# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l7, l11, l3, l13, l2, l9, l4, l6, l10, l8, l0, l12
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _a10HAT0 ∧ x2 = _a15HAT0 ∧ x3 = _b11HAT0 ∧ x4 = _b16HAT0 ∧ x5 = _c12HAT0 ∧ x6 = _c17HAT0 ∧ x7 = _m13HAT0 ∧ x8 = _ret_max24HAT0 ∧ x9 = _ret_min14HAT0 ∧ x10 = _tmp620HAT0 ∧ x11 = _tmp923HAT0 ∧ x12 = _tmp9HAT0 ∧ x13 = _tmpHAT0 ∧ x14 = _tmp___0HAT0 ∧ x15 = _tmp___1HAT0 ∧ x16 = _x_promoted_1HAT0 ∧ x17 = _y_promoted_2HAT0 ∧ x18 = _zHAT0 ∧ x1 = _a10HATpost ∧ x2 = _a15HATpost ∧ x3 = _b11HATpost ∧ x4 = _b16HATpost ∧ x5 = _c12HATpost ∧ x6 = _c17HATpost ∧ x7 = _m13HATpost ∧ x8 = _ret_max24HATpost ∧ x9 = _ret_min14HATpost ∧ x10 = _tmp620HATpost ∧ x11 = _tmp923HATpost ∧ x12 = _tmp9HATpost ∧ x13 = _tmpHATpost ∧ x14 = _tmp___0HATpost ∧ x15 = _tmp___1HATpost ∧ x16 = _x_promoted_1HATpost ∧ x17 = _y_promoted_2HATpost ∧ x18 = _zHATpost ∧ _zHAT0 = _zHATpost ∧ _y_promoted_2HAT0 = _y_promoted_2HATpost ∧ _x_promoted_1HAT0 = _x_promoted_1HATpost ∧ _tmp___1HAT0 = _tmp___1HATpost ∧ _tmp___0HAT0 = _tmp___0HATpost ∧ _tmp923HAT0 = _tmp923HATpost ∧ _tmp9HAT0 = _tmp9HATpost ∧ _tmp620HAT0 = _tmp620HATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _ret_min14HAT0 = _ret_min14HATpost ∧ _ret_max24HAT0 = _ret_max24HATpost ∧ _m13HAT0 = _m13HATpost ∧ _c17HAT0 = _c17HATpost ∧ _c12HAT0 = _c12HATpost ∧ _b16HAT0 = _b16HATpost ∧ _b11HAT0 = _b11HATpost ∧ _a15HAT0 = _a15HATpost ∧ _a10HAT0 = _a10HATpost 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 ∧ x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x4 = _x21 ∧ x5 = _x22 ∧ x6 = _x23 ∧ x7 = _x24 ∧ x8 = _x25 ∧ x9 = _x26 ∧ x10 = _x27 ∧ x11 = _x28 ∧ x12 = _x29 ∧ x13 = _x30 ∧ x14 = _x31 ∧ x15 = _x32 ∧ x16 = _x33 ∧ x17 = _x34 ∧ x18 = _x35 ∧ _x16 = _x34 ∧ _x15 = _x33 ∧ _x14 = _x32 ∧ _x10 = _x28 ∧ _x11 = _x29 ∧ _x9 = _x27 ∧ _x12 = _x30 ∧ _x8 = _x26 ∧ _x6 = _x24 ∧ _x5 = _x23 ∧ _x4 = _x22 ∧ _x3 = _x21 ∧ _x2 = _x20 ∧ _x1 = _x19 ∧ _x = _x18 ∧ _x35 = _x35 ∧ _x31 = _x25 ∧ _x25 = _x1 l4 3 l5: x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x4 = _x39 ∧ x5 = _x40 ∧ x6 = _x41 ∧ x7 = _x42 ∧ x8 = _x43 ∧ x9 = _x44 ∧ x10 = _x45 ∧ x11 = _x46 ∧ x12 = _x47 ∧ x13 = _x48 ∧ x14 = _x49 ∧ x15 = _x50 ∧ x16 = _x51 ∧ x17 = _x52 ∧ x18 = _x53 ∧ x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x4 = _x57 ∧ x5 = _x58 ∧ x6 = _x59 ∧ x7 = _x60 ∧ x8 = _x61 ∧ x9 = _x62 ∧ x10 = _x63 ∧ x11 = _x64 ∧ x12 = _x65 ∧ x13 = _x66 ∧ x14 = _x67 ∧ x15 = _x68 ∧ x16 = _x69 ∧ x17 = _x70 ∧ x18 = _x71 ∧ _x53 = _x71 ∧ _x52 = _x70 ∧ _x51 = _x69 ∧ _x50 = _x68 ∧ _x49 = _x67 ∧ _x46 = _x64 ∧ _x47 = _x65 ∧ _x45 = _x63 ∧ _x48 = _x66 ∧ _x44 = _x62 ∧ _x43 = _x61 ∧ _x42 = _x60 ∧ _x41 = _x59 ∧ _x40 = _x58 ∧ _x39 = _x57 ∧ _x38 = _x56 ∧ _x37 = _x55 ∧ _x36 = _x54 ∧ 1 + _x52 ≤ _x51 l4 4 l3: x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x6 = _x77 ∧ x7 = _x78 ∧ x8 = _x79 ∧ x9 = _x80 ∧ x10 = _x81 ∧ x11 = _x82 ∧ x12 = _x83 ∧ x13 = _x84 ∧ x14 = _x85 ∧ x15 = _x86 ∧ x16 = _x87 ∧ x17 = _x88 ∧ x18 = _x89 ∧ x1 = _x90 ∧ x2 = _x91 ∧ x3 = _x92 ∧ x4 = _x93 ∧ x5 = _x94 ∧ x6 = _x95 ∧ x7 = _x96 ∧ x8 = _x97 ∧ x9 = _x98 ∧ x10 = _x99 ∧ x11 = _x100 ∧ x12 = _x101 ∧ x13 = _x102 ∧ x14 = _x103 ∧ x15 = _x104 ∧ x16 = _x105 ∧ x17 = _x106 ∧ x18 = _x107 ∧ _x89 = _x107 ∧ _x88 = _x106 ∧ _x87 = _x105 ∧ _x86 = _x104 ∧ _x85 = _x103 ∧ _x82 = _x100 ∧ _x81 = _x99 ∧ _x84 = _x102 ∧ _x80 = _x98 ∧ _x79 = _x97 ∧ _x78 = _x96 ∧ _x77 = _x95 ∧ _x76 = _x94 ∧ _x75 = _x93 ∧ _x74 = _x92 ∧ _x73 = _x91 ∧ _x72 = _x90 ∧ _x101 = _x101 ∧ _x87 ≤ _x88 l6 5 l2: x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x4 = _x111 ∧ x5 = _x112 ∧ x6 = _x113 ∧ x7 = _x114 ∧ x8 = _x115 ∧ x9 = _x116 ∧ x10 = _x117 ∧ x11 = _x118 ∧ x12 = _x119 ∧ x13 = _x120 ∧ x14 = _x121 ∧ x15 = _x122 ∧ x16 = _x123 ∧ x17 = _x124 ∧ x18 = _x125 ∧ x1 = _x126 ∧ x2 = _x127 ∧ x3 = _x128 ∧ x4 = _x129 ∧ x5 = _x130 ∧ x6 = _x131 ∧ x7 = _x132 ∧ x8 = _x133 ∧ x9 = _x134 ∧ x10 = _x135 ∧ x11 = _x136 ∧ x12 = _x137 ∧ x13 = _x138 ∧ x14 = _x139 ∧ x15 = _x140 ∧ x16 = _x141 ∧ x17 = _x142 ∧ x18 = _x143 ∧ _x125 = _x143 ∧ _x124 = _x142 ∧ _x123 = _x141 ∧ _x122 = _x140 ∧ _x121 = _x139 ∧ _x118 = _x136 ∧ _x119 = _x137 ∧ _x117 = _x135 ∧ _x120 = _x138 ∧ _x116 = _x134 ∧ _x115 = _x133 ∧ _x114 = _x132 ∧ _x113 = _x131 ∧ _x112 = _x130 ∧ _x111 = _x129 ∧ _x110 = _x128 ∧ _x109 = _x127 ∧ _x108 = _x126 ∧ 1 + _x113 ≤ _x109 l6 6 l2: x1 = _x144 ∧ x2 = _x145 ∧ x3 = _x146 ∧ x4 = _x147 ∧ x5 = _x148 ∧ x6 = _x149 ∧ x7 = _x150 ∧ x8 = _x151 ∧ x9 = _x152 ∧ x10 = _x153 ∧ x11 = _x154 ∧ x12 = _x155 ∧ x13 = _x156 ∧ x14 = _x157 ∧ x15 = _x158 ∧ x16 = _x159 ∧ x17 = _x160 ∧ x18 = _x161 ∧ x1 = _x162 ∧ x2 = _x163 ∧ x3 = _x164 ∧ x4 = _x165 ∧ x5 = _x166 ∧ x6 = _x167 ∧ x7 = _x168 ∧ x8 = _x169 ∧ x9 = _x170 ∧ x10 = _x171 ∧ x11 = _x172 ∧ x12 = _x173 ∧ x13 = _x174 ∧ x14 = _x175 ∧ x15 = _x176 ∧ x16 = _x177 ∧ x17 = _x178 ∧ x18 = _x179 ∧ _x161 = _x179 ∧ _x160 = _x178 ∧ _x159 = _x177 ∧ _x158 = _x176 ∧ _x157 = _x175 ∧ _x155 = _x173 ∧ _x153 = _x171 ∧ _x156 = _x174 ∧ _x152 = _x170 ∧ _x151 = _x169 ∧ _x150 = _x168 ∧ _x149 = _x167 ∧ _x148 = _x166 ∧ _x147 = _x165 ∧ _x146 = _x164 ∧ _x145 = _x163 ∧ _x144 = _x162 ∧ _x172 = _x172 ∧ _x145 ≤ _x149 l7 7 l6: x1 = _x180 ∧ x2 = _x181 ∧ x3 = _x182 ∧ x4 = _x183 ∧ x5 = _x184 ∧ x6 = _x185 ∧ x7 = _x186 ∧ x8 = _x187 ∧ x9 = _x188 ∧ x10 = _x189 ∧ x11 = _x190 ∧ x12 = _x191 ∧ x13 = _x192 ∧ x14 = _x193 ∧ x15 = _x194 ∧ x16 = _x195 ∧ x17 = _x196 ∧ x18 = _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 ∧ _x197 = _x215 ∧ _x196 = _x214 ∧ _x195 = _x213 ∧ _x194 = _x212 ∧ _x193 = _x211 ∧ _x190 = _x208 ∧ _x191 = _x209 ∧ _x189 = _x207 ∧ _x192 = _x210 ∧ _x188 = _x206 ∧ _x187 = _x205 ∧ _x186 = _x204 ∧ _x185 = _x203 ∧ _x184 = _x202 ∧ _x183 = _x201 ∧ _x182 = _x200 ∧ _x181 = _x199 ∧ _x180 = _x198 ∧ 1 + _x183 ≤ _x181 l7 8 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 ∧ x13 = _x228 ∧ x14 = _x229 ∧ x15 = _x230 ∧ x16 = _x231 ∧ x17 = _x232 ∧ x18 = _x233 ∧ 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 ∧ x14 = _x247 ∧ x15 = _x248 ∧ x16 = _x249 ∧ x17 = _x250 ∧ x18 = _x251 ∧ _x233 = _x251 ∧ _x232 = _x250 ∧ _x231 = _x249 ∧ _x230 = _x248 ∧ _x229 = _x247 ∧ _x226 = _x244 ∧ _x227 = _x245 ∧ _x228 = _x246 ∧ _x224 = _x242 ∧ _x223 = _x241 ∧ _x222 = _x240 ∧ _x221 = _x239 ∧ _x220 = _x238 ∧ _x219 = _x237 ∧ _x218 = _x236 ∧ _x217 = _x235 ∧ _x216 = _x234 ∧ _x243 = _x243 ∧ _x217 ≤ _x219 l8 9 l9: x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ x8 = _x259 ∧ x9 = _x260 ∧ x10 = _x261 ∧ x11 = _x262 ∧ x12 = _x263 ∧ x13 = _x264 ∧ x14 = _x265 ∧ x15 = _x266 ∧ x16 = _x267 ∧ x17 = _x268 ∧ x18 = _x269 ∧ x1 = _x270 ∧ x2 = _x271 ∧ x3 = _x272 ∧ x4 = _x273 ∧ x5 = _x274 ∧ x6 = _x275 ∧ x7 = _x276 ∧ x8 = _x277 ∧ x9 = _x278 ∧ x10 = _x279 ∧ x11 = _x280 ∧ x12 = _x281 ∧ x13 = _x282 ∧ x14 = _x283 ∧ x15 = _x284 ∧ x16 = _x285 ∧ x17 = _x286 ∧ x18 = _x287 ∧ _x269 = _x287 ∧ _x268 = _x286 ∧ _x267 = _x285 ∧ _x266 = _x284 ∧ _x265 = _x283 ∧ _x262 = _x280 ∧ _x263 = _x281 ∧ _x261 = _x279 ∧ _x264 = _x282 ∧ _x260 = _x278 ∧ _x259 = _x277 ∧ _x257 = _x275 ∧ _x256 = _x274 ∧ _x255 = _x273 ∧ _x254 = _x272 ∧ _x253 = _x271 ∧ _x252 = _x270 ∧ _x276 = _x256 ∧ 1 + _x256 ≤ _x254 l8 10 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 ∧ x13 = _x300 ∧ x14 = _x301 ∧ x15 = _x302 ∧ x16 = _x303 ∧ x17 = _x304 ∧ x18 = _x305 ∧ x1 = _x306 ∧ x2 = _x307 ∧ x3 = _x308 ∧ x4 = _x309 ∧ x5 = _x310 ∧ x6 = _x311 ∧ x7 = _x312 ∧ x8 = _x313 ∧ x9 = _x314 ∧ x10 = _x315 ∧ x11 = _x316 ∧ x12 = _x317 ∧ x13 = _x318 ∧ x14 = _x319 ∧ x15 = _x320 ∧ x16 = _x321 ∧ x17 = _x322 ∧ x18 = _x323 ∧ _x305 = _x323 ∧ _x304 = _x322 ∧ _x303 = _x321 ∧ _x302 = _x320 ∧ _x301 = _x319 ∧ _x298 = _x316 ∧ _x299 = _x317 ∧ _x297 = _x315 ∧ _x300 = _x318 ∧ _x296 = _x314 ∧ _x295 = _x313 ∧ _x293 = _x311 ∧ _x292 = _x310 ∧ _x291 = _x309 ∧ _x290 = _x308 ∧ _x289 = _x307 ∧ _x288 = _x306 ∧ _x312 = _x290 ∧ _x290 ≤ _x292 l9 11 l3: x1 = _x324 ∧ x2 = _x325 ∧ x3 = _x326 ∧ x4 = _x327 ∧ x5 = _x328 ∧ x6 = _x329 ∧ x7 = _x330 ∧ x8 = _x331 ∧ x9 = _x332 ∧ x10 = _x333 ∧ x11 = _x334 ∧ x12 = _x335 ∧ x13 = _x336 ∧ x14 = _x337 ∧ x15 = _x338 ∧ x16 = _x339 ∧ x17 = _x340 ∧ x18 = _x341 ∧ x1 = _x342 ∧ x2 = _x343 ∧ x3 = _x344 ∧ x4 = _x345 ∧ x5 = _x346 ∧ x6 = _x347 ∧ x7 = _x348 ∧ x8 = _x349 ∧ x9 = _x350 ∧ x10 = _x351 ∧ x11 = _x352 ∧ x12 = _x353 ∧ x13 = _x354 ∧ x14 = _x355 ∧ x15 = _x356 ∧ x16 = _x357 ∧ x17 = _x358 ∧ x18 = _x359 ∧ _x341 = _x359 ∧ _x340 = _x358 ∧ _x338 = _x356 ∧ _x337 = _x355 ∧ _x334 = _x352 ∧ _x335 = _x353 ∧ _x333 = _x351 ∧ _x331 = _x349 ∧ _x330 = _x348 ∧ _x329 = _x347 ∧ _x328 = _x346 ∧ _x327 = _x345 ∧ _x326 = _x344 ∧ _x325 = _x343 ∧ _x324 = _x342 ∧ _x357 = _x354 + _x339 ∧ _x354 = _x350 ∧ _x350 = _x330 l10 12 l9: x1 = _x360 ∧ x2 = _x361 ∧ x3 = _x362 ∧ x4 = _x363 ∧ x5 = _x364 ∧ x6 = _x365 ∧ x7 = _x366 ∧ x8 = _x367 ∧ x9 = _x368 ∧ x10 = _x369 ∧ x11 = _x370 ∧ x12 = _x371 ∧ x13 = _x372 ∧ x14 = _x373 ∧ x15 = _x374 ∧ x16 = _x375 ∧ x17 = _x376 ∧ x18 = _x377 ∧ x1 = _x378 ∧ x2 = _x379 ∧ x3 = _x380 ∧ x4 = _x381 ∧ x5 = _x382 ∧ x6 = _x383 ∧ x7 = _x384 ∧ x8 = _x385 ∧ x9 = _x386 ∧ x10 = _x387 ∧ x11 = _x388 ∧ x12 = _x389 ∧ x13 = _x390 ∧ x14 = _x391 ∧ x15 = _x392 ∧ x16 = _x393 ∧ x17 = _x394 ∧ x18 = _x395 ∧ _x377 = _x395 ∧ _x376 = _x394 ∧ _x375 = _x393 ∧ _x374 = _x392 ∧ _x373 = _x391 ∧ _x370 = _x388 ∧ _x371 = _x389 ∧ _x369 = _x387 ∧ _x372 = _x390 ∧ _x368 = _x386 ∧ _x367 = _x385 ∧ _x365 = _x383 ∧ _x364 = _x382 ∧ _x363 = _x381 ∧ _x362 = _x380 ∧ _x361 = _x379 ∧ _x360 = _x378 ∧ _x384 = _x364 ∧ 1 + _x364 ≤ _x360 l10 13 l9: 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 ∧ x1 = _x414 ∧ x2 = _x415 ∧ x3 = _x416 ∧ x4 = _x417 ∧ x5 = _x418 ∧ x6 = _x419 ∧ x7 = _x420 ∧ x8 = _x421 ∧ x9 = _x422 ∧ x10 = _x423 ∧ x11 = _x424 ∧ x12 = _x425 ∧ x13 = _x426 ∧ x14 = _x427 ∧ x15 = _x428 ∧ x16 = _x429 ∧ x17 = _x430 ∧ x18 = _x431 ∧ _x413 = _x431 ∧ _x412 = _x430 ∧ _x411 = _x429 ∧ _x410 = _x428 ∧ _x409 = _x427 ∧ _x406 = _x424 ∧ _x407 = _x425 ∧ _x405 = _x423 ∧ _x408 = _x426 ∧ _x404 = _x422 ∧ _x403 = _x421 ∧ _x401 = _x419 ∧ _x400 = _x418 ∧ _x399 = _x417 ∧ _x398 = _x416 ∧ _x397 = _x415 ∧ _x396 = _x414 ∧ _x420 = _x396 ∧ _x396 ≤ _x400 l11 14 l8: x1 = _x432 ∧ x2 = _x433 ∧ x3 = _x434 ∧ x4 = _x435 ∧ x5 = _x436 ∧ x6 = _x437 ∧ x7 = _x438 ∧ x8 = _x439 ∧ x9 = _x440 ∧ x10 = _x441 ∧ x11 = _x442 ∧ x12 = _x443 ∧ x13 = _x444 ∧ x14 = _x445 ∧ x15 = _x446 ∧ x16 = _x447 ∧ x17 = _x448 ∧ x18 = _x449 ∧ x1 = _x450 ∧ x2 = _x451 ∧ x3 = _x452 ∧ x4 = _x453 ∧ x5 = _x454 ∧ x6 = _x455 ∧ x7 = _x456 ∧ x8 = _x457 ∧ x9 = _x458 ∧ x10 = _x459 ∧ x11 = _x460 ∧ x12 = _x461 ∧ x13 = _x462 ∧ x14 = _x463 ∧ x15 = _x464 ∧ x16 = _x465 ∧ x17 = _x466 ∧ x18 = _x467 ∧ _x449 = _x467 ∧ _x448 = _x466 ∧ _x447 = _x465 ∧ _x446 = _x464 ∧ _x445 = _x463 ∧ _x442 = _x460 ∧ _x443 = _x461 ∧ _x441 = _x459 ∧ _x444 = _x462 ∧ _x440 = _x458 ∧ _x439 = _x457 ∧ _x438 = _x456 ∧ _x437 = _x455 ∧ _x436 = _x454 ∧ _x435 = _x453 ∧ _x434 = _x452 ∧ _x433 = _x451 ∧ _x432 = _x450 ∧ 1 + _x434 ≤ _x432 l11 15 l10: 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 ∧ x14 = _x481 ∧ x15 = _x482 ∧ x16 = _x483 ∧ x17 = _x484 ∧ x18 = _x485 ∧ x1 = _x486 ∧ x2 = _x487 ∧ x3 = _x488 ∧ x4 = _x489 ∧ x5 = _x490 ∧ x6 = _x491 ∧ x7 = _x492 ∧ x8 = _x493 ∧ x9 = _x494 ∧ x10 = _x495 ∧ x11 = _x496 ∧ x12 = _x497 ∧ x13 = _x498 ∧ x14 = _x499 ∧ x15 = _x500 ∧ x16 = _x501 ∧ x17 = _x502 ∧ x18 = _x503 ∧ _x485 = _x503 ∧ _x484 = _x502 ∧ _x483 = _x501 ∧ _x482 = _x500 ∧ _x481 = _x499 ∧ _x478 = _x496 ∧ _x479 = _x497 ∧ _x477 = _x495 ∧ _x480 = _x498 ∧ _x476 = _x494 ∧ _x475 = _x493 ∧ _x474 = _x492 ∧ _x473 = _x491 ∧ _x472 = _x490 ∧ _x471 = _x489 ∧ _x470 = _x488 ∧ _x469 = _x487 ∧ _x468 = _x486 ∧ _x468 ≤ _x470 l5 16 l7: x1 = _x504 ∧ x2 = _x505 ∧ x3 = _x506 ∧ x4 = _x507 ∧ x5 = _x508 ∧ x6 = _x509 ∧ x7 = _x510 ∧ x8 = _x511 ∧ x9 = _x512 ∧ x10 = _x513 ∧ x11 = _x514 ∧ x12 = _x515 ∧ x13 = _x516 ∧ x14 = _x517 ∧ x15 = _x518 ∧ x16 = _x519 ∧ x17 = _x520 ∧ x18 = _x521 ∧ x1 = _x522 ∧ x2 = _x523 ∧ x3 = _x524 ∧ x4 = _x525 ∧ x5 = _x526 ∧ x6 = _x527 ∧ x7 = _x528 ∧ x8 = _x529 ∧ x9 = _x530 ∧ x10 = _x531 ∧ x11 = _x532 ∧ x12 = _x533 ∧ x13 = _x534 ∧ x14 = _x535 ∧ x15 = _x536 ∧ x16 = _x537 ∧ x17 = _x538 ∧ x18 = _x539 ∧ _x521 = _x539 ∧ _x520 = _x538 ∧ _x519 = _x537 ∧ _x518 = _x536 ∧ _x517 = _x535 ∧ _x514 = _x532 ∧ _x515 = _x533 ∧ _x513 = _x531 ∧ _x516 = _x534 ∧ _x512 = _x530 ∧ _x511 = _x529 ∧ _x510 = _x528 ∧ _x508 = _x526 ∧ _x506 = _x524 ∧ _x504 = _x522 ∧ _x527 = _x519 ∧ _x525 = _x520 ∧ _x523 = _x521 ∧ 1 + _x521 ≤ _x519 l5 17 l11: x1 = _x540 ∧ x2 = _x541 ∧ x3 = _x542 ∧ x4 = _x543 ∧ x5 = _x544 ∧ x6 = _x545 ∧ x7 = _x546 ∧ x8 = _x547 ∧ x9 = _x548 ∧ x10 = _x549 ∧ x11 = _x550 ∧ x12 = _x551 ∧ x13 = _x552 ∧ x14 = _x553 ∧ x15 = _x554 ∧ x16 = _x555 ∧ x17 = _x556 ∧ x18 = _x557 ∧ x1 = _x558 ∧ x2 = _x559 ∧ x3 = _x560 ∧ x4 = _x561 ∧ x5 = _x562 ∧ x6 = _x563 ∧ x7 = _x564 ∧ x8 = _x565 ∧ x9 = _x566 ∧ x10 = _x567 ∧ x11 = _x568 ∧ x12 = _x569 ∧ x13 = _x570 ∧ x14 = _x571 ∧ x15 = _x572 ∧ x16 = _x573 ∧ x17 = _x574 ∧ x18 = _x575 ∧ _x557 = _x575 ∧ _x556 = _x574 ∧ _x555 = _x573 ∧ _x554 = _x572 ∧ _x553 = _x571 ∧ _x550 = _x568 ∧ _x551 = _x569 ∧ _x549 = _x567 ∧ _x552 = _x570 ∧ _x548 = _x566 ∧ _x547 = _x565 ∧ _x546 = _x564 ∧ _x545 = _x563 ∧ _x543 = _x561 ∧ _x541 = _x559 ∧ _x562 = _x557 ∧ _x560 = _x556 ∧ _x558 = _x555 ∧ _x555 ≤ _x557 l3 18 l0: x1 = _x576 ∧ x2 = _x577 ∧ x3 = _x578 ∧ x4 = _x579 ∧ x5 = _x580 ∧ x6 = _x581 ∧ x7 = _x582 ∧ x8 = _x583 ∧ x9 = _x584 ∧ x10 = _x585 ∧ x11 = _x586 ∧ x12 = _x587 ∧ x13 = _x588 ∧ x14 = _x589 ∧ x15 = _x590 ∧ x16 = _x591 ∧ x17 = _x592 ∧ x18 = _x593 ∧ x1 = _x594 ∧ x2 = _x595 ∧ x3 = _x596 ∧ x4 = _x597 ∧ x5 = _x598 ∧ x6 = _x599 ∧ x7 = _x600 ∧ x8 = _x601 ∧ x9 = _x602 ∧ x10 = _x603 ∧ x11 = _x604 ∧ x12 = _x605 ∧ x13 = _x606 ∧ x14 = _x607 ∧ x15 = _x608 ∧ x16 = _x609 ∧ x17 = _x610 ∧ x18 = _x611 ∧ _x593 = _x611 ∧ _x592 = _x610 ∧ _x591 = _x609 ∧ _x589 = _x607 ∧ _x586 = _x604 ∧ _x587 = _x605 ∧ _x585 = _x603 ∧ _x588 = _x606 ∧ _x584 = _x602 ∧ _x583 = _x601 ∧ _x582 = _x600 ∧ _x581 = _x599 ∧ _x580 = _x598 ∧ _x579 = _x597 ∧ _x578 = _x596 ∧ _x577 = _x595 ∧ _x576 = _x594 ∧ _x608 = _x592 − _x593 ∧ 1 + _x593 ≤ _x592 l3 19 l0: x1 = _x612 ∧ x2 = _x613 ∧ x3 = _x614 ∧ x4 = _x615 ∧ x5 = _x616 ∧ x6 = _x617 ∧ x7 = _x618 ∧ x8 = _x619 ∧ x9 = _x620 ∧ x10 = _x621 ∧ x11 = _x622 ∧ x12 = _x623 ∧ x13 = _x624 ∧ x14 = _x625 ∧ x15 = _x626 ∧ x16 = _x627 ∧ x17 = _x628 ∧ x18 = _x629 ∧ x1 = _x630 ∧ x2 = _x631 ∧ x3 = _x632 ∧ x4 = _x633 ∧ x5 = _x634 ∧ x6 = _x635 ∧ x7 = _x636 ∧ x8 = _x637 ∧ x9 = _x638 ∧ x10 = _x639 ∧ x11 = _x640 ∧ x12 = _x641 ∧ x13 = _x642 ∧ x14 = _x643 ∧ x15 = _x644 ∧ x16 = _x645 ∧ x17 = _x646 ∧ x18 = _x647 ∧ _x629 = _x647 ∧ _x628 = _x646 ∧ _x627 = _x645 ∧ _x625 = _x643 ∧ _x622 = _x640 ∧ _x623 = _x641 ∧ _x621 = _x639 ∧ _x624 = _x642 ∧ _x620 = _x638 ∧ _x619 = _x637 ∧ _x618 = _x636 ∧ _x617 = _x635 ∧ _x616 = _x634 ∧ _x615 = _x633 ∧ _x614 = _x632 ∧ _x613 = _x631 ∧ _x612 = _x630 ∧ _x644 = _x628 + _x629 ∧ _x628 ≤ _x629 l12 20 l4: x1 = _x648 ∧ x2 = _x649 ∧ x3 = _x650 ∧ x4 = _x651 ∧ x5 = _x652 ∧ x6 = _x653 ∧ x7 = _x654 ∧ x8 = _x655 ∧ x9 = _x656 ∧ x10 = _x657 ∧ x11 = _x658 ∧ x12 = _x659 ∧ x13 = _x660 ∧ x14 = _x661 ∧ x15 = _x662 ∧ x16 = _x663 ∧ x17 = _x664 ∧ x18 = _x665 ∧ x1 = _x666 ∧ x2 = _x667 ∧ x3 = _x668 ∧ x4 = _x669 ∧ x5 = _x670 ∧ x6 = _x671 ∧ x7 = _x672 ∧ x8 = _x673 ∧ x9 = _x674 ∧ x10 = _x675 ∧ x11 = _x676 ∧ x12 = _x677 ∧ x13 = _x678 ∧ x14 = _x679 ∧ x15 = _x680 ∧ x16 = _x681 ∧ x17 = _x682 ∧ x18 = _x683 ∧ _x662 = _x680 ∧ _x661 = _x679 ∧ _x658 = _x676 ∧ _x659 = _x677 ∧ _x657 = _x675 ∧ _x660 = _x678 ∧ _x656 = _x674 ∧ _x655 = _x673 ∧ _x654 = _x672 ∧ _x653 = _x671 ∧ _x652 = _x670 ∧ _x651 = _x669 ∧ _x650 = _x668 ∧ _x649 = _x667 ∧ _x648 = _x666 ∧ _x683 = 1 ∧ _x682 = 2 ∧ _x681 = 10 l13 21 l12: x1 = _x684 ∧ x2 = _x685 ∧ x3 = _x686 ∧ x4 = _x687 ∧ x5 = _x688 ∧ x6 = _x689 ∧ x7 = _x690 ∧ x8 = _x691 ∧ x9 = _x692 ∧ x10 = _x693 ∧ x11 = _x694 ∧ x12 = _x695 ∧ x13 = _x696 ∧ x14 = _x697 ∧ x15 = _x698 ∧ x16 = _x699 ∧ x17 = _x700 ∧ x18 = _x701 ∧ 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 ∧ x14 = _x715 ∧ x15 = _x716 ∧ x16 = _x717 ∧ x17 = _x718 ∧ x18 = _x719 ∧ _x701 = _x719 ∧ _x700 = _x718 ∧ _x699 = _x717 ∧ _x698 = _x716 ∧ _x697 = _x715 ∧ _x694 = _x712 ∧ _x695 = _x713 ∧ _x693 = _x711 ∧ _x696 = _x714 ∧ _x692 = _x710 ∧ _x691 = _x709 ∧ _x690 = _x708 ∧ _x689 = _x707 ∧ _x688 = _x706 ∧ _x687 = _x705 ∧ _x686 = _x704 ∧ _x685 = _x703 ∧ _x684 = _x702

## 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 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 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 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 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 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 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 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 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 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 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

There exist no SCC in the program graph.

## Tool configuration

AProVE

• version: AProVE Commit ID: unknown
• strategy: Statistics for single proof: 100.00 % (2 real / 0 unknown / 0 assumptions / 2 total proof steps)