x274 ∧ x3 = _x275 ∧ x4 = _x276 ∧ x5 = _x277 ∧ x6 = _x278 ∧ x7 = _x279 ∧ x8 = _x280 ∧ x9 = _x281 ∧ x10 = _x282 ∧ _x272 = _x282 ∧ _x271 = _x281 ∧ _x269 = _x279 ∧ _x268 = _x278 ∧ _x267 = _x277 ∧ _x266 = _x276 ∧ _x265 = _x275 ∧ _x264 = _x274 ∧ _x263 = _x273 ∧ _x280 = 1 + _x270 ∧ 1 + _x270 ≤ _x263 l12 16 l11: x1 = _x283 ∧ x2 = _x284 ∧ x3 = _x285 ∧ x4 = _x286 ∧ x5 = _x287 ∧ x6 = _x288 ∧ x7 = _x289 ∧ x8 = _x290 ∧ x9 = _x291 ∧ x10 = _x292 ∧ x1 = _x293 ∧ x2 = _x294 ∧ x3 = _x295 ∧ x4 = _x296 ∧ x5 = _x297 ∧ x6 = _x298 ∧ x7 = _x299 ∧ x8 = _x300 ∧ x9 = _x301 ∧ x10 = _x302 ∧ _x292 = _x302 ∧ _x291 = _x301 ∧ _x289 = _x299 ∧ _x288 = _x298 ∧ _x287 = _x297 ∧ _x286 = _x296 ∧ _x285 = _x295 ∧ _x284 = _x294 ∧ _x290 = _x300 ∧ _x283 = _x293 l10 17 l13: x1 = _x303 ∧ x2 = _x304 ∧ x3 = _x305 ∧ x4 = _x306 ∧ x5 = _x307 ∧ x6 = _x308 ∧ x7 = _x309 ∧ x8 = _x310 ∧ x9 = _x311 ∧ x10 = _x312 ∧ x1 = _x313 ∧ x2 = _x314 ∧ x3 = _x315 ∧ x4 = _x316 ∧ x5 = _x317 ∧ x6 = _x318 ∧ x7 = _x319 ∧ x8 = _x320 ∧ x9 = _x321 ∧ x10 = _x322 ∧ _x312 = _x322 ∧ _x311 = _x321 ∧ _x309 = _x319 ∧ _x308 = _x318 ∧ _x307 = _x317 ∧ _x306 = _x316 ∧ _x305 = _x315 ∧ _x304 = _x314 ∧ _x303 = _x313 ∧ _x320 = 0 ∧ _x303 ≤ _x304 l10 18 l9: x1 = _x323 ∧ x2 = _x324 ∧ x3 = _x325 ∧ x4 = _x326 ∧ x5 = _x327 ∧ x6 = _x328 ∧ x7 = _x329 ∧ x8 = _x330 ∧ x9 = _x331 ∧ x10 = _x332 ∧ x1 = _x333 ∧ x2 = _x334 ∧ x3 = _x335 ∧ x4 = _x336 ∧ x5 = _x337 ∧ x6 = _x338 ∧ x7 = _x339 ∧ x8 = _x340 ∧ x9 = _x341 ∧ x10 = _x342 ∧ _x332 = _x342 ∧ _x331 = _x341 ∧ _x329 = _x339 ∧ _x328 = _x338 ∧ _x327 = _x337 ∧ _x326 = _x336 ∧ _x325 = _x335 ∧ _x330 = _x340 ∧ _x323 = _x333 ∧ _x334 = 1 + _x324 ∧ 1 + _x324 ≤ _x323 l8 19 l7: x1 = _x343 ∧ x2 = _x344 ∧ x3 = _x345 ∧ x4 = _x346 ∧ x5 = _x347 ∧ x6 = _x348 ∧ x7 = _x349 ∧ x8 = _x350 ∧ x9 = _x351 ∧ x10 = _x352 ∧ x1 = _x353 ∧ x2 = _x354 ∧ x3 = _x355 ∧ x4 = _x356 ∧ x5 = _x357 ∧ x6 = _x358 ∧ x7 = _x359 ∧ x8 = _x360 ∧ x9 = _x361 ∧ x10 = _x362 ∧ _x352 = _x362 ∧ _x351 = _x361 ∧ _x349 = _x359 ∧ _x348 = _x358 ∧ _x347 = _x357 ∧ _x346 = _x356 ∧ _x345 = _x355 ∧ _x344 = _x354 ∧ _x350 = _x360 ∧ _x343 = _x353 l6 20 l9: x1 = _x363 ∧ x2 = _x364 ∧ x3 = _x365 ∧ x4 = _x366 ∧ x5 = _x367 ∧ x6 = _x368 ∧ x7 = _x369 ∧ x8 = _x370 ∧ x9 = _x371 ∧ x10 = _x372 ∧ x1 = _x373 ∧ x2 = _x374 ∧ x3 = _x375 ∧ x4 = _x376 ∧ x5 = _x377 ∧ x6 = _x378 ∧ x7 = _x379 ∧ x8 = _x380 ∧ x9 = _x381 ∧ x10 = _x382 ∧ _x363 ≤ _x369 ∧ _x383 = 0 ∧ _x374 = 0 ∧ _x363 = _x373 ∧ _x370 = _x380 ∧ _x365 = _x375 ∧ _x366 = _x376 ∧ _x367 = _x377 ∧ _x368 = _x378 ∧ _x369 = _x379 ∧ _x371 = _x381 ∧ _x372 = _x382 l6 21 l5: x1 = _x384 ∧ x2 = _x385 ∧ x3 = _x386 ∧ x4 = _x387 ∧ x5 = _x388 ∧ x6 = _x389 ∧ x7 = _x390 ∧ x8 = _x391 ∧ x9 = _x392 ∧ x10 = _x393 ∧ x1 = _x394 ∧ x2 = _x395 ∧ x3 = _x396 ∧ x4 = _x397 ∧ x5 = _x398 ∧ x6 = _x399 ∧ x7 = _x400 ∧ x8 = _x401 ∧ x9 = _x402 ∧ x10 = _x403 ∧ _x393 = _x403 ∧ _x392 = _x402 ∧ _x389 = _x399 ∧ _x388 = _x398 ∧ _x387 = _x397 ∧ _x386 = _x396 ∧ _x385 = _x395 ∧ _x391 = _x401 ∧ _x384 = _x394 ∧ _x400 = 1 + _x390 ∧ 1 + _x390 ≤ _x384 l4 22 l2: x1 = _x404 ∧ x2 = _x405 ∧ x3 = _x406 ∧ x4 = _x407 ∧ x5 = _x408 ∧ x6 = _x409 ∧ x7 = _x410 ∧ x8 = _x411 ∧ x9 = _x412 ∧ x10 = _x413 ∧ x1 = _x414 ∧ x2 = _x415 ∧ x3 = _x416 ∧ x4 = _x417 ∧ x5 = _x418 ∧ x6 = _x419 ∧ x7 = _x420 ∧ x8 = _x421 ∧ x9 = _x422 ∧ x10 = _x423 ∧ _x413 = _x423 ∧ _x412 = _x422 ∧ _x410 = _x420 ∧ _x409 = _x419 ∧ _x408 = _x418 ∧ _x407 = _x417 ∧ _x406 = _x416 ∧ _x405 = _x415 ∧ _x411 = _x421 ∧ _x404 = _x414 l1 23 l5: x1 = _x424 ∧ x2 = _x425 ∧ x3 = _x426 ∧ x4 = _x427 ∧ x5 = _x428 ∧ x6 = _x429 ∧ x7 = _x430 ∧ x8 = _x431 ∧ x9 = _x432 ∧ x10 = _x433 ∧ x1 = _x434 ∧ x2 = _x435 ∧ x3 = _x436 ∧ x4 = _x437 ∧ x5 = _x438 ∧ x6 = _x439 ∧ x7 = _x440 ∧ x8 = _x441 ∧ x9 = _x442 ∧ x10 = _x443 ∧ _x424 ≤ _x429 ∧ _x444 = 0 ∧ _x440 = 0 ∧ _x424 = _x434 ∧ _x431 = _x441 ∧ _x425 = _x435 ∧ _x426 = _x436 ∧ _x427 = _x437 ∧ _x428 = _x438 ∧ _x429 = _x439 ∧ _x432 = _x442 ∧ _x433 = _x443 l1 24 l0: x1 = _x445 ∧ x2 = _x446 ∧ x3 = _x447 ∧ x4 = _x448 ∧ x5 = _x449 ∧ x6 = _x450 ∧ x7 = _x451 ∧ x8 = _x452 ∧ x9 = _x453 ∧ x10 = _x454 ∧ x1 = _x455 ∧ x2 = _x456 ∧ x3 = _x457 ∧ x4 = _x458 ∧ x5 = _x459 ∧ x6 = _x460 ∧ x7 = _x461 ∧ x8 = _x462 ∧ x9 = _x463 ∧ x10 = _x464 ∧ _x454 = _x464 ∧ _x453 = _x463 ∧ _x451 = _x461 ∧ _x449 = _x459 ∧ _x448 = _x458 ∧ _x447 = _x457 ∧ _x446 = _x456 ∧ _x452 = _x462 ∧ _x445 = _x455 ∧ _x460 = 1 + _x450 ∧ 1 + _x450 ≤ _x445 l17 25 l0: x1 = _x465 ∧ x2 = _x466 ∧ x3 = _x467 ∧ x4 = _x468 ∧ x5 = _x469 ∧ x6 = _x470 ∧ x7 = _x471 ∧ x8 = _x472 ∧ x9 = _x473 ∧ x10 = _x474 ∧ x1 = _x475 ∧ x2 = _x476 ∧ x3 = _x477 ∧ x4 = _x478 ∧ x5 = _x479 ∧ x6 = _x480 ∧ x7 = _x481 ∧ x8 = _x482 ∧ x9 = _x483 ∧ x10 = _x484 ∧ _x482 = 0 ∧ _x483 = _x483 ∧ _x484 = _x484 ∧ _x485 = 0 ∧ _x480 = 0 ∧ _x465 = _x475 ∧ _x466 = _x476 ∧ _x467 = _x477 ∧ _x468 = _x478 ∧ _x469 = _x479 ∧ _x471 = _x481 l18 26 l17: x1 = _x486 ∧ x2 = _x487 ∧ x3 = _x488 ∧ x4 = _x489 ∧ x5 = _x490 ∧ x6 = _x491 ∧ x7 = _x492 ∧ x8 = _x493 ∧ x9 = _x494 ∧ x10 = _x495 ∧ x1 = _x496 ∧ x2 = _x497 ∧ x3 = _x498 ∧ x4 = _x499 ∧ x5 = _x500 ∧ x6 = _x501 ∧ x7 = _x502 ∧ x8 = _x503 ∧ x9 = _x504 ∧ x10 = _x505 ∧ _x495 = _x505 ∧ _x494 = _x504 ∧ _x492 = _x502 ∧ _x491 = _x501 ∧ _x490 = _x500 ∧ _x489 = _x499 ∧ _x488 = _x498 ∧ _x487 = _x497 ∧ _x493 = _x503 ∧ _x486 = _x496

## 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 l7 l7 l7: 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 l1 l1 l1: 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 l2 l2 l2: 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 l14 l14 l14: 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 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 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 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
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 8 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/8

Here we consider the SCC { l1, l0 }.

### 2.1.1 Transition Removal

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

 l0: −1 + x1 − x6 l1: −1 + x1 − x6

### 2.1.2 Transition Removal

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

 l0: 0 l1: −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 2/8

Here we consider the SCC { l5, l6 }.

### 2.2.1 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by 0.

 l5: 2⋅x1 − 2⋅x7 + 1 l6: 2⋅x1 − 2⋅x7

### 2.2.2 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 0.

 l5: 0 l6: −1

### 2.2.3 Trivial Cooperation Program

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

### 2.3 SCC Subproblem 3/8

Here we consider the SCC { l10, l9 }.

### 2.3.1 Transition Removal

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

 l9: 2⋅x1 − 2⋅x2 + 1 l10: 2⋅x1 − 2⋅x2

### 2.3.2 Transition Removal

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

 l9: 0 l10: −1

### 2.3.3 Trivial Cooperation Program

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

### 2.4 SCC Subproblem 4/8

Here we consider the SCC { l13, l14 }.

### 2.4.1 Transition Removal

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

 l13: 2⋅x1 − 2⋅x8 + 1 l14: 2⋅x1 − 2⋅x8

### 2.4.2 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 0.

 l13: 0 l14: −1

### 2.4.3 Trivial Cooperation Program

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

### 2.5 SCC Subproblem 5/8

Here we consider the SCC { l16, l15 }.

### 2.5.1 Transition Removal

We remove transition 12 using the following ranking functions, which are bounded by 0.

 l16: −1 + x1 − x3 l15: −1 + x1 − x3

### 2.5.2 Transition Removal

We remove transition 13 using the following ranking functions, which are bounded by 0.

 l16: 0 l15: −1

### 2.5.3 Trivial Cooperation Program

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

### 2.6 SCC Subproblem 6/8

Here we consider the SCC { l11, l12 }.

### 2.6.1 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 0.

 l12: 2⋅x1 − 2⋅x4 + 1 l11: 2⋅x1 − 2⋅x4

### 2.6.2 Transition Removal

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

 l12: 0 l11: −1

### 2.6.3 Trivial Cooperation Program

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

### 2.7 SCC Subproblem 7/8

Here we consider the SCC { l7, l8 }.

### 2.7.1 Transition Removal

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

 l8: 2⋅x1 − 2⋅x5 + 1 l7: 2⋅x1 − 2⋅x5

### 2.7.2 Transition Removal

We remove transition 19 using the following ranking functions, which are bounded by 0.

 l8: 0 l7: −1

### 2.7.3 Trivial Cooperation Program

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

### 2.8 SCC Subproblem 8/8

Here we consider the SCC { l4, l2 }.

### 2.8.1 Transition Removal

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

 l4: 2⋅x1 − 2⋅x8 + 1 l2: 2⋅x1 − 2⋅x8

### 2.8.2 Transition Removal

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

 l4: 0 l2: −1

### 2.8.3 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 % (26 real / 0 unknown / 0 assumptions / 26 total proof steps)