# 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 = ___const_10HAT0 ∧ x2 = _a10HAT0 ∧ x3 = _a15HAT0 ∧ x4 = _b11HAT0 ∧ x5 = _b16HAT0 ∧ x6 = _c12HAT0 ∧ x7 = _c17HAT0 ∧ x8 = _m13HAT0 ∧ x9 = _ret_max24HAT0 ∧ x10 = _ret_min14HAT0 ∧ x11 = _tmp620HAT0 ∧ x12 = _tmp923HAT0 ∧ x13 = _tmp9HAT0 ∧ x14 = _tmpHAT0 ∧ x15 = _tmp___0HAT0 ∧ x16 = _tmp___1HAT0 ∧ x17 = _x_promoted_1HAT0 ∧ x18 = _y_promoted_2HAT0 ∧ x19 = _zHAT0 ∧ x1 = ___const_10HATpost ∧ x2 = _a10HATpost ∧ x3 = _a15HATpost ∧ x4 = _b11HATpost ∧ x5 = _b16HATpost ∧ x6 = _c12HATpost ∧ x7 = _c17HATpost ∧ x8 = _m13HATpost ∧ x9 = _ret_max24HATpost ∧ x10 = _ret_min14HATpost ∧ x11 = _tmp620HATpost ∧ x12 = _tmp923HATpost ∧ x13 = _tmp9HATpost ∧ x14 = _tmpHATpost ∧ x15 = _tmp___0HATpost ∧ x16 = _tmp___1HATpost ∧ x17 = _x_promoted_1HATpost ∧ x18 = _y_promoted_2HATpost ∧ x19 = _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 ∧ ___const_10HAT0 = ___const_10HATpost 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 ∧ x1 = _x19 ∧ x2 = _x20 ∧ x3 = _x21 ∧ x4 = _x22 ∧ x5 = _x23 ∧ x6 = _x24 ∧ x7 = _x25 ∧ x8 = _x26 ∧ x9 = _x27 ∧ x10 = _x28 ∧ x11 = _x29 ∧ x12 = _x30 ∧ x13 = _x31 ∧ x14 = _x32 ∧ x15 = _x33 ∧ x16 = _x34 ∧ x17 = _x35 ∧ x18 = _x36 ∧ x19 = _x37 ∧ _x17 = _x36 ∧ _x16 = _x35 ∧ _x15 = _x34 ∧ _x11 = _x30 ∧ _x12 = _x31 ∧ _x10 = _x29 ∧ _x13 = _x32 ∧ _x9 = _x28 ∧ _x7 = _x26 ∧ _x6 = _x25 ∧ _x5 = _x24 ∧ _x4 = _x23 ∧ _x3 = _x22 ∧ _x2 = _x21 ∧ _x1 = _x20 ∧ _x = _x19 ∧ _x37 = _x37 ∧ _x33 = _x27 ∧ _x27 = _x2 l4 3 l5: x1 = _x38 ∧ x2 = _x39 ∧ x3 = _x40 ∧ x4 = _x41 ∧ x5 = _x42 ∧ x6 = _x43 ∧ x7 = _x44 ∧ x8 = _x45 ∧ x9 = _x46 ∧ x10 = _x47 ∧ x11 = _x48 ∧ x12 = _x49 ∧ x13 = _x50 ∧ x14 = _x51 ∧ x15 = _x52 ∧ x16 = _x53 ∧ x17 = _x54 ∧ x18 = _x55 ∧ x19 = _x56 ∧ x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ x4 = _x60 ∧ x5 = _x61 ∧ x6 = _x62 ∧ x7 = _x63 ∧ x8 = _x64 ∧ x9 = _x65 ∧ x10 = _x66 ∧ x11 = _x67 ∧ x12 = _x68 ∧ x13 = _x69 ∧ x14 = _x70 ∧ x15 = _x71 ∧ x16 = _x72 ∧ x17 = _x73 ∧ x18 = _x74 ∧ x19 = _x75 ∧ _x56 = _x75 ∧ _x55 = _x74 ∧ _x54 = _x73 ∧ _x53 = _x72 ∧ _x52 = _x71 ∧ _x49 = _x68 ∧ _x50 = _x69 ∧ _x48 = _x67 ∧ _x51 = _x70 ∧ _x47 = _x66 ∧ _x46 = _x65 ∧ _x45 = _x64 ∧ _x44 = _x63 ∧ _x43 = _x62 ∧ _x42 = _x61 ∧ _x41 = _x60 ∧ _x40 = _x59 ∧ _x39 = _x58 ∧ _x38 = _x57 ∧ 1 + _x55 ≤ _x54 l4 4 l3: x1 = _x76 ∧ x2 = _x77 ∧ x3 = _x78 ∧ x4 = _x79 ∧ x5 = _x80 ∧ x6 = _x81 ∧ x7 = _x82 ∧ x8 = _x83 ∧ x9 = _x84 ∧ x10 = _x85 ∧ x11 = _x86 ∧ x12 = _x87 ∧ x13 = _x88 ∧ x14 = _x89 ∧ x15 = _x90 ∧ x16 = _x91 ∧ x17 = _x92 ∧ x18 = _x93 ∧ x19 = _x94 ∧ x1 = _x95 ∧ x2 = _x96 ∧ x3 = _x97 ∧ x4 = _x98 ∧ x5 = _x99 ∧ x6 = _x100 ∧ x7 = _x101 ∧ x8 = _x102 ∧ x9 = _x103 ∧ x10 = _x104 ∧ x11 = _x105 ∧ x12 = _x106 ∧ x13 = _x107 ∧ x14 = _x108 ∧ x15 = _x109 ∧ x16 = _x110 ∧ x17 = _x111 ∧ x18 = _x112 ∧ x19 = _x113 ∧ _x94 = _x113 ∧ _x93 = _x112 ∧ _x92 = _x111 ∧ _x91 = _x110 ∧ _x90 = _x109 ∧ _x87 = _x106 ∧ _x86 = _x105 ∧ _x89 = _x108 ∧ _x85 = _x104 ∧ _x84 = _x103 ∧ _x83 = _x102 ∧ _x82 = _x101 ∧ _x81 = _x100 ∧ _x80 = _x99 ∧ _x79 = _x98 ∧ _x78 = _x97 ∧ _x77 = _x96 ∧ _x76 = _x95 ∧ _x107 = _x107 ∧ _x92 ≤ _x93 l6 5 l2: x1 = _x114 ∧ x2 = _x115 ∧ x3 = _x116 ∧ x4 = _x117 ∧ x5 = _x118 ∧ x6 = _x119 ∧ x7 = _x120 ∧ x8 = _x121 ∧ x9 = _x122 ∧ x10 = _x123 ∧ x11 = _x124 ∧ x12 = _x125 ∧ x13 = _x126 ∧ x14 = _x127 ∧ x15 = _x128 ∧ x16 = _x129 ∧ x17 = _x130 ∧ x18 = _x131 ∧ x19 = _x132 ∧ x1 = _x133 ∧ x2 = _x134 ∧ x3 = _x135 ∧ x4 = _x136 ∧ x5 = _x137 ∧ x6 = _x138 ∧ x7 = _x139 ∧ x8 = _x140 ∧ x9 = _x141 ∧ x10 = _x142 ∧ x11 = _x143 ∧ x12 = _x144 ∧ x13 = _x145 ∧ x14 = _x146 ∧ x15 = _x147 ∧ x16 = _x148 ∧ x17 = _x149 ∧ x18 = _x150 ∧ x19 = _x151 ∧ _x132 = _x151 ∧ _x131 = _x150 ∧ _x130 = _x149 ∧ _x129 = _x148 ∧ _x128 = _x147 ∧ _x125 = _x144 ∧ _x126 = _x145 ∧ _x124 = _x143 ∧ _x127 = _x146 ∧ _x123 = _x142 ∧ _x122 = _x141 ∧ _x121 = _x140 ∧ _x120 = _x139 ∧ _x119 = _x138 ∧ _x118 = _x137 ∧ _x117 = _x136 ∧ _x116 = _x135 ∧ _x115 = _x134 ∧ _x114 = _x133 ∧ 1 + _x120 ≤ _x116 l6 6 l2: x1 = _x152 ∧ x2 = _x153 ∧ x3 = _x154 ∧ x4 = _x155 ∧ x5 = _x156 ∧ x6 = _x157 ∧ x7 = _x158 ∧ x8 = _x159 ∧ x9 = _x160 ∧ x10 = _x161 ∧ x11 = _x162 ∧ x12 = _x163 ∧ x13 = _x164 ∧ x14 = _x165 ∧ x15 = _x166 ∧ x16 = _x167 ∧ x17 = _x168 ∧ x18 = _x169 ∧ x19 = _x170 ∧ x1 = _x171 ∧ x2 = _x172 ∧ x3 = _x173 ∧ x4 = _x174 ∧ x5 = _x175 ∧ x6 = _x176 ∧ x7 = _x177 ∧ x8 = _x178 ∧ x9 = _x179 ∧ x10 = _x180 ∧ x11 = _x181 ∧ x12 = _x182 ∧ x13 = _x183 ∧ x14 = _x184 ∧ x15 = _x185 ∧ x16 = _x186 ∧ x17 = _x187 ∧ x18 = _x188 ∧ x19 = _x189 ∧ _x170 = _x189 ∧ _x169 = _x188 ∧ _x168 = _x187 ∧ _x167 = _x186 ∧ _x166 = _x185 ∧ _x164 = _x183 ∧ _x162 = _x181 ∧ _x165 = _x184 ∧ _x161 = _x180 ∧ _x160 = _x179 ∧ _x159 = _x178 ∧ _x158 = _x177 ∧ _x157 = _x176 ∧ _x156 = _x175 ∧ _x155 = _x174 ∧ _x154 = _x173 ∧ _x153 = _x172 ∧ _x152 = _x171 ∧ _x182 = _x182 ∧ _x154 ≤ _x158 l7 7 l6: x1 = _x190 ∧ x2 = _x191 ∧ x3 = _x192 ∧ x4 = _x193 ∧ x5 = _x194 ∧ x6 = _x195 ∧ x7 = _x196 ∧ x8 = _x197 ∧ x9 = _x198 ∧ x10 = _x199 ∧ x11 = _x200 ∧ x12 = _x201 ∧ x13 = _x202 ∧ x14 = _x203 ∧ x15 = _x204 ∧ x16 = _x205 ∧ x17 = _x206 ∧ x18 = _x207 ∧ x19 = _x208 ∧ x1 = _x209 ∧ x2 = _x210 ∧ x3 = _x211 ∧ x4 = _x212 ∧ x5 = _x213 ∧ x6 = _x214 ∧ x7 = _x215 ∧ x8 = _x216 ∧ x9 = _x217 ∧ x10 = _x218 ∧ x11 = _x219 ∧ x12 = _x220 ∧ x13 = _x221 ∧ x14 = _x222 ∧ x15 = _x223 ∧ x16 = _x224 ∧ x17 = _x225 ∧ x18 = _x226 ∧ x19 = _x227 ∧ _x208 = _x227 ∧ _x207 = _x226 ∧ _x206 = _x225 ∧ _x205 = _x224 ∧ _x204 = _x223 ∧ _x201 = _x220 ∧ _x202 = _x221 ∧ _x200 = _x219 ∧ _x203 = _x222 ∧ _x199 = _x218 ∧ _x198 = _x217 ∧ _x197 = _x216 ∧ _x196 = _x215 ∧ _x195 = _x214 ∧ _x194 = _x213 ∧ _x193 = _x212 ∧ _x192 = _x211 ∧ _x191 = _x210 ∧ _x190 = _x209 ∧ 1 + _x194 ≤ _x192 l7 8 l6: x1 = _x228 ∧ x2 = _x229 ∧ x3 = _x230 ∧ x4 = _x231 ∧ x5 = _x232 ∧ x6 = _x233 ∧ x7 = _x234 ∧ x8 = _x235 ∧ x9 = _x236 ∧ x10 = _x237 ∧ x11 = _x238 ∧ x12 = _x239 ∧ x13 = _x240 ∧ x14 = _x241 ∧ x15 = _x242 ∧ x16 = _x243 ∧ x17 = _x244 ∧ x18 = _x245 ∧ x19 = _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 ∧ x14 = _x260 ∧ x15 = _x261 ∧ x16 = _x262 ∧ x17 = _x263 ∧ x18 = _x264 ∧ x19 = _x265 ∧ _x246 = _x265 ∧ _x245 = _x264 ∧ _x244 = _x263 ∧ _x243 = _x262 ∧ _x242 = _x261 ∧ _x239 = _x258 ∧ _x240 = _x259 ∧ _x241 = _x260 ∧ _x237 = _x256 ∧ _x236 = _x255 ∧ _x235 = _x254 ∧ _x234 = _x253 ∧ _x233 = _x252 ∧ _x232 = _x251 ∧ _x231 = _x250 ∧ _x230 = _x249 ∧ _x229 = _x248 ∧ _x228 = _x247 ∧ _x257 = _x257 ∧ _x230 ≤ _x232 l8 9 l9: x1 = _x266 ∧ x2 = _x267 ∧ x3 = _x268 ∧ x4 = _x269 ∧ x5 = _x270 ∧ x6 = _x271 ∧ x7 = _x272 ∧ x8 = _x273 ∧ x9 = _x274 ∧ x10 = _x275 ∧ x11 = _x276 ∧ x12 = _x277 ∧ x13 = _x278 ∧ x14 = _x279 ∧ x15 = _x280 ∧ x16 = _x281 ∧ x17 = _x282 ∧ x18 = _x283 ∧ x19 = _x284 ∧ x1 = _x285 ∧ x2 = _x286 ∧ x3 = _x287 ∧ x4 = _x288 ∧ x5 = _x289 ∧ x6 = _x290 ∧ x7 = _x291 ∧ x8 = _x292 ∧ x9 = _x293 ∧ x10 = _x294 ∧ x11 = _x295 ∧ x12 = _x296 ∧ x13 = _x297 ∧ x14 = _x298 ∧ x15 = _x299 ∧ x16 = _x300 ∧ x17 = _x301 ∧ x18 = _x302 ∧ x19 = _x303 ∧ _x284 = _x303 ∧ _x283 = _x302 ∧ _x282 = _x301 ∧ _x281 = _x300 ∧ _x280 = _x299 ∧ _x277 = _x296 ∧ _x278 = _x297 ∧ _x276 = _x295 ∧ _x279 = _x298 ∧ _x275 = _x294 ∧ _x274 = _x293 ∧ _x272 = _x291 ∧ _x271 = _x290 ∧ _x270 = _x289 ∧ _x269 = _x288 ∧ _x268 = _x287 ∧ _x267 = _x286 ∧ _x266 = _x285 ∧ _x292 = _x271 ∧ 1 + _x271 ≤ _x269 l8 10 l9: x1 = _x304 ∧ x2 = _x305 ∧ x3 = _x306 ∧ x4 = _x307 ∧ x5 = _x308 ∧ x6 = _x309 ∧ x7 = _x310 ∧ x8 = _x311 ∧ x9 = _x312 ∧ x10 = _x313 ∧ x11 = _x314 ∧ x12 = _x315 ∧ x13 = _x316 ∧ x14 = _x317 ∧ x15 = _x318 ∧ x16 = _x319 ∧ x17 = _x320 ∧ x18 = _x321 ∧ x19 = _x322 ∧ x1 = _x323 ∧ x2 = _x324 ∧ x3 = _x325 ∧ x4 = _x326 ∧ x5 = _x327 ∧ x6 = _x328 ∧ x7 = _x329 ∧ x8 = _x330 ∧ x9 = _x331 ∧ x10 = _x332 ∧ x11 = _x333 ∧ x12 = _x334 ∧ x13 = _x335 ∧ x14 = _x336 ∧ x15 = _x337 ∧ x16 = _x338 ∧ x17 = _x339 ∧ x18 = _x340 ∧ x19 = _x341 ∧ _x322 = _x341 ∧ _x321 = _x340 ∧ _x320 = _x339 ∧ _x319 = _x338 ∧ _x318 = _x337 ∧ _x315 = _x334 ∧ _x316 = _x335 ∧ _x314 = _x333 ∧ _x317 = _x336 ∧ _x313 = _x332 ∧ _x312 = _x331 ∧ _x310 = _x329 ∧ _x309 = _x328 ∧ _x308 = _x327 ∧ _x307 = _x326 ∧ _x306 = _x325 ∧ _x305 = _x324 ∧ _x304 = _x323 ∧ _x330 = _x307 ∧ _x307 ≤ _x309 l9 11 l3: 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 ∧ x19 = _x360 ∧ x1 = _x361 ∧ x2 = _x362 ∧ x3 = _x363 ∧ x4 = _x364 ∧ x5 = _x365 ∧ x6 = _x366 ∧ x7 = _x367 ∧ x8 = _x368 ∧ x9 = _x369 ∧ x10 = _x370 ∧ x11 = _x371 ∧ x12 = _x372 ∧ x13 = _x373 ∧ x14 = _x374 ∧ x15 = _x375 ∧ x16 = _x376 ∧ x17 = _x377 ∧ x18 = _x378 ∧ x19 = _x379 ∧ _x360 = _x379 ∧ _x359 = _x378 ∧ _x357 = _x376 ∧ _x356 = _x375 ∧ _x353 = _x372 ∧ _x354 = _x373 ∧ _x352 = _x371 ∧ _x350 = _x369 ∧ _x349 = _x368 ∧ _x348 = _x367 ∧ _x347 = _x366 ∧ _x346 = _x365 ∧ _x345 = _x364 ∧ _x344 = _x363 ∧ _x343 = _x362 ∧ _x342 = _x361 ∧ _x377 = _x374 + _x358 ∧ _x374 = _x370 ∧ _x370 = _x349 l10 12 l9: x1 = _x380 ∧ x2 = _x381 ∧ x3 = _x382 ∧ x4 = _x383 ∧ x5 = _x384 ∧ x6 = _x385 ∧ x7 = _x386 ∧ x8 = _x387 ∧ x9 = _x388 ∧ x10 = _x389 ∧ x11 = _x390 ∧ x12 = _x391 ∧ x13 = _x392 ∧ x14 = _x393 ∧ x15 = _x394 ∧ x16 = _x395 ∧ x17 = _x396 ∧ x18 = _x397 ∧ x19 = _x398 ∧ x1 = _x399 ∧ x2 = _x400 ∧ x3 = _x401 ∧ x4 = _x402 ∧ x5 = _x403 ∧ x6 = _x404 ∧ x7 = _x405 ∧ x8 = _x406 ∧ x9 = _x407 ∧ x10 = _x408 ∧ x11 = _x409 ∧ x12 = _x410 ∧ x13 = _x411 ∧ x14 = _x412 ∧ x15 = _x413 ∧ x16 = _x414 ∧ x17 = _x415 ∧ x18 = _x416 ∧ x19 = _x417 ∧ _x398 = _x417 ∧ _x397 = _x416 ∧ _x396 = _x415 ∧ _x395 = _x414 ∧ _x394 = _x413 ∧ _x391 = _x410 ∧ _x392 = _x411 ∧ _x390 = _x409 ∧ _x393 = _x412 ∧ _x389 = _x408 ∧ _x388 = _x407 ∧ _x386 = _x405 ∧ _x385 = _x404 ∧ _x384 = _x403 ∧ _x383 = _x402 ∧ _x382 = _x401 ∧ _x381 = _x400 ∧ _x380 = _x399 ∧ _x406 = _x385 ∧ 1 + _x385 ≤ _x381 l10 13 l9: 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 ∧ x1 = _x437 ∧ x2 = _x438 ∧ x3 = _x439 ∧ x4 = _x440 ∧ x5 = _x441 ∧ x6 = _x442 ∧ x7 = _x443 ∧ x8 = _x444 ∧ x9 = _x445 ∧ x10 = _x446 ∧ x11 = _x447 ∧ x12 = _x448 ∧ x13 = _x449 ∧ x14 = _x450 ∧ x15 = _x451 ∧ x16 = _x452 ∧ x17 = _x453 ∧ x18 = _x454 ∧ x19 = _x455 ∧ _x436 = _x455 ∧ _x435 = _x454 ∧ _x434 = _x453 ∧ _x433 = _x452 ∧ _x432 = _x451 ∧ _x429 = _x448 ∧ _x430 = _x449 ∧ _x428 = _x447 ∧ _x431 = _x450 ∧ _x427 = _x446 ∧ _x426 = _x445 ∧ _x424 = _x443 ∧ _x423 = _x442 ∧ _x422 = _x441 ∧ _x421 = _x440 ∧ _x420 = _x439 ∧ _x419 = _x438 ∧ _x418 = _x437 ∧ _x444 = _x419 ∧ _x419 ≤ _x423 l11 14 l8: x1 = _x456 ∧ x2 = _x457 ∧ x3 = _x458 ∧ x4 = _x459 ∧ x5 = _x460 ∧ x6 = _x461 ∧ x7 = _x462 ∧ x8 = _x463 ∧ x9 = _x464 ∧ x10 = _x465 ∧ x11 = _x466 ∧ x12 = _x467 ∧ x13 = _x468 ∧ x14 = _x469 ∧ x15 = _x470 ∧ x16 = _x471 ∧ x17 = _x472 ∧ x18 = _x473 ∧ x19 = _x474 ∧ x1 = _x475 ∧ x2 = _x476 ∧ x3 = _x477 ∧ x4 = _x478 ∧ x5 = _x479 ∧ x6 = _x480 ∧ x7 = _x481 ∧ x8 = _x482 ∧ x9 = _x483 ∧ x10 = _x484 ∧ x11 = _x485 ∧ x12 = _x486 ∧ x13 = _x487 ∧ x14 = _x488 ∧ x15 = _x489 ∧ x16 = _x490 ∧ x17 = _x491 ∧ x18 = _x492 ∧ x19 = _x493 ∧ _x474 = _x493 ∧ _x473 = _x492 ∧ _x472 = _x491 ∧ _x471 = _x490 ∧ _x470 = _x489 ∧ _x467 = _x486 ∧ _x468 = _x487 ∧ _x466 = _x485 ∧ _x469 = _x488 ∧ _x465 = _x484 ∧ _x464 = _x483 ∧ _x463 = _x482 ∧ _x462 = _x481 ∧ _x461 = _x480 ∧ _x460 = _x479 ∧ _x459 = _x478 ∧ _x458 = _x477 ∧ _x457 = _x476 ∧ _x456 = _x475 ∧ 1 + _x459 ≤ _x457 l11 15 l10: 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 ∧ x14 = _x507 ∧ x15 = _x508 ∧ x16 = _x509 ∧ x17 = _x510 ∧ x18 = _x511 ∧ x19 = _x512 ∧ x1 = _x513 ∧ x2 = _x514 ∧ x3 = _x515 ∧ x4 = _x516 ∧ x5 = _x517 ∧ x6 = _x518 ∧ x7 = _x519 ∧ x8 = _x520 ∧ x9 = _x521 ∧ x10 = _x522 ∧ x11 = _x523 ∧ x12 = _x524 ∧ x13 = _x525 ∧ x14 = _x526 ∧ x15 = _x527 ∧ x16 = _x528 ∧ x17 = _x529 ∧ x18 = _x530 ∧ x19 = _x531 ∧ _x512 = _x531 ∧ _x511 = _x530 ∧ _x510 = _x529 ∧ _x509 = _x528 ∧ _x508 = _x527 ∧ _x505 = _x524 ∧ _x506 = _x525 ∧ _x504 = _x523 ∧ _x507 = _x526 ∧ _x503 = _x522 ∧ _x502 = _x521 ∧ _x501 = _x520 ∧ _x500 = _x519 ∧ _x499 = _x518 ∧ _x498 = _x517 ∧ _x497 = _x516 ∧ _x496 = _x515 ∧ _x495 = _x514 ∧ _x494 = _x513 ∧ _x495 ≤ _x497 l5 16 l7: x1 = _x532 ∧ x2 = _x533 ∧ x3 = _x534 ∧ x4 = _x535 ∧ x5 = _x536 ∧ x6 = _x537 ∧ x7 = _x538 ∧ x8 = _x539 ∧ x9 = _x540 ∧ x10 = _x541 ∧ x11 = _x542 ∧ x12 = _x543 ∧ x13 = _x544 ∧ x14 = _x545 ∧ x15 = _x546 ∧ x16 = _x547 ∧ x17 = _x548 ∧ x18 = _x549 ∧ x19 = _x550 ∧ x1 = _x551 ∧ x2 = _x552 ∧ x3 = _x553 ∧ x4 = _x554 ∧ x5 = _x555 ∧ x6 = _x556 ∧ x7 = _x557 ∧ x8 = _x558 ∧ x9 = _x559 ∧ x10 = _x560 ∧ x11 = _x561 ∧ x12 = _x562 ∧ x13 = _x563 ∧ x14 = _x564 ∧ x15 = _x565 ∧ x16 = _x566 ∧ x17 = _x567 ∧ x18 = _x568 ∧ x19 = _x569 ∧ _x550 = _x569 ∧ _x549 = _x568 ∧ _x548 = _x567 ∧ _x547 = _x566 ∧ _x546 = _x565 ∧ _x543 = _x562 ∧ _x544 = _x563 ∧ _x542 = _x561 ∧ _x545 = _x564 ∧ _x541 = _x560 ∧ _x540 = _x559 ∧ _x539 = _x558 ∧ _x537 = _x556 ∧ _x535 = _x554 ∧ _x533 = _x552 ∧ _x532 = _x551 ∧ _x557 = _x548 ∧ _x555 = _x549 ∧ _x553 = _x550 ∧ 1 + _x550 ≤ _x548 l5 17 l11: x1 = _x570 ∧ x2 = _x571 ∧ x3 = _x572 ∧ x4 = _x573 ∧ x5 = _x574 ∧ x6 = _x575 ∧ x7 = _x576 ∧ x8 = _x577 ∧ x9 = _x578 ∧ x10 = _x579 ∧ x11 = _x580 ∧ x12 = _x581 ∧ x13 = _x582 ∧ x14 = _x583 ∧ x15 = _x584 ∧ x16 = _x585 ∧ x17 = _x586 ∧ x18 = _x587 ∧ x19 = _x588 ∧ x1 = _x589 ∧ x2 = _x590 ∧ x3 = _x591 ∧ x4 = _x592 ∧ x5 = _x593 ∧ x6 = _x594 ∧ x7 = _x595 ∧ x8 = _x596 ∧ x9 = _x597 ∧ x10 = _x598 ∧ x11 = _x599 ∧ x12 = _x600 ∧ x13 = _x601 ∧ x14 = _x602 ∧ x15 = _x603 ∧ x16 = _x604 ∧ x17 = _x605 ∧ x18 = _x606 ∧ x19 = _x607 ∧ _x588 = _x607 ∧ _x587 = _x606 ∧ _x586 = _x605 ∧ _x585 = _x604 ∧ _x584 = _x603 ∧ _x581 = _x600 ∧ _x582 = _x601 ∧ _x580 = _x599 ∧ _x583 = _x602 ∧ _x579 = _x598 ∧ _x578 = _x597 ∧ _x577 = _x596 ∧ _x576 = _x595 ∧ _x574 = _x593 ∧ _x572 = _x591 ∧ _x570 = _x589 ∧ _x594 = _x588 ∧ _x592 = _x587 ∧ _x590 = _x586 ∧ _x586 ≤ _x588 l3 18 l0: x1 = _x608 ∧ x2 = _x609 ∧ x3 = _x610 ∧ x4 = _x611 ∧ x5 = _x612 ∧ x6 = _x613 ∧ x7 = _x614 ∧ x8 = _x615 ∧ x9 = _x616 ∧ x10 = _x617 ∧ x11 = _x618 ∧ x12 = _x619 ∧ x13 = _x620 ∧ x14 = _x621 ∧ x15 = _x622 ∧ x16 = _x623 ∧ x17 = _x624 ∧ x18 = _x625 ∧ x19 = _x626 ∧ x1 = _x627 ∧ x2 = _x628 ∧ x3 = _x629 ∧ x4 = _x630 ∧ x5 = _x631 ∧ x6 = _x632 ∧ x7 = _x633 ∧ x8 = _x634 ∧ x9 = _x635 ∧ x10 = _x636 ∧ x11 = _x637 ∧ x12 = _x638 ∧ x13 = _x639 ∧ x14 = _x640 ∧ x15 = _x641 ∧ x16 = _x642 ∧ x17 = _x643 ∧ x18 = _x644 ∧ x19 = _x645 ∧ _x626 = _x645 ∧ _x625 = _x644 ∧ _x624 = _x643 ∧ _x622 = _x641 ∧ _x619 = _x638 ∧ _x620 = _x639 ∧ _x618 = _x637 ∧ _x621 = _x640 ∧ _x617 = _x636 ∧ _x616 = _x635 ∧ _x615 = _x634 ∧ _x614 = _x633 ∧ _x613 = _x632 ∧ _x612 = _x631 ∧ _x611 = _x630 ∧ _x610 = _x629 ∧ _x609 = _x628 ∧ _x608 = _x627 ∧ _x642 = _x625 − _x626 ∧ 1 + _x626 ≤ _x625 l3 19 l0: x1 = _x646 ∧ x2 = _x647 ∧ x3 = _x648 ∧ x4 = _x649 ∧ x5 = _x650 ∧ x6 = _x651 ∧ x7 = _x652 ∧ x8 = _x653 ∧ x9 = _x654 ∧ x10 = _x655 ∧ x11 = _x656 ∧ x12 = _x657 ∧ x13 = _x658 ∧ x14 = _x659 ∧ x15 = _x660 ∧ x16 = _x661 ∧ x17 = _x662 ∧ x18 = _x663 ∧ x19 = _x664 ∧ x1 = _x665 ∧ x2 = _x666 ∧ x3 = _x667 ∧ x4 = _x668 ∧ x5 = _x669 ∧ x6 = _x670 ∧ x7 = _x671 ∧ x8 = _x672 ∧ x9 = _x673 ∧ x10 = _x674 ∧ x11 = _x675 ∧ x12 = _x676 ∧ x13 = _x677 ∧ x14 = _x678 ∧ x15 = _x679 ∧ x16 = _x680 ∧ x17 = _x681 ∧ x18 = _x682 ∧ x19 = _x683 ∧ _x664 = _x683 ∧ _x663 = _x682 ∧ _x662 = _x681 ∧ _x660 = _x679 ∧ _x657 = _x676 ∧ _x658 = _x677 ∧ _x656 = _x675 ∧ _x659 = _x678 ∧ _x655 = _x674 ∧ _x654 = _x673 ∧ _x653 = _x672 ∧ _x652 = _x671 ∧ _x651 = _x670 ∧ _x650 = _x669 ∧ _x649 = _x668 ∧ _x648 = _x667 ∧ _x647 = _x666 ∧ _x646 = _x665 ∧ _x680 = _x663 + _x664 ∧ _x663 ≤ _x664 l12 20 l4: 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 ∧ x19 = _x702 ∧ x1 = _x703 ∧ x2 = _x704 ∧ x3 = _x705 ∧ x4 = _x706 ∧ x5 = _x707 ∧ x6 = _x708 ∧ x7 = _x709 ∧ x8 = _x710 ∧ x9 = _x711 ∧ x10 = _x712 ∧ x11 = _x713 ∧ x12 = _x714 ∧ x13 = _x715 ∧ x14 = _x716 ∧ x15 = _x717 ∧ x16 = _x718 ∧ x17 = _x719 ∧ x18 = _x720 ∧ x19 = _x721 ∧ _x699 = _x718 ∧ _x698 = _x717 ∧ _x695 = _x714 ∧ _x696 = _x715 ∧ _x694 = _x713 ∧ _x697 = _x716 ∧ _x693 = _x712 ∧ _x692 = _x711 ∧ _x691 = _x710 ∧ _x690 = _x709 ∧ _x689 = _x708 ∧ _x688 = _x707 ∧ _x687 = _x706 ∧ _x686 = _x705 ∧ _x685 = _x704 ∧ _x684 = _x703 ∧ _x721 = 1 ∧ _x720 = 2 ∧ _x719 = _x684 l13 21 l12: x1 = _x722 ∧ x2 = _x723 ∧ x3 = _x724 ∧ x4 = _x725 ∧ x5 = _x726 ∧ x6 = _x727 ∧ x7 = _x728 ∧ x8 = _x729 ∧ x9 = _x730 ∧ x10 = _x731 ∧ x11 = _x732 ∧ x12 = _x733 ∧ x13 = _x734 ∧ x14 = _x735 ∧ x15 = _x736 ∧ x16 = _x737 ∧ x17 = _x738 ∧ x18 = _x739 ∧ x19 = _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 ∧ x14 = _x754 ∧ x15 = _x755 ∧ x16 = _x756 ∧ x17 = _x757 ∧ x18 = _x758 ∧ x19 = _x759 ∧ _x740 = _x759 ∧ _x739 = _x758 ∧ _x738 = _x757 ∧ _x737 = _x756 ∧ _x736 = _x755 ∧ _x733 = _x752 ∧ _x734 = _x753 ∧ _x732 = _x751 ∧ _x735 = _x754 ∧ _x731 = _x750 ∧ _x730 = _x749 ∧ _x729 = _x748 ∧ _x728 = _x747 ∧ _x727 = _x746 ∧ _x726 = _x745 ∧ _x725 = _x744 ∧ _x724 = _x743 ∧ _x723 = _x742 ∧ _x722 = _x741

## 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 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 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 ∧ x19 = x19 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 ∧ x19 = x19 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 ∧ x19 = x19 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 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 ∧ x19 = x19 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 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 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 ∧ x19 = x19 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 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 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 ∧ x19 = x19
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)