# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l7, l6, l1, l8, l3, l0, l2
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _ctr23HAT0 ∧ x2 = _iHAT0 ∧ x3 = _seedHAT0 ∧ x4 = _tmp05HAT0 ∧ x5 = _tmp1013HAT0 ∧ x6 = _tmp1114HAT0 ∧ x7 = _tmp1215HAT0 ∧ x8 = _tmp1316HAT0 ∧ x9 = _tmp16HAT0 ∧ x10 = _tmp27HAT0 ∧ x11 = _tmp38HAT0 ∧ x12 = _tmp49HAT0 ∧ x13 = _tmp510HAT0 ∧ x14 = _tmp611HAT0 ∧ x15 = _tmp712HAT0 ∧ x16 = _z117HAT0 ∧ x17 = _z218HAT0 ∧ x18 = _z319HAT0 ∧ x19 = _z420HAT0 ∧ x20 = _z521HAT0 ∧ x1 = _ctr23HATpost ∧ x2 = _iHATpost ∧ x3 = _seedHATpost ∧ x4 = _tmp05HATpost ∧ x5 = _tmp1013HATpost ∧ x6 = _tmp1114HATpost ∧ x7 = _tmp1215HATpost ∧ x8 = _tmp1316HATpost ∧ x9 = _tmp16HATpost ∧ x10 = _tmp27HATpost ∧ x11 = _tmp38HATpost ∧ x12 = _tmp49HATpost ∧ x13 = _tmp510HATpost ∧ x14 = _tmp611HATpost ∧ x15 = _tmp712HATpost ∧ x16 = _z117HATpost ∧ x17 = _z218HATpost ∧ x18 = _z319HATpost ∧ x19 = _z420HATpost ∧ x20 = _z521HATpost ∧ _z521HAT0 = _z521HATpost ∧ _z420HAT0 = _z420HATpost ∧ _z319HAT0 = _z319HATpost ∧ _z218HAT0 = _z218HATpost ∧ _z117HAT0 = _z117HATpost ∧ _tmp712HAT0 = _tmp712HATpost ∧ _tmp611HAT0 = _tmp611HATpost ∧ _tmp510HAT0 = _tmp510HATpost ∧ _tmp49HAT0 = _tmp49HATpost ∧ _tmp38HAT0 = _tmp38HATpost ∧ _tmp27HAT0 = _tmp27HATpost ∧ _tmp16HAT0 = _tmp16HATpost ∧ _tmp1316HAT0 = _tmp1316HATpost ∧ _tmp1215HAT0 = _tmp1215HATpost ∧ _tmp1114HAT0 = _tmp1114HATpost ∧ _tmp1013HAT0 = _tmp1013HATpost ∧ _tmp05HAT0 = _tmp05HATpost ∧ _seedHAT0 = _seedHATpost ∧ _iHAT0 = _iHATpost ∧ _ctr23HATpost = 7 ∧ 64 ≤ _iHAT0 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 ∧ x13 = _x12 ∧ x14 = _x13 ∧ x15 = _x14 ∧ x16 = _x15 ∧ x17 = _x16 ∧ x18 = _x17 ∧ x19 = _x18 ∧ x20 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x23 ∧ x5 = _x24 ∧ x6 = _x25 ∧ x7 = _x26 ∧ x8 = _x27 ∧ x9 = _x28 ∧ x10 = _x29 ∧ x11 = _x30 ∧ x12 = _x31 ∧ x13 = _x32 ∧ x14 = _x33 ∧ x15 = _x34 ∧ x16 = _x35 ∧ x17 = _x36 ∧ x18 = _x37 ∧ x19 = _x38 ∧ x20 = _x39 ∧ _x19 = _x39 ∧ _x18 = _x38 ∧ _x17 = _x37 ∧ _x16 = _x36 ∧ _x15 = _x35 ∧ _x14 = _x34 ∧ _x13 = _x33 ∧ _x12 = _x32 ∧ _x11 = _x31 ∧ _x10 = _x30 ∧ _x9 = _x29 ∧ _x8 = _x28 ∧ _x7 = _x27 ∧ _x6 = _x26 ∧ _x5 = _x25 ∧ _x4 = _x24 ∧ _x3 = _x23 ∧ _x = _x20 ∧ _x21 = 1 + _x1 ∧ _x22 = _x22 ∧ 1 + _x1 ≤ 64 l3 3 l4: x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x7 = _x46 ∧ x8 = _x47 ∧ x9 = _x48 ∧ x10 = _x49 ∧ x11 = _x50 ∧ x12 = _x51 ∧ x13 = _x52 ∧ x14 = _x53 ∧ x15 = _x54 ∧ x16 = _x55 ∧ x17 = _x56 ∧ x18 = _x57 ∧ x19 = _x58 ∧ x20 = _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 ∧ x13 = _x72 ∧ x14 = _x73 ∧ x15 = _x74 ∧ x16 = _x75 ∧ x17 = _x76 ∧ x18 = _x77 ∧ x19 = _x78 ∧ x20 = _x79 ∧ _x59 = _x79 ∧ _x58 = _x78 ∧ _x57 = _x77 ∧ _x56 = _x76 ∧ _x55 = _x75 ∧ _x54 = _x74 ∧ _x53 = _x73 ∧ _x52 = _x72 ∧ _x51 = _x71 ∧ _x50 = _x70 ∧ _x49 = _x69 ∧ _x48 = _x68 ∧ _x47 = _x67 ∧ _x46 = _x66 ∧ _x45 = _x65 ∧ _x44 = _x64 ∧ _x43 = _x63 ∧ _x42 = _x62 ∧ _x41 = _x61 ∧ _x40 = _x60 ∧ 1 + _x40 ≤ 0 l3 4 l5: x1 = _x80 ∧ x2 = _x81 ∧ x3 = _x82 ∧ x4 = _x83 ∧ x5 = _x84 ∧ x6 = _x85 ∧ x7 = _x86 ∧ x8 = _x87 ∧ x9 = _x88 ∧ x10 = _x89 ∧ x11 = _x90 ∧ x12 = _x91 ∧ x13 = _x92 ∧ x14 = _x93 ∧ x15 = _x94 ∧ x16 = _x95 ∧ x17 = _x96 ∧ x18 = _x97 ∧ x19 = _x98 ∧ x20 = _x99 ∧ x1 = _x100 ∧ x2 = _x101 ∧ x3 = _x102 ∧ x4 = _x103 ∧ x5 = _x104 ∧ x6 = _x105 ∧ x7 = _x106 ∧ x8 = _x107 ∧ x9 = _x108 ∧ x10 = _x109 ∧ x11 = _x110 ∧ x12 = _x111 ∧ x13 = _x112 ∧ x14 = _x113 ∧ x15 = _x114 ∧ x16 = _x115 ∧ x17 = _x116 ∧ x18 = _x117 ∧ x19 = _x118 ∧ x20 = _x119 ∧ 0 ≤ _x80 ∧ _x103 = _x103 ∧ _x120 = _x120 ∧ _x108 = _x108 ∧ _x121 = _x121 ∧ _x109 = _x109 ∧ _x122 = _x122 ∧ _x110 = _x110 ∧ _x123 = _x123 ∧ _x104 = _x103 + _x110 ∧ _x107 = _x103 − _x110 ∧ _x105 = _x108 + _x109 ∧ _x106 = _x108 − _x109 ∧ _x124 = _x124 ∧ _x125 = _x123 + _x120 ∧ _x126 = _x122 + _x121 ∧ _x127 = _x123 + _x121 ∧ _x128 = _x122 + _x120 ∧ _x119 = _x119 ∧ _x111 = _x111 ∧ _x112 = _x112 ∧ _x113 = _x113 ∧ _x114 = _x114 ∧ _x115 = _x115 ∧ _x116 = _x116 ∧ _x129 = _x129 ∧ _x130 = _x130 ∧ _x117 = _x129 + _x119 ∧ _x118 = _x130 + _x119 ∧ _x100 = −1 + _x80 ∧ _x81 = _x101 ∧ _x82 = _x102 l2 5 l0: x1 = _x131 ∧ x2 = _x132 ∧ x3 = _x133 ∧ x4 = _x134 ∧ x5 = _x135 ∧ x6 = _x136 ∧ x7 = _x137 ∧ x8 = _x138 ∧ x9 = _x139 ∧ x10 = _x140 ∧ x11 = _x141 ∧ x12 = _x142 ∧ x13 = _x143 ∧ x14 = _x144 ∧ x15 = _x145 ∧ x16 = _x146 ∧ x17 = _x147 ∧ x18 = _x148 ∧ x19 = _x149 ∧ x20 = _x150 ∧ x1 = _x151 ∧ x2 = _x152 ∧ x3 = _x153 ∧ x4 = _x154 ∧ x5 = _x155 ∧ x6 = _x156 ∧ x7 = _x157 ∧ x8 = _x158 ∧ x9 = _x159 ∧ x10 = _x160 ∧ x11 = _x161 ∧ x12 = _x162 ∧ x13 = _x163 ∧ x14 = _x164 ∧ x15 = _x165 ∧ x16 = _x166 ∧ x17 = _x167 ∧ x18 = _x168 ∧ x19 = _x169 ∧ x20 = _x170 ∧ _x150 = _x170 ∧ _x149 = _x169 ∧ _x148 = _x168 ∧ _x147 = _x167 ∧ _x146 = _x166 ∧ _x145 = _x165 ∧ _x144 = _x164 ∧ _x143 = _x163 ∧ _x142 = _x162 ∧ _x141 = _x161 ∧ _x140 = _x160 ∧ _x139 = _x159 ∧ _x138 = _x158 ∧ _x137 = _x157 ∧ _x136 = _x156 ∧ _x135 = _x155 ∧ _x134 = _x154 ∧ _x133 = _x153 ∧ _x132 = _x152 ∧ _x131 = _x151 l1 6 l6: 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 ∧ x20 = _x190 ∧ x1 = _x191 ∧ x2 = _x192 ∧ x3 = _x193 ∧ x4 = _x194 ∧ x5 = _x195 ∧ x6 = _x196 ∧ x7 = _x197 ∧ x8 = _x198 ∧ x9 = _x199 ∧ x10 = _x200 ∧ x11 = _x201 ∧ x12 = _x202 ∧ x13 = _x203 ∧ x14 = _x204 ∧ x15 = _x205 ∧ x16 = _x206 ∧ x17 = _x207 ∧ x18 = _x208 ∧ x19 = _x209 ∧ x20 = _x210 ∧ _x190 = _x210 ∧ _x189 = _x209 ∧ _x188 = _x208 ∧ _x187 = _x207 ∧ _x186 = _x206 ∧ _x185 = _x205 ∧ _x184 = _x204 ∧ _x183 = _x203 ∧ _x182 = _x202 ∧ _x181 = _x201 ∧ _x180 = _x200 ∧ _x179 = _x199 ∧ _x178 = _x198 ∧ _x177 = _x197 ∧ _x176 = _x196 ∧ _x175 = _x195 ∧ _x174 = _x194 ∧ _x173 = _x193 ∧ _x172 = _x192 ∧ _x171 = _x191 l5 7 l3: x1 = _x211 ∧ x2 = _x212 ∧ x3 = _x213 ∧ x4 = _x214 ∧ x5 = _x215 ∧ x6 = _x216 ∧ x7 = _x217 ∧ x8 = _x218 ∧ x9 = _x219 ∧ x10 = _x220 ∧ x11 = _x221 ∧ x12 = _x222 ∧ x13 = _x223 ∧ x14 = _x224 ∧ x15 = _x225 ∧ x16 = _x226 ∧ x17 = _x227 ∧ x18 = _x228 ∧ x19 = _x229 ∧ x20 = _x230 ∧ x1 = _x231 ∧ x2 = _x232 ∧ x3 = _x233 ∧ x4 = _x234 ∧ x5 = _x235 ∧ x6 = _x236 ∧ x7 = _x237 ∧ x8 = _x238 ∧ x9 = _x239 ∧ x10 = _x240 ∧ x11 = _x241 ∧ x12 = _x242 ∧ x13 = _x243 ∧ x14 = _x244 ∧ x15 = _x245 ∧ x16 = _x246 ∧ x17 = _x247 ∧ x18 = _x248 ∧ x19 = _x249 ∧ x20 = _x250 ∧ _x230 = _x250 ∧ _x229 = _x249 ∧ _x228 = _x248 ∧ _x227 = _x247 ∧ _x226 = _x246 ∧ _x225 = _x245 ∧ _x224 = _x244 ∧ _x223 = _x243 ∧ _x222 = _x242 ∧ _x221 = _x241 ∧ _x220 = _x240 ∧ _x219 = _x239 ∧ _x218 = _x238 ∧ _x217 = _x237 ∧ _x216 = _x236 ∧ _x215 = _x235 ∧ _x214 = _x234 ∧ _x213 = _x233 ∧ _x212 = _x232 ∧ _x211 = _x231 l6 8 l5: x1 = _x251 ∧ x2 = _x252 ∧ x3 = _x253 ∧ x4 = _x254 ∧ x5 = _x255 ∧ x6 = _x256 ∧ x7 = _x257 ∧ x8 = _x258 ∧ x9 = _x259 ∧ x10 = _x260 ∧ x11 = _x261 ∧ x12 = _x262 ∧ x13 = _x263 ∧ x14 = _x264 ∧ x15 = _x265 ∧ x16 = _x266 ∧ x17 = _x267 ∧ x18 = _x268 ∧ x19 = _x269 ∧ x20 = _x270 ∧ x1 = _x271 ∧ x2 = _x272 ∧ x3 = _x273 ∧ x4 = _x274 ∧ x5 = _x275 ∧ x6 = _x276 ∧ x7 = _x277 ∧ x8 = _x278 ∧ x9 = _x279 ∧ x10 = _x280 ∧ x11 = _x281 ∧ x12 = _x282 ∧ x13 = _x283 ∧ x14 = _x284 ∧ x15 = _x285 ∧ x16 = _x286 ∧ x17 = _x287 ∧ x18 = _x288 ∧ x19 = _x289 ∧ x20 = _x290 ∧ _x270 = _x290 ∧ _x269 = _x289 ∧ _x268 = _x288 ∧ _x267 = _x287 ∧ _x266 = _x286 ∧ _x265 = _x285 ∧ _x264 = _x284 ∧ _x263 = _x283 ∧ _x262 = _x282 ∧ _x261 = _x281 ∧ _x260 = _x280 ∧ _x259 = _x279 ∧ _x258 = _x278 ∧ _x257 = _x277 ∧ _x256 = _x276 ∧ _x255 = _x275 ∧ _x254 = _x274 ∧ _x253 = _x273 ∧ _x252 = _x272 ∧ _x271 = 7 ∧ 1 + _x251 ≤ 0 l6 9 l1: x1 = _x291 ∧ x2 = _x292 ∧ x3 = _x293 ∧ x4 = _x294 ∧ x5 = _x295 ∧ x6 = _x296 ∧ x7 = _x297 ∧ x8 = _x298 ∧ x9 = _x299 ∧ x10 = _x300 ∧ x11 = _x301 ∧ x12 = _x302 ∧ x13 = _x303 ∧ x14 = _x304 ∧ x15 = _x305 ∧ x16 = _x306 ∧ x17 = _x307 ∧ x18 = _x308 ∧ x19 = _x309 ∧ x20 = _x310 ∧ x1 = _x311 ∧ x2 = _x312 ∧ x3 = _x313 ∧ x4 = _x314 ∧ x5 = _x315 ∧ x6 = _x316 ∧ x7 = _x317 ∧ x8 = _x318 ∧ x9 = _x319 ∧ x10 = _x320 ∧ x11 = _x321 ∧ x12 = _x322 ∧ x13 = _x323 ∧ x14 = _x324 ∧ x15 = _x325 ∧ x16 = _x326 ∧ x17 = _x327 ∧ x18 = _x328 ∧ x19 = _x329 ∧ x20 = _x330 ∧ 0 ≤ _x291 ∧ _x314 = _x314 ∧ _x331 = _x331 ∧ _x319 = _x319 ∧ _x332 = _x332 ∧ _x320 = _x320 ∧ _x333 = _x333 ∧ _x321 = _x321 ∧ _x334 = _x334 ∧ _x315 = _x314 + _x321 ∧ _x318 = _x314 − _x321 ∧ _x316 = _x319 + _x320 ∧ _x317 = _x319 − _x320 ∧ _x335 = _x335 ∧ _x336 = _x334 + _x331 ∧ _x337 = _x333 + _x332 ∧ _x338 = _x334 + _x332 ∧ _x339 = _x333 + _x331 ∧ _x330 = _x330 ∧ _x322 = _x322 ∧ _x323 = _x323 ∧ _x324 = _x324 ∧ _x325 = _x325 ∧ _x326 = _x326 ∧ _x327 = _x327 ∧ _x340 = _x340 ∧ _x341 = _x341 ∧ _x328 = _x340 + _x330 ∧ _x329 = _x341 + _x330 ∧ _x311 = −1 + _x291 ∧ _x292 = _x312 ∧ _x293 = _x313 l7 10 l2: 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 ∧ x20 = _x361 ∧ x1 = _x362 ∧ x2 = _x363 ∧ x3 = _x364 ∧ x4 = _x365 ∧ x5 = _x366 ∧ x6 = _x367 ∧ x7 = _x368 ∧ x8 = _x369 ∧ x9 = _x370 ∧ x10 = _x371 ∧ x11 = _x372 ∧ x12 = _x373 ∧ x13 = _x374 ∧ x14 = _x375 ∧ x15 = _x376 ∧ x16 = _x377 ∧ x17 = _x378 ∧ x18 = _x379 ∧ x19 = _x380 ∧ x20 = _x381 ∧ _x361 = _x381 ∧ _x360 = _x380 ∧ _x359 = _x379 ∧ _x358 = _x378 ∧ _x357 = _x377 ∧ _x356 = _x376 ∧ _x355 = _x375 ∧ _x354 = _x374 ∧ _x353 = _x373 ∧ _x352 = _x372 ∧ _x351 = _x371 ∧ _x350 = _x370 ∧ _x349 = _x369 ∧ _x348 = _x368 ∧ _x347 = _x367 ∧ _x346 = _x366 ∧ _x345 = _x365 ∧ _x342 = _x362 ∧ _x363 = 0 ∧ _x364 = 0 l8 11 l7: x1 = _x382 ∧ x2 = _x383 ∧ x3 = _x384 ∧ x4 = _x385 ∧ x5 = _x386 ∧ x6 = _x387 ∧ x7 = _x388 ∧ x8 = _x389 ∧ x9 = _x390 ∧ x10 = _x391 ∧ x11 = _x392 ∧ x12 = _x393 ∧ x13 = _x394 ∧ x14 = _x395 ∧ x15 = _x396 ∧ x16 = _x397 ∧ x17 = _x398 ∧ x18 = _x399 ∧ x19 = _x400 ∧ x20 = _x401 ∧ x1 = _x402 ∧ x2 = _x403 ∧ x3 = _x404 ∧ x4 = _x405 ∧ x5 = _x406 ∧ x6 = _x407 ∧ x7 = _x408 ∧ x8 = _x409 ∧ x9 = _x410 ∧ x10 = _x411 ∧ x11 = _x412 ∧ x12 = _x413 ∧ x13 = _x414 ∧ x14 = _x415 ∧ x15 = _x416 ∧ x16 = _x417 ∧ x17 = _x418 ∧ x18 = _x419 ∧ x19 = _x420 ∧ x20 = _x421 ∧ _x401 = _x421 ∧ _x400 = _x420 ∧ _x399 = _x419 ∧ _x398 = _x418 ∧ _x397 = _x417 ∧ _x396 = _x416 ∧ _x395 = _x415 ∧ _x394 = _x414 ∧ _x393 = _x413 ∧ _x392 = _x412 ∧ _x391 = _x411 ∧ _x390 = _x410 ∧ _x389 = _x409 ∧ _x388 = _x408 ∧ _x387 = _x407 ∧ _x386 = _x406 ∧ _x385 = _x405 ∧ _x384 = _x404 ∧ _x383 = _x403 ∧ _x382 = _x402

## 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 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 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 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 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 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 ∧ x20 = x20 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 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
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 { l0, l2 }.

### 2.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by −126.

 l0: −2⋅x2 l2: −2⋅x2 + 1

### 2.1.2 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by 0.

 l2: 0 l0: −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 { l6, l1 }.

### 2.2.1 Transition Removal

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

 l1: 2⋅x1 + 1 l6: 2⋅x1

### 2.2.2 Transition Removal

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

 l1: 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 { l5, l3 }.

### 2.3.1 Transition Removal

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

 l5: x1 l3: x1

### 2.3.2 Transition Removal

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

 l5: 0 l3: −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)