LTS Termination Proof

Input

Integer Transition System

Initial Location: l5, l4, l7, l6, l10, l11, l1, l3, l0, l2, l9

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = _oldX0HAT0 ∧ x2 = _oldX1HAT0 ∧ x3 = _oldX2HAT0 ∧ x4 = _oldX3HAT0 ∧ x5 = _oldX4HAT0 ∧ x6 = _oldX5HAT0 ∧ x7 = _oldX6HAT0 ∧ x8 = _oldX7HAT0 ∧ x9 = _x0HAT0 ∧ x10 = _x1HAT0 ∧ x11 = _x2HAT0 ∧ x12 = _x3HAT0 ∧ x1 = _oldX0HATpost ∧ x2 = _oldX1HATpost ∧ x3 = _oldX2HATpost ∧ x4 = _oldX3HATpost ∧ x5 = _oldX4HATpost ∧ x6 = _oldX5HATpost ∧ x7 = _oldX6HATpost ∧ x8 = _oldX7HATpost ∧ x9 = _x0HATpost ∧ x10 = _x1HATpost ∧ x11 = _x2HATpost ∧ x12 = _x3HATpost ∧ _oldX7HAT0 = _oldX7HATpost ∧ _oldX6HAT0 = _oldX6HATpost ∧ _oldX5HAT0 = _oldX5HATpost ∧ _oldX4HAT0 = _oldX4HATpost ∧ _x3HATpost = _oldX3HATpost ∧ _x2HATpost = _oldX2HATpost ∧ _x1HATpost = _oldX1HATpost ∧ _x0HATpost = _oldX0HATpost ∧ −1 + _oldX3HATpost ≤ 0 ∧ _oldX3HATpost = _x3HAT0 ∧ _oldX2HATpost = _x2HAT0 ∧ _oldX1HATpost = _x1HAT0 ∧ _oldX0HATpost = _x0HAT0
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 ∧ x12 = _x11 ∧ x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x4 = _x15 ∧ x5 = _x16 ∧ x6 = _x17 ∧ x7 = _x18 ∧ x8 = _x19 ∧ x9 = _x20 ∧ x10 = _x21 ∧ x11 = _x22 ∧ x12 = _x23 ∧ _x7 = _x19 ∧ _x6 = _x18 ∧ _x5 = _x17 ∧ _x4 = _x16 ∧ _x23 = −1 + _x15 ∧ _x22 = _x14 ∧ _x21 = _x13 ∧ _x20 = _x12 ∧ 1 ≤ −1 + _x15 ∧ _x15 = _x11 ∧ _x14 = _x10 ∧ _x13 = _x9 ∧ _x12 = _x8
l2	3	l0:	x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x4 = _x27 ∧ x5 = _x28 ∧ x6 = _x29 ∧ x7 = _x30 ∧ x8 = _x31 ∧ x9 = _x32 ∧ x10 = _x33 ∧ x11 = _x34 ∧ x12 = _x35 ∧ x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x4 = _x39 ∧ x5 = _x40 ∧ x6 = _x41 ∧ x7 = _x42 ∧ x8 = _x43 ∧ x9 = _x44 ∧ x10 = _x45 ∧ x11 = _x46 ∧ x12 = _x47 ∧ _x35 = _x47 ∧ _x34 = _x46 ∧ _x33 = _x45 ∧ _x32 = _x44 ∧ _x31 = _x43 ∧ _x30 = _x42 ∧ _x29 = _x41 ∧ _x28 = _x40 ∧ _x27 = _x39 ∧ _x26 = _x38 ∧ _x25 = _x37 ∧ _x24 = _x36
l3	4	l1:	x1 = _x48 ∧ x2 = _x49 ∧ x3 = _x50 ∧ x4 = _x51 ∧ x5 = _x52 ∧ x6 = _x53 ∧ x7 = _x54 ∧ x8 = _x55 ∧ x9 = _x56 ∧ x10 = _x57 ∧ x11 = _x58 ∧ x12 = _x59 ∧ x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x63 ∧ x5 = _x64 ∧ x6 = _x65 ∧ x7 = _x66 ∧ x8 = _x67 ∧ x9 = _x68 ∧ x10 = _x69 ∧ x11 = _x70 ∧ x12 = _x71 ∧ _x55 = _x67 ∧ _x54 = _x66 ∧ _x53 = _x65 ∧ _x71 = _x64 ∧ _x70 = _x62 ∧ _x69 = _x61 ∧ _x68 = _x60 ∧ _x62 ≤ 0 ∧ _x64 = _x64 ∧ _x63 = _x59 ∧ _x62 = _x58 ∧ _x61 = _x57 ∧ _x60 = _x56
l3	5	l0:	x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x6 = _x77 ∧ x7 = _x78 ∧ x8 = _x79 ∧ x9 = _x80 ∧ x10 = _x81 ∧ x11 = _x82 ∧ x12 = _x83 ∧ x1 = _x84 ∧ x2 = _x85 ∧ x3 = _x86 ∧ x4 = _x87 ∧ x5 = _x88 ∧ x6 = _x89 ∧ x7 = _x90 ∧ x8 = _x91 ∧ x9 = _x92 ∧ x10 = _x93 ∧ x11 = _x94 ∧ x12 = _x95 ∧ _x79 = _x91 ∧ _x78 = _x90 ∧ _x77 = _x89 ∧ _x76 = _x88 ∧ _x95 = _x86 ∧ _x94 = _x86 ∧ _x93 = _x85 ∧ _x92 = _x84 ∧ 1 ≤ _x86 ∧ _x87 = _x83 ∧ _x86 = _x82 ∧ _x85 = _x81 ∧ _x84 = _x80
l4	6	l5:	x1 = _x96 ∧ x2 = _x97 ∧ x3 = _x98 ∧ x4 = _x99 ∧ x5 = _x100 ∧ x6 = _x101 ∧ x7 = _x102 ∧ x8 = _x103 ∧ x9 = _x104 ∧ x10 = _x105 ∧ x11 = _x106 ∧ x12 = _x107 ∧ x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x4 = _x111 ∧ x5 = _x112 ∧ x6 = _x113 ∧ x7 = _x114 ∧ x8 = _x115 ∧ x9 = _x116 ∧ x10 = _x117 ∧ x11 = _x118 ∧ x12 = _x119 ∧ _x103 = _x115 ∧ _x102 = _x114 ∧ _x101 = _x113 ∧ _x119 = _x112 ∧ _x118 = −8 + _x110 ∧ _x117 = _x109 ∧ _x116 = _x108 ∧ _x112 = _x112 ∧ _x111 = _x107 ∧ _x110 = _x106 ∧ _x109 = _x105 ∧ _x108 = _x104
l5	7	l3:	x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x4 = _x123 ∧ x5 = _x124 ∧ x6 = _x125 ∧ x7 = _x126 ∧ x8 = _x127 ∧ x9 = _x128 ∧ x10 = _x129 ∧ x11 = _x130 ∧ x12 = _x131 ∧ x1 = _x132 ∧ x2 = _x133 ∧ x3 = _x134 ∧ x4 = _x135 ∧ x5 = _x136 ∧ x6 = _x137 ∧ x7 = _x138 ∧ x8 = _x139 ∧ x9 = _x140 ∧ x10 = _x141 ∧ x11 = _x142 ∧ x12 = _x143 ∧ _x127 = _x139 ∧ _x126 = _x138 ∧ _x125 = _x137 ∧ _x143 = _x136 ∧ _x142 = _x134 ∧ _x141 = _x133 ∧ _x140 = _x132 ∧ _x134 ≤ 7 ∧ _x136 = _x136 ∧ _x135 = _x131 ∧ _x134 = _x130 ∧ _x133 = _x129 ∧ _x132 = _x128
l5	8	l4:	x1 = _x144 ∧ x2 = _x145 ∧ x3 = _x146 ∧ x4 = _x147 ∧ x5 = _x148 ∧ x6 = _x149 ∧ x7 = _x150 ∧ x8 = _x151 ∧ x9 = _x152 ∧ x10 = _x153 ∧ x11 = _x154 ∧ x12 = _x155 ∧ x1 = _x156 ∧ x2 = _x157 ∧ x3 = _x158 ∧ x4 = _x159 ∧ x5 = _x160 ∧ x6 = _x161 ∧ x7 = _x162 ∧ x8 = _x163 ∧ x9 = _x164 ∧ x10 = _x165 ∧ x11 = _x166 ∧ x12 = _x167 ∧ _x151 = _x163 ∧ _x150 = _x162 ∧ _x149 = _x161 ∧ _x167 = _x160 ∧ _x166 = _x158 ∧ _x165 = _x157 ∧ _x164 = _x156 ∧ 8 ≤ _x158 ∧ _x160 = _x160 ∧ _x159 = _x155 ∧ _x158 = _x154 ∧ _x157 = _x153 ∧ _x156 = _x152
l6	9	l5:	x1 = _x168 ∧ x2 = _x169 ∧ x3 = _x170 ∧ x4 = _x171 ∧ x5 = _x172 ∧ x6 = _x173 ∧ x7 = _x174 ∧ x8 = _x175 ∧ x9 = _x176 ∧ x10 = _x177 ∧ x11 = _x178 ∧ x12 = _x179 ∧ x1 = _x180 ∧ x2 = _x181 ∧ x3 = _x182 ∧ x4 = _x183 ∧ x5 = _x184 ∧ x6 = _x185 ∧ x7 = _x186 ∧ x8 = _x187 ∧ x9 = _x188 ∧ x10 = _x189 ∧ x11 = _x190 ∧ x12 = _x191 ∧ _x175 = _x187 ∧ _x174 = _x186 ∧ _x173 = _x185 ∧ _x191 = _x184 ∧ _x190 = _x181 ∧ _x189 = _x181 ∧ _x188 = _x180 ∧ _x184 = _x184 ∧ _x183 = _x179 ∧ _x182 = _x178 ∧ _x181 = _x177 ∧ _x180 = _x176
l7	10	l8:	x1 = _x192 ∧ x2 = _x193 ∧ x3 = _x194 ∧ x4 = _x195 ∧ x5 = _x196 ∧ x6 = _x197 ∧ x7 = _x198 ∧ x8 = _x199 ∧ x9 = _x200 ∧ x10 = _x201 ∧ x11 = _x202 ∧ x12 = _x203 ∧ x1 = _x204 ∧ x2 = _x205 ∧ x3 = _x206 ∧ x4 = _x207 ∧ x5 = _x208 ∧ x6 = _x209 ∧ x7 = _x210 ∧ x8 = _x211 ∧ x9 = _x212 ∧ x10 = _x213 ∧ x11 = _x214 ∧ x12 = _x215 ∧ _x215 = _x211 ∧ _x214 = _x210 ∧ _x213 = _x209 ∧ _x212 = _x208 ∧ _x211 = _x211 ∧ _x210 = _x210 ∧ _x209 = _x209 ∧ _x208 = _x208 ∧ _x207 = _x203 ∧ _x206 = _x202 ∧ _x205 = _x201 ∧ _x204 = _x200
l9	11	l6:	x1 = _x216 ∧ x2 = _x217 ∧ x3 = _x218 ∧ x4 = _x219 ∧ x5 = _x220 ∧ x6 = _x221 ∧ x7 = _x222 ∧ x8 = _x223 ∧ x9 = _x224 ∧ x10 = _x225 ∧ x11 = _x226 ∧ x12 = _x227 ∧ x1 = _x228 ∧ x2 = _x229 ∧ x3 = _x230 ∧ x4 = _x231 ∧ x5 = _x232 ∧ x6 = _x233 ∧ x7 = _x234 ∧ x8 = _x235 ∧ x9 = _x236 ∧ x10 = _x237 ∧ x11 = _x238 ∧ x12 = _x239 ∧ _x223 = _x235 ∧ _x222 = _x234 ∧ _x239 = _x233 ∧ _x238 = _x232 ∧ _x237 = _x229 ∧ _x236 = _x228 ∧ _x233 = _x233 ∧ _x232 = _x232 ∧ _x231 = _x227 ∧ _x230 = _x226 ∧ _x229 = _x225 ∧ _x228 = _x224
l9	12	l7:	x1 = _x240 ∧ x2 = _x241 ∧ x3 = _x242 ∧ x4 = _x243 ∧ x5 = _x244 ∧ x6 = _x245 ∧ x7 = _x246 ∧ x8 = _x247 ∧ x9 = _x248 ∧ x10 = _x249 ∧ x11 = _x250 ∧ x12 = _x251 ∧ x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ x8 = _x259 ∧ x9 = _x260 ∧ x10 = _x261 ∧ x11 = _x262 ∧ x12 = _x263 ∧ _x247 = _x259 ∧ _x246 = _x258 ∧ _x263 = _x257 ∧ _x262 = _x256 ∧ _x261 = _x253 ∧ _x260 = _x252 ∧ _x257 = _x257 ∧ _x256 = _x256 ∧ _x255 = _x251 ∧ _x254 = _x250 ∧ _x253 = _x249 ∧ _x252 = _x248
l1	13	l8:	x1 = _x264 ∧ x2 = _x265 ∧ x3 = _x266 ∧ x4 = _x267 ∧ x5 = _x268 ∧ x6 = _x269 ∧ x7 = _x270 ∧ x8 = _x271 ∧ x9 = _x272 ∧ x10 = _x273 ∧ x11 = _x274 ∧ x12 = _x275 ∧ x1 = _x276 ∧ x2 = _x277 ∧ x3 = _x278 ∧ x4 = _x279 ∧ x5 = _x280 ∧ x6 = _x281 ∧ x7 = _x282 ∧ x8 = _x283 ∧ x9 = _x284 ∧ x10 = _x285 ∧ x11 = _x286 ∧ x12 = _x287 ∧ _x287 = _x283 ∧ _x286 = _x282 ∧ _x285 = _x281 ∧ _x284 = _x280 ∧ _x283 = _x283 ∧ _x282 = _x282 ∧ _x281 = _x281 ∧ _x280 = _x280 ∧ _x279 = _x275 ∧ _x278 = _x274 ∧ _x277 = _x273 ∧ _x276 = _x272
l10	14	l9:	x1 = _x288 ∧ x2 = _x289 ∧ x3 = _x290 ∧ x4 = _x291 ∧ x5 = _x292 ∧ x6 = _x293 ∧ x7 = _x294 ∧ x8 = _x295 ∧ x9 = _x296 ∧ x10 = _x297 ∧ x11 = _x298 ∧ x12 = _x299 ∧ x1 = _x300 ∧ x2 = _x301 ∧ x3 = _x302 ∧ x4 = _x303 ∧ x5 = _x304 ∧ x6 = _x305 ∧ x7 = _x306 ∧ x8 = _x307 ∧ x9 = _x308 ∧ x10 = _x309 ∧ x11 = _x310 ∧ x12 = _x311 ∧ _x295 = _x307 ∧ _x294 = _x306 ∧ _x311 = _x305 ∧ _x310 = _x304 ∧ _x309 = _x301 ∧ _x308 = _x300 ∧ _x305 = _x305 ∧ _x304 = _x304 ∧ _x303 = _x299 ∧ _x302 = _x298 ∧ _x301 = _x297 ∧ _x300 = _x296
l10	15	l0:	x1 = _x312 ∧ x2 = _x313 ∧ x3 = _x314 ∧ x4 = _x315 ∧ x5 = _x316 ∧ x6 = _x317 ∧ x7 = _x318 ∧ x8 = _x319 ∧ x9 = _x320 ∧ x10 = _x321 ∧ x11 = _x322 ∧ x12 = _x323 ∧ x1 = _x324 ∧ x2 = _x325 ∧ x3 = _x326 ∧ x4 = _x327 ∧ x5 = _x328 ∧ x6 = _x329 ∧ x7 = _x330 ∧ x8 = _x331 ∧ x9 = _x332 ∧ x10 = _x333 ∧ x11 = _x334 ∧ x12 = _x335 ∧ _x323 = _x335 ∧ _x322 = _x334 ∧ _x321 = _x333 ∧ _x320 = _x332 ∧ _x319 = _x331 ∧ _x318 = _x330 ∧ _x317 = _x329 ∧ _x316 = _x328 ∧ _x315 = _x327 ∧ _x314 = _x326 ∧ _x313 = _x325 ∧ _x312 = _x324
l10	16	l3:	x1 = _x336 ∧ x2 = _x337 ∧ x3 = _x338 ∧ x4 = _x339 ∧ x5 = _x340 ∧ x6 = _x341 ∧ x7 = _x342 ∧ x8 = _x343 ∧ x9 = _x344 ∧ x10 = _x345 ∧ x11 = _x346 ∧ x12 = _x347 ∧ x1 = _x348 ∧ x2 = _x349 ∧ x3 = _x350 ∧ x4 = _x351 ∧ x5 = _x352 ∧ x6 = _x353 ∧ x7 = _x354 ∧ x8 = _x355 ∧ x9 = _x356 ∧ x10 = _x357 ∧ x11 = _x358 ∧ x12 = _x359 ∧ _x347 = _x359 ∧ _x346 = _x358 ∧ _x345 = _x357 ∧ _x344 = _x356 ∧ _x343 = _x355 ∧ _x342 = _x354 ∧ _x341 = _x353 ∧ _x340 = _x352 ∧ _x339 = _x351 ∧ _x338 = _x350 ∧ _x337 = _x349 ∧ _x336 = _x348
l10	17	l4:	x1 = _x360 ∧ x2 = _x361 ∧ x3 = _x362 ∧ x4 = _x363 ∧ x5 = _x364 ∧ x6 = _x365 ∧ x7 = _x366 ∧ x8 = _x367 ∧ x9 = _x368 ∧ x10 = _x369 ∧ x11 = _x370 ∧ x12 = _x371 ∧ x1 = _x372 ∧ x2 = _x373 ∧ x3 = _x374 ∧ x4 = _x375 ∧ x5 = _x376 ∧ x6 = _x377 ∧ x7 = _x378 ∧ x8 = _x379 ∧ x9 = _x380 ∧ x10 = _x381 ∧ x11 = _x382 ∧ x12 = _x383 ∧ _x371 = _x383 ∧ _x370 = _x382 ∧ _x369 = _x381 ∧ _x368 = _x380 ∧ _x367 = _x379 ∧ _x366 = _x378 ∧ _x365 = _x377 ∧ _x364 = _x376 ∧ _x363 = _x375 ∧ _x362 = _x374 ∧ _x361 = _x373 ∧ _x360 = _x372
l10	18	l5:	x1 = _x384 ∧ x2 = _x385 ∧ x3 = _x386 ∧ x4 = _x387 ∧ x5 = _x388 ∧ x6 = _x389 ∧ x7 = _x390 ∧ x8 = _x391 ∧ x9 = _x392 ∧ x10 = _x393 ∧ x11 = _x394 ∧ x12 = _x395 ∧ x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x5 = _x400 ∧ x6 = _x401 ∧ x7 = _x402 ∧ x8 = _x403 ∧ x9 = _x404 ∧ x10 = _x405 ∧ x11 = _x406 ∧ x12 = _x407 ∧ _x395 = _x407 ∧ _x394 = _x406 ∧ _x393 = _x405 ∧ _x392 = _x404 ∧ _x391 = _x403 ∧ _x390 = _x402 ∧ _x389 = _x401 ∧ _x388 = _x400 ∧ _x387 = _x399 ∧ _x386 = _x398 ∧ _x385 = _x397 ∧ _x384 = _x396
l10	19	l8:	x1 = _x408 ∧ x2 = _x409 ∧ x3 = _x410 ∧ x4 = _x411 ∧ x5 = _x412 ∧ x6 = _x413 ∧ x7 = _x414 ∧ x8 = _x415 ∧ x9 = _x416 ∧ x10 = _x417 ∧ x11 = _x418 ∧ x12 = _x419 ∧ x1 = _x420 ∧ x2 = _x421 ∧ x3 = _x422 ∧ x4 = _x423 ∧ x5 = _x424 ∧ x6 = _x425 ∧ x7 = _x426 ∧ x8 = _x427 ∧ x9 = _x428 ∧ x10 = _x429 ∧ x11 = _x430 ∧ x12 = _x431 ∧ _x419 = _x431 ∧ _x418 = _x430 ∧ _x417 = _x429 ∧ _x416 = _x428 ∧ _x415 = _x427 ∧ _x414 = _x426 ∧ _x413 = _x425 ∧ _x412 = _x424 ∧ _x411 = _x423 ∧ _x410 = _x422 ∧ _x409 = _x421 ∧ _x408 = _x420
l10	20	l6:	x1 = _x432 ∧ x2 = _x433 ∧ x3 = _x434 ∧ x4 = _x435 ∧ x5 = _x436 ∧ x6 = _x437 ∧ x7 = _x438 ∧ x8 = _x439 ∧ x9 = _x440 ∧ x10 = _x441 ∧ x11 = _x442 ∧ x12 = _x443 ∧ x1 = _x444 ∧ x2 = _x445 ∧ x3 = _x446 ∧ x4 = _x447 ∧ x5 = _x448 ∧ x6 = _x449 ∧ x7 = _x450 ∧ x8 = _x451 ∧ x9 = _x452 ∧ x10 = _x453 ∧ x11 = _x454 ∧ x12 = _x455 ∧ _x443 = _x455 ∧ _x442 = _x454 ∧ _x441 = _x453 ∧ _x440 = _x452 ∧ _x439 = _x451 ∧ _x438 = _x450 ∧ _x437 = _x449 ∧ _x436 = _x448 ∧ _x435 = _x447 ∧ _x434 = _x446 ∧ _x433 = _x445 ∧ _x432 = _x444
l10	21	l7:	x1 = _x456 ∧ x2 = _x457 ∧ x3 = _x458 ∧ x4 = _x459 ∧ x5 = _x460 ∧ x6 = _x461 ∧ x7 = _x462 ∧ x8 = _x463 ∧ x9 = _x464 ∧ x10 = _x465 ∧ x11 = _x466 ∧ x12 = _x467 ∧ x1 = _x468 ∧ x2 = _x469 ∧ x3 = _x470 ∧ x4 = _x471 ∧ x5 = _x472 ∧ x6 = _x473 ∧ x7 = _x474 ∧ x8 = _x475 ∧ x9 = _x476 ∧ x10 = _x477 ∧ x11 = _x478 ∧ x12 = _x479 ∧ _x467 = _x479 ∧ _x466 = _x478 ∧ _x465 = _x477 ∧ _x464 = _x476 ∧ _x463 = _x475 ∧ _x462 = _x474 ∧ _x461 = _x473 ∧ _x460 = _x472 ∧ _x459 = _x471 ∧ _x458 = _x470 ∧ _x457 = _x469 ∧ _x456 = _x468
l10	22	l9:	x1 = _x480 ∧ x2 = _x481 ∧ x3 = _x482 ∧ x4 = _x483 ∧ x5 = _x484 ∧ x6 = _x485 ∧ x7 = _x486 ∧ x8 = _x487 ∧ x9 = _x488 ∧ x10 = _x489 ∧ x11 = _x490 ∧ x12 = _x491 ∧ x1 = _x492 ∧ x2 = _x493 ∧ x3 = _x494 ∧ x4 = _x495 ∧ x5 = _x496 ∧ x6 = _x497 ∧ x7 = _x498 ∧ x8 = _x499 ∧ x9 = _x500 ∧ x10 = _x501 ∧ x11 = _x502 ∧ x12 = _x503 ∧ _x491 = _x503 ∧ _x490 = _x502 ∧ _x489 = _x501 ∧ _x488 = _x500 ∧ _x487 = _x499 ∧ _x486 = _x498 ∧ _x485 = _x497 ∧ _x484 = _x496 ∧ _x483 = _x495 ∧ _x482 = _x494 ∧ _x481 = _x493 ∧ _x480 = _x492
l10	23	l1:	x1 = _x504 ∧ x2 = _x505 ∧ x3 = _x506 ∧ x4 = _x507 ∧ x5 = _x508 ∧ x6 = _x509 ∧ x7 = _x510 ∧ x8 = _x511 ∧ x9 = _x512 ∧ x10 = _x513 ∧ x11 = _x514 ∧ x12 = _x515 ∧ x1 = _x516 ∧ x2 = _x517 ∧ x3 = _x518 ∧ x4 = _x519 ∧ x5 = _x520 ∧ x6 = _x521 ∧ x7 = _x522 ∧ x8 = _x523 ∧ x9 = _x524 ∧ x10 = _x525 ∧ x11 = _x526 ∧ x12 = _x527 ∧ _x515 = _x527 ∧ _x514 = _x526 ∧ _x513 = _x525 ∧ _x512 = _x524 ∧ _x511 = _x523 ∧ _x510 = _x522 ∧ _x509 = _x521 ∧ _x508 = _x520 ∧ _x507 = _x519 ∧ _x506 = _x518 ∧ _x505 = _x517 ∧ _x504 = _x516
l11	24	l10:	x1 = _x528 ∧ x2 = _x529 ∧ x3 = _x530 ∧ x4 = _x531 ∧ x5 = _x532 ∧ x6 = _x533 ∧ x7 = _x534 ∧ x8 = _x535 ∧ x9 = _x536 ∧ x10 = _x537 ∧ x11 = _x538 ∧ x12 = _x539 ∧ x1 = _x540 ∧ x2 = _x541 ∧ x3 = _x542 ∧ x4 = _x543 ∧ x5 = _x544 ∧ x6 = _x545 ∧ x7 = _x546 ∧ x8 = _x547 ∧ x9 = _x548 ∧ x10 = _x549 ∧ x11 = _x550 ∧ x12 = _x551 ∧ _x539 = _x551 ∧ _x538 = _x550 ∧ _x537 = _x549 ∧ _x536 = _x548 ∧ _x535 = _x547 ∧ _x534 = _x546 ∧ _x533 = _x545 ∧ _x532 = _x544 ∧ _x531 = _x543 ∧ _x530 = _x542 ∧ _x529 = _x541 ∧ _x528 = _x540

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
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
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
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 ∧ x12 = x12
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
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
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
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
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
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
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

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 { l5, l4 }.

2.1.1 Transition Removal

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

l4:	x11 − 4
l5:	x11

2.1.2 Transition Removal

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

l4:	0
l5:	−1

2.1.3 Trivial Cooperation Program

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

2.2 SCC Subproblem 2/2

Here we consider the SCC { l0, l2 }.

2.2.1 Transition Removal

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

l0:	2⋅x12
l2:	2⋅x12 + 1

2.2.2 Transition Removal

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

l2:	0
l0:	−1

2.2.3 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 % (10 real / 0 unknown / 0 assumptions / 10 total proof steps)