# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l4, l7, l6, l1, l8, l0, l2
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _nNHAT0 ∧ x2 = _nPow___010HAT0 ∧ x3 = _nPow___015HAT0 ∧ x4 = _nPow___020HAT0 ∧ x5 = _naHAT0 ∧ x6 = _nbHAT0 ∧ x7 = _ncHAT0 ∧ x8 = _ni11HAT0 ∧ x9 = _ni16HAT0 ∧ x10 = _ni21HAT0 ∧ x11 = _np14HAT0 ∧ x12 = _np19HAT0 ∧ x13 = _np9HAT0 ∧ x14 = _nx13HAT0 ∧ x15 = _nx18HAT0 ∧ x16 = _nx8HAT0 ∧ x17 = _ret_nPow12HAT0 ∧ x18 = _ret_nPow17HAT0 ∧ x19 = _ret_nPow22HAT0 ∧ x20 = _tmpHAT0 ∧ x21 = _tmp___0HAT0 ∧ x22 = _tmp___1HAT0 ∧ x1 = _nNHATpost ∧ x2 = _nPow___010HATpost ∧ x3 = _nPow___015HATpost ∧ x4 = _nPow___020HATpost ∧ x5 = _naHATpost ∧ x6 = _nbHATpost ∧ x7 = _ncHATpost ∧ x8 = _ni11HATpost ∧ x9 = _ni16HATpost ∧ x10 = _ni21HATpost ∧ x11 = _np14HATpost ∧ x12 = _np19HATpost ∧ x13 = _np9HATpost ∧ x14 = _nx13HATpost ∧ x15 = _nx18HATpost ∧ x16 = _nx8HATpost ∧ x17 = _ret_nPow12HATpost ∧ x18 = _ret_nPow17HATpost ∧ x19 = _ret_nPow22HATpost ∧ x20 = _tmpHATpost ∧ x21 = _tmp___0HATpost ∧ x22 = _tmp___1HATpost ∧ _tmp___1HAT0 = _tmp___1HATpost ∧ _tmp___0HAT0 = _tmp___0HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _ret_nPow22HAT0 = _ret_nPow22HATpost ∧ _ret_nPow17HAT0 = _ret_nPow17HATpost ∧ _ret_nPow12HAT0 = _ret_nPow12HATpost ∧ _nx8HAT0 = _nx8HATpost ∧ _nx18HAT0 = _nx18HATpost ∧ _nx13HAT0 = _nx13HATpost ∧ _np9HAT0 = _np9HATpost ∧ _np19HAT0 = _np19HATpost ∧ _np14HAT0 = _np14HATpost ∧ _ni21HAT0 = _ni21HATpost ∧ _ni16HAT0 = _ni16HATpost ∧ _ni11HAT0 = _ni11HATpost ∧ _ncHAT0 = _ncHATpost ∧ _nbHAT0 = _nbHATpost ∧ _naHAT0 = _naHATpost ∧ _nPow___020HAT0 = _nPow___020HATpost ∧ _nPow___015HAT0 = _nPow___015HATpost ∧ _nPow___010HAT0 = _nPow___010HATpost ∧ _nNHAT0 = _nNHATpost 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 ∧ x14 = _x13 ∧ x15 = _x14 ∧ x16 = _x15 ∧ x17 = _x16 ∧ x18 = _x17 ∧ x19 = _x18 ∧ x20 = _x19 ∧ x21 = _x20 ∧ x22 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ x3 = _x24 ∧ x4 = _x25 ∧ x5 = _x26 ∧ x6 = _x27 ∧ x7 = _x28 ∧ x8 = _x29 ∧ x9 = _x30 ∧ x10 = _x31 ∧ x11 = _x32 ∧ x12 = _x33 ∧ x13 = _x34 ∧ x14 = _x35 ∧ x15 = _x36 ∧ x16 = _x37 ∧ x17 = _x38 ∧ x18 = _x39 ∧ x19 = _x40 ∧ x20 = _x41 ∧ x21 = _x42 ∧ x22 = _x43 ∧ _x20 = _x42 ∧ _x19 = _x41 ∧ _x17 = _x39 ∧ _x16 = _x38 ∧ _x15 = _x37 ∧ _x14 = _x36 ∧ _x13 = _x35 ∧ _x12 = _x34 ∧ _x11 = _x33 ∧ _x10 = _x32 ∧ _x9 = _x31 ∧ _x8 = _x30 ∧ _x7 = _x29 ∧ _x6 = _x28 ∧ _x5 = _x27 ∧ _x4 = _x26 ∧ _x3 = _x25 ∧ _x2 = _x24 ∧ _x1 = _x23 ∧ _x = _x22 ∧ _x43 = _x40 ∧ _x40 = _x3 ∧ _x11 ≤ _x9 l2 3 l4: x1 = _x44 ∧ x2 = _x45 ∧ x3 = _x46 ∧ x4 = _x47 ∧ x5 = _x48 ∧ x6 = _x49 ∧ x7 = _x50 ∧ x8 = _x51 ∧ x9 = _x52 ∧ x10 = _x53 ∧ x11 = _x54 ∧ x12 = _x55 ∧ x13 = _x56 ∧ x14 = _x57 ∧ x15 = _x58 ∧ x16 = _x59 ∧ x17 = _x60 ∧ x18 = _x61 ∧ x19 = _x62 ∧ x20 = _x63 ∧ x21 = _x64 ∧ x22 = _x65 ∧ x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x4 = _x69 ∧ x5 = _x70 ∧ x6 = _x71 ∧ x7 = _x72 ∧ x8 = _x73 ∧ x9 = _x74 ∧ x10 = _x75 ∧ x11 = _x76 ∧ x12 = _x77 ∧ x13 = _x78 ∧ x14 = _x79 ∧ x15 = _x80 ∧ x16 = _x81 ∧ x17 = _x82 ∧ x18 = _x83 ∧ x19 = _x84 ∧ x20 = _x85 ∧ x21 = _x86 ∧ x22 = _x87 ∧ _x65 = _x87 ∧ _x64 = _x86 ∧ _x63 = _x85 ∧ _x62 = _x84 ∧ _x61 = _x83 ∧ _x60 = _x82 ∧ _x59 = _x81 ∧ _x58 = _x80 ∧ _x57 = _x79 ∧ _x56 = _x78 ∧ _x55 = _x77 ∧ _x54 = _x76 ∧ _x52 = _x74 ∧ _x51 = _x73 ∧ _x50 = _x72 ∧ _x49 = _x71 ∧ _x48 = _x70 ∧ _x46 = _x68 ∧ _x45 = _x67 ∧ _x44 = _x66 ∧ _x75 = 1 + _x53 ∧ _x69 = _x69 ∧ 1 + _x53 ≤ _x55 l5 4 l6: x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x90 ∧ x4 = _x91 ∧ x5 = _x92 ∧ x6 = _x93 ∧ x7 = _x94 ∧ x8 = _x95 ∧ x9 = _x96 ∧ x10 = _x97 ∧ x11 = _x98 ∧ x12 = _x99 ∧ x13 = _x100 ∧ x14 = _x101 ∧ x15 = _x102 ∧ x16 = _x103 ∧ x17 = _x104 ∧ x18 = _x105 ∧ x19 = _x106 ∧ x20 = _x107 ∧ x21 = _x108 ∧ x22 = _x109 ∧ x1 = _x110 ∧ x2 = _x111 ∧ x3 = _x112 ∧ x4 = _x113 ∧ x5 = _x114 ∧ x6 = _x115 ∧ x7 = _x116 ∧ x8 = _x117 ∧ x9 = _x118 ∧ x10 = _x119 ∧ x11 = _x120 ∧ x12 = _x121 ∧ x13 = _x122 ∧ x14 = _x123 ∧ x15 = _x124 ∧ x16 = _x125 ∧ x17 = _x126 ∧ x18 = _x127 ∧ x19 = _x128 ∧ x20 = _x129 ∧ x21 = _x130 ∧ x22 = _x131 ∧ _x109 = _x131 ∧ _x108 = _x130 ∧ _x107 = _x129 ∧ _x106 = _x128 ∧ _x105 = _x127 ∧ _x104 = _x126 ∧ _x103 = _x125 ∧ _x102 = _x124 ∧ _x101 = _x123 ∧ _x100 = _x122 ∧ _x99 = _x121 ∧ _x98 = _x120 ∧ _x97 = _x119 ∧ _x96 = _x118 ∧ _x95 = _x117 ∧ _x94 = _x116 ∧ _x93 = _x115 ∧ _x92 = _x114 ∧ _x91 = _x113 ∧ _x90 = _x112 ∧ _x89 = _x111 ∧ _x88 = _x110 l6 5 l4: x1 = _x132 ∧ x2 = _x133 ∧ x3 = _x134 ∧ x4 = _x135 ∧ x5 = _x136 ∧ x6 = _x137 ∧ x7 = _x138 ∧ x8 = _x139 ∧ x9 = _x140 ∧ x10 = _x141 ∧ x11 = _x142 ∧ x12 = _x143 ∧ x13 = _x144 ∧ x14 = _x145 ∧ x15 = _x146 ∧ x16 = _x147 ∧ x17 = _x148 ∧ x18 = _x149 ∧ x19 = _x150 ∧ x20 = _x151 ∧ x21 = _x152 ∧ x22 = _x153 ∧ x1 = _x154 ∧ x2 = _x155 ∧ x3 = _x156 ∧ x4 = _x157 ∧ x5 = _x158 ∧ x6 = _x159 ∧ x7 = _x160 ∧ x8 = _x161 ∧ x9 = _x162 ∧ x10 = _x163 ∧ x11 = _x164 ∧ x12 = _x165 ∧ x13 = _x166 ∧ x14 = _x167 ∧ x15 = _x168 ∧ x16 = _x169 ∧ x17 = _x170 ∧ x18 = _x171 ∧ x19 = _x172 ∧ x20 = _x173 ∧ x21 = _x174 ∧ x22 = _x175 ∧ _x153 = _x175 ∧ _x151 = _x173 ∧ _x150 = _x172 ∧ _x148 = _x170 ∧ _x147 = _x169 ∧ _x145 = _x167 ∧ _x144 = _x166 ∧ _x142 = _x164 ∧ _x140 = _x162 ∧ _x139 = _x161 ∧ _x138 = _x160 ∧ _x137 = _x159 ∧ _x136 = _x158 ∧ _x134 = _x156 ∧ _x133 = _x155 ∧ _x132 = _x154 ∧ _x163 = 0 ∧ _x157 = 1 ∧ _x165 = _x132 ∧ _x168 = _x138 ∧ _x174 = _x171 ∧ _x171 = _x134 ∧ _x142 ≤ _x140 l6 6 l5: x1 = _x176 ∧ x2 = _x177 ∧ x3 = _x178 ∧ x4 = _x179 ∧ x5 = _x180 ∧ x6 = _x181 ∧ x7 = _x182 ∧ x8 = _x183 ∧ x9 = _x184 ∧ x10 = _x185 ∧ x11 = _x186 ∧ x12 = _x187 ∧ x13 = _x188 ∧ x14 = _x189 ∧ x15 = _x190 ∧ x16 = _x191 ∧ x17 = _x192 ∧ x18 = _x193 ∧ x19 = _x194 ∧ x20 = _x195 ∧ x21 = _x196 ∧ x22 = _x197 ∧ x1 = _x198 ∧ x2 = _x199 ∧ x3 = _x200 ∧ x4 = _x201 ∧ x5 = _x202 ∧ x6 = _x203 ∧ x7 = _x204 ∧ x8 = _x205 ∧ x9 = _x206 ∧ x10 = _x207 ∧ x11 = _x208 ∧ x12 = _x209 ∧ x13 = _x210 ∧ x14 = _x211 ∧ x15 = _x212 ∧ x16 = _x213 ∧ x17 = _x214 ∧ x18 = _x215 ∧ x19 = _x216 ∧ x20 = _x217 ∧ x21 = _x218 ∧ x22 = _x219 ∧ _x197 = _x219 ∧ _x196 = _x218 ∧ _x195 = _x217 ∧ _x194 = _x216 ∧ _x193 = _x215 ∧ _x192 = _x214 ∧ _x191 = _x213 ∧ _x190 = _x212 ∧ _x189 = _x211 ∧ _x188 = _x210 ∧ _x187 = _x209 ∧ _x186 = _x208 ∧ _x185 = _x207 ∧ _x183 = _x205 ∧ _x182 = _x204 ∧ _x181 = _x203 ∧ _x180 = _x202 ∧ _x179 = _x201 ∧ _x177 = _x199 ∧ _x176 = _x198 ∧ _x206 = 1 + _x184 ∧ _x200 = _x200 ∧ 1 + _x184 ≤ _x186 l4 7 l2: x1 = _x220 ∧ x2 = _x221 ∧ x3 = _x222 ∧ x4 = _x223 ∧ x5 = _x224 ∧ x6 = _x225 ∧ x7 = _x226 ∧ x8 = _x227 ∧ x9 = _x228 ∧ x10 = _x229 ∧ x11 = _x230 ∧ x12 = _x231 ∧ x13 = _x232 ∧ x14 = _x233 ∧ x15 = _x234 ∧ x16 = _x235 ∧ x17 = _x236 ∧ x18 = _x237 ∧ x19 = _x238 ∧ x20 = _x239 ∧ x21 = _x240 ∧ x22 = _x241 ∧ x1 = _x242 ∧ x2 = _x243 ∧ x3 = _x244 ∧ x4 = _x245 ∧ x5 = _x246 ∧ x6 = _x247 ∧ x7 = _x248 ∧ x8 = _x249 ∧ x9 = _x250 ∧ x10 = _x251 ∧ x11 = _x252 ∧ x12 = _x253 ∧ x13 = _x254 ∧ x14 = _x255 ∧ x15 = _x256 ∧ x16 = _x257 ∧ x17 = _x258 ∧ x18 = _x259 ∧ x19 = _x260 ∧ x20 = _x261 ∧ x21 = _x262 ∧ x22 = _x263 ∧ _x241 = _x263 ∧ _x240 = _x262 ∧ _x239 = _x261 ∧ _x238 = _x260 ∧ _x237 = _x259 ∧ _x236 = _x258 ∧ _x235 = _x257 ∧ _x234 = _x256 ∧ _x233 = _x255 ∧ _x232 = _x254 ∧ _x231 = _x253 ∧ _x230 = _x252 ∧ _x229 = _x251 ∧ _x228 = _x250 ∧ _x227 = _x249 ∧ _x226 = _x248 ∧ _x225 = _x247 ∧ _x224 = _x246 ∧ _x223 = _x245 ∧ _x222 = _x244 ∧ _x221 = _x243 ∧ _x220 = _x242 l1 8 l5: x1 = _x264 ∧ x2 = _x265 ∧ x3 = _x266 ∧ x4 = _x267 ∧ x5 = _x268 ∧ x6 = _x269 ∧ x7 = _x270 ∧ x8 = _x271 ∧ x9 = _x272 ∧ x10 = _x273 ∧ x11 = _x274 ∧ x12 = _x275 ∧ x13 = _x276 ∧ x14 = _x277 ∧ x15 = _x278 ∧ x16 = _x279 ∧ x17 = _x280 ∧ x18 = _x281 ∧ x19 = _x282 ∧ x20 = _x283 ∧ x21 = _x284 ∧ x22 = _x285 ∧ 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 ∧ x14 = _x299 ∧ x15 = _x300 ∧ x16 = _x301 ∧ x17 = _x302 ∧ x18 = _x303 ∧ x19 = _x304 ∧ x20 = _x305 ∧ x21 = _x306 ∧ x22 = _x307 ∧ _x285 = _x307 ∧ _x284 = _x306 ∧ _x282 = _x304 ∧ _x281 = _x303 ∧ _x279 = _x301 ∧ _x278 = _x300 ∧ _x276 = _x298 ∧ _x275 = _x297 ∧ _x273 = _x295 ∧ _x271 = _x293 ∧ _x270 = _x292 ∧ _x269 = _x291 ∧ _x268 = _x290 ∧ _x267 = _x289 ∧ _x265 = _x287 ∧ _x264 = _x286 ∧ _x294 = 0 ∧ _x288 = 1 ∧ _x296 = _x264 ∧ _x299 = _x269 ∧ _x305 = _x302 ∧ _x302 = _x265 ∧ _x276 ≤ _x271 l1 9 l0: x1 = _x308 ∧ x2 = _x309 ∧ x3 = _x310 ∧ x4 = _x311 ∧ x5 = _x312 ∧ x6 = _x313 ∧ x7 = _x314 ∧ x8 = _x315 ∧ x9 = _x316 ∧ x10 = _x317 ∧ x11 = _x318 ∧ x12 = _x319 ∧ x13 = _x320 ∧ x14 = _x321 ∧ x15 = _x322 ∧ x16 = _x323 ∧ x17 = _x324 ∧ x18 = _x325 ∧ x19 = _x326 ∧ x20 = _x327 ∧ x21 = _x328 ∧ x22 = _x329 ∧ x1 = _x330 ∧ x2 = _x331 ∧ x3 = _x332 ∧ x4 = _x333 ∧ x5 = _x334 ∧ x6 = _x335 ∧ x7 = _x336 ∧ x8 = _x337 ∧ x9 = _x338 ∧ x10 = _x339 ∧ x11 = _x340 ∧ x12 = _x341 ∧ x13 = _x342 ∧ x14 = _x343 ∧ x15 = _x344 ∧ x16 = _x345 ∧ x17 = _x346 ∧ x18 = _x347 ∧ x19 = _x348 ∧ x20 = _x349 ∧ x21 = _x350 ∧ x22 = _x351 ∧ _x329 = _x351 ∧ _x328 = _x350 ∧ _x327 = _x349 ∧ _x326 = _x348 ∧ _x325 = _x347 ∧ _x324 = _x346 ∧ _x323 = _x345 ∧ _x322 = _x344 ∧ _x321 = _x343 ∧ _x320 = _x342 ∧ _x319 = _x341 ∧ _x318 = _x340 ∧ _x317 = _x339 ∧ _x316 = _x338 ∧ _x314 = _x336 ∧ _x313 = _x335 ∧ _x312 = _x334 ∧ _x311 = _x333 ∧ _x310 = _x332 ∧ _x308 = _x330 ∧ _x337 = 1 + _x315 ∧ _x331 = _x331 ∧ 1 + _x315 ≤ _x320 l7 10 l0: x1 = _x352 ∧ x2 = _x353 ∧ x3 = _x354 ∧ x4 = _x355 ∧ x5 = _x356 ∧ x6 = _x357 ∧ x7 = _x358 ∧ x8 = _x359 ∧ x9 = _x360 ∧ x10 = _x361 ∧ x11 = _x362 ∧ x12 = _x363 ∧ x13 = _x364 ∧ x14 = _x365 ∧ x15 = _x366 ∧ x16 = _x367 ∧ x17 = _x368 ∧ x18 = _x369 ∧ x19 = _x370 ∧ x20 = _x371 ∧ x21 = _x372 ∧ x22 = _x373 ∧ x1 = _x374 ∧ x2 = _x375 ∧ x3 = _x376 ∧ x4 = _x377 ∧ x5 = _x378 ∧ x6 = _x379 ∧ x7 = _x380 ∧ x8 = _x381 ∧ x9 = _x382 ∧ x10 = _x383 ∧ x11 = _x384 ∧ x12 = _x385 ∧ x13 = _x386 ∧ x14 = _x387 ∧ x15 = _x388 ∧ x16 = _x389 ∧ x17 = _x390 ∧ x18 = _x391 ∧ x19 = _x392 ∧ x20 = _x393 ∧ x21 = _x394 ∧ x22 = _x395 ∧ _x373 = _x395 ∧ _x372 = _x394 ∧ _x371 = _x393 ∧ _x370 = _x392 ∧ _x369 = _x391 ∧ _x368 = _x390 ∧ _x366 = _x388 ∧ _x365 = _x387 ∧ _x363 = _x385 ∧ _x362 = _x384 ∧ _x361 = _x383 ∧ _x360 = _x382 ∧ _x358 = _x380 ∧ _x357 = _x379 ∧ _x356 = _x378 ∧ _x355 = _x377 ∧ _x354 = _x376 ∧ _x381 = 0 ∧ _x375 = 1 ∧ _x386 = _x374 ∧ _x389 = _x356 ∧ _x374 = 3 l8 11 l7: x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x5 = _x400 ∧ x6 = _x401 ∧ x7 = _x402 ∧ x8 = _x403 ∧ x9 = _x404 ∧ x10 = _x405 ∧ x11 = _x406 ∧ x12 = _x407 ∧ x13 = _x408 ∧ x14 = _x409 ∧ x15 = _x410 ∧ x16 = _x411 ∧ x17 = _x412 ∧ x18 = _x413 ∧ x19 = _x414 ∧ x20 = _x415 ∧ x21 = _x416 ∧ x22 = _x417 ∧ x1 = _x418 ∧ x2 = _x419 ∧ x3 = _x420 ∧ x4 = _x421 ∧ x5 = _x422 ∧ x6 = _x423 ∧ x7 = _x424 ∧ x8 = _x425 ∧ x9 = _x426 ∧ x10 = _x427 ∧ x11 = _x428 ∧ x12 = _x429 ∧ x13 = _x430 ∧ x14 = _x431 ∧ x15 = _x432 ∧ x16 = _x433 ∧ x17 = _x434 ∧ x18 = _x435 ∧ x19 = _x436 ∧ x20 = _x437 ∧ x21 = _x438 ∧ x22 = _x439 ∧ _x417 = _x439 ∧ _x416 = _x438 ∧ _x415 = _x437 ∧ _x414 = _x436 ∧ _x413 = _x435 ∧ _x412 = _x434 ∧ _x411 = _x433 ∧ _x410 = _x432 ∧ _x409 = _x431 ∧ _x408 = _x430 ∧ _x407 = _x429 ∧ _x406 = _x428 ∧ _x405 = _x427 ∧ _x404 = _x426 ∧ _x403 = _x425 ∧ _x402 = _x424 ∧ _x401 = _x423 ∧ _x400 = _x422 ∧ _x399 = _x421 ∧ _x398 = _x420 ∧ _x397 = _x419 ∧ _x396 = _x418

## 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 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 ∧ x13 = x13 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/3

Here we consider the SCC { l1, l0 }.

### 2.1.1 Transition Removal

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

 l0: −2⋅x8 + 2⋅x13 + 1 l1: −2⋅x8 + 2⋅x13

### 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 2/3

Here we consider the SCC { l5, l6 }.

### 2.2.1 Transition Removal

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

 l5: −1 − x9 + x11 l6: −1 − x9 + x11

### 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 3/3

Here we consider the SCC { l4, l2 }.

### 2.3.1 Transition Removal

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

 l4: −1 − x10 + x12 l2: −1 − x10 + x12

### 2.3.2 Transition Removal

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

 l4: 0 l2: −1

### 2.3.3 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 % (14 real / 0 unknown / 0 assumptions / 14 total proof steps)