# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l7, l11, l1, l13, l3, l2, l9, l14, l4, l6, l10, l8, l15, l16, l0
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _Index15HAT0 ∧ x2 = _Inner14HAT0 ∧ x3 = _InnerIndex6HAT0 ∧ x4 = _InnerIndex9HAT0 ∧ x5 = _Outer13HAT0 ∧ x6 = _OuterIndex5HAT0 ∧ x7 = _OuterIndex8HAT0 ∧ x8 = _SeedHAT0 ∧ x9 = ___const_20HAT0 ∧ x10 = _ret_RandomInteger16HAT0 ∧ x11 = _ret_RandomInteger17HAT0 ∧ x1 = _Index15HATpost ∧ x2 = _Inner14HATpost ∧ x3 = _InnerIndex6HATpost ∧ x4 = _InnerIndex9HATpost ∧ x5 = _Outer13HATpost ∧ x6 = _OuterIndex5HATpost ∧ x7 = _OuterIndex8HATpost ∧ x8 = _SeedHATpost ∧ x9 = ___const_20HATpost ∧ x10 = _ret_RandomInteger16HATpost ∧ x11 = _ret_RandomInteger17HATpost ∧ _ret_RandomInteger17HAT0 = _ret_RandomInteger17HATpost ∧ _ret_RandomInteger16HAT0 = _ret_RandomInteger16HATpost ∧ ___const_20HAT0 = ___const_20HATpost ∧ _SeedHAT0 = _SeedHATpost ∧ _OuterIndex8HAT0 = _OuterIndex8HATpost ∧ _OuterIndex5HAT0 = _OuterIndex5HATpost ∧ _Outer13HAT0 = _Outer13HATpost ∧ _InnerIndex9HAT0 = _InnerIndex9HATpost ∧ _InnerIndex6HAT0 = _InnerIndex6HATpost ∧ _Inner14HAT0 = _Inner14HATpost ∧ _Index15HAT0 = _Index15HATpost 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 ∧ x1 = _x11 ∧ x2 = _x12 ∧ x3 = _x13 ∧ x4 = _x14 ∧ x5 = _x15 ∧ x6 = _x16 ∧ x7 = _x17 ∧ x8 = _x18 ∧ x9 = _x19 ∧ x10 = _x20 ∧ x11 = _x21 ∧ _x10 = _x21 ∧ _x9 = _x20 ∧ _x8 = _x19 ∧ _x7 = _x18 ∧ _x6 = _x17 ∧ _x5 = _x16 ∧ _x4 = _x15 ∧ _x3 = _x14 ∧ _x2 = _x13 ∧ _x1 = _x12 ∧ _x = _x11 l4 3 l5: x1 = _x22 ∧ x2 = _x23 ∧ x3 = _x24 ∧ x4 = _x25 ∧ x5 = _x26 ∧ x6 = _x27 ∧ x7 = _x28 ∧ x8 = _x29 ∧ x9 = _x30 ∧ x10 = _x31 ∧ x11 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ x4 = _x36 ∧ x5 = _x37 ∧ x6 = _x38 ∧ x7 = _x39 ∧ x8 = _x40 ∧ x9 = _x41 ∧ x10 = _x42 ∧ x11 = _x43 ∧ _x32 = _x43 ∧ _x31 = _x42 ∧ _x30 = _x41 ∧ _x29 = _x40 ∧ _x28 = _x39 ∧ _x27 = _x38 ∧ _x26 = _x37 ∧ _x25 = _x36 ∧ _x24 = _x35 ∧ _x23 = _x34 ∧ _x22 = _x33 l6 4 l7: x1 = _x44 ∧ x2 = _x45 ∧ x3 = _x46 ∧ x4 = _x47 ∧ x5 = _x48 ∧ x6 = _x49 ∧ x7 = _x50 ∧ x8 = _x51 ∧ x9 = _x52 ∧ x10 = _x53 ∧ x11 = _x54 ∧ x1 = _x55 ∧ x2 = _x56 ∧ x3 = _x57 ∧ x4 = _x58 ∧ x5 = _x59 ∧ x6 = _x60 ∧ x7 = _x61 ∧ x8 = _x62 ∧ x9 = _x63 ∧ x10 = _x64 ∧ x11 = _x65 ∧ _x54 = _x65 ∧ _x53 = _x64 ∧ _x52 = _x63 ∧ _x51 = _x62 ∧ _x50 = _x61 ∧ _x49 = _x60 ∧ _x48 = _x59 ∧ _x47 = _x58 ∧ _x46 = _x57 ∧ _x44 = _x55 ∧ _x56 = 1 + _x45 ∧ _x52 ≤ _x44 l6 5 l8: x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x4 = _x69 ∧ x5 = _x70 ∧ x6 = _x71 ∧ x7 = _x72 ∧ x8 = _x73 ∧ x9 = _x74 ∧ x10 = _x75 ∧ x11 = _x76 ∧ x1 = _x77 ∧ x2 = _x78 ∧ x3 = _x79 ∧ x4 = _x80 ∧ x5 = _x81 ∧ x6 = _x82 ∧ x7 = _x83 ∧ x8 = _x84 ∧ x9 = _x85 ∧ x10 = _x86 ∧ x11 = _x87 ∧ _x76 = _x87 ∧ _x75 = _x86 ∧ _x74 = _x85 ∧ _x73 = _x84 ∧ _x72 = _x83 ∧ _x71 = _x82 ∧ _x70 = _x81 ∧ _x69 = _x80 ∧ _x68 = _x79 ∧ _x67 = _x78 ∧ _x77 = 1 + _x66 ∧ 1 + _x66 ≤ _x74 l9 6 l10: x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x90 ∧ x4 = _x91 ∧ x5 = _x92 ∧ x6 = _x93 ∧ x7 = _x94 ∧ x8 = _x95 ∧ x9 = _x96 ∧ x10 = _x97 ∧ x11 = _x98 ∧ x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x101 ∧ x4 = _x102 ∧ x5 = _x103 ∧ x6 = _x104 ∧ x7 = _x105 ∧ x8 = _x106 ∧ x9 = _x107 ∧ x10 = _x108 ∧ x11 = _x109 ∧ _x98 = _x109 ∧ _x97 = _x108 ∧ _x96 = _x107 ∧ _x95 = _x106 ∧ _x94 = _x105 ∧ _x93 = _x104 ∧ _x91 = _x102 ∧ _x90 = _x101 ∧ _x89 = _x100 ∧ _x88 = _x99 ∧ _x103 = 1 + _x92 ∧ _x96 ≤ _x89 l9 7 l8: x1 = _x110 ∧ x2 = _x111 ∧ x3 = _x112 ∧ x4 = _x113 ∧ x5 = _x114 ∧ x6 = _x115 ∧ x7 = _x116 ∧ x8 = _x117 ∧ x9 = _x118 ∧ x10 = _x119 ∧ x11 = _x120 ∧ x1 = _x121 ∧ x2 = _x122 ∧ x3 = _x123 ∧ x4 = _x124 ∧ x5 = _x125 ∧ x6 = _x126 ∧ x7 = _x127 ∧ x8 = _x128 ∧ x9 = _x129 ∧ x10 = _x130 ∧ x11 = _x131 ∧ _x120 = _x131 ∧ _x119 = _x130 ∧ _x118 = _x129 ∧ _x117 = _x128 ∧ _x116 = _x127 ∧ _x115 = _x126 ∧ _x114 = _x125 ∧ _x113 = _x124 ∧ _x112 = _x123 ∧ _x111 = _x122 ∧ _x121 = 0 ∧ 1 + _x111 ≤ _x118 l11 8 l12: x1 = _x132 ∧ x2 = _x133 ∧ x3 = _x134 ∧ x4 = _x135 ∧ x5 = _x136 ∧ x6 = _x137 ∧ x7 = _x138 ∧ x8 = _x139 ∧ x9 = _x140 ∧ x10 = _x141 ∧ x11 = _x142 ∧ x1 = _x143 ∧ x2 = _x144 ∧ x3 = _x145 ∧ x4 = _x146 ∧ x5 = _x147 ∧ x6 = _x148 ∧ x7 = _x149 ∧ x8 = _x150 ∧ x9 = _x151 ∧ x10 = _x152 ∧ x11 = _x153 ∧ _x142 = _x153 ∧ _x141 = _x152 ∧ _x140 = _x151 ∧ _x139 = _x150 ∧ _x138 = _x149 ∧ _x137 = _x148 ∧ _x136 = _x147 ∧ _x135 = _x146 ∧ _x134 = _x145 ∧ _x133 = _x144 ∧ _x132 = _x143 ∧ _x140 ≤ _x136 l11 9 l7: x1 = _x154 ∧ x2 = _x155 ∧ x3 = _x156 ∧ x4 = _x157 ∧ x5 = _x158 ∧ x6 = _x159 ∧ x7 = _x160 ∧ x8 = _x161 ∧ x9 = _x162 ∧ x10 = _x163 ∧ x11 = _x164 ∧ x1 = _x165 ∧ x2 = _x166 ∧ x3 = _x167 ∧ x4 = _x168 ∧ x5 = _x169 ∧ x6 = _x170 ∧ x7 = _x171 ∧ x8 = _x172 ∧ x9 = _x173 ∧ x10 = _x174 ∧ x11 = _x175 ∧ _x164 = _x175 ∧ _x163 = _x174 ∧ _x162 = _x173 ∧ _x161 = _x172 ∧ _x160 = _x171 ∧ _x159 = _x170 ∧ _x158 = _x169 ∧ _x157 = _x168 ∧ _x156 = _x167 ∧ _x154 = _x165 ∧ _x166 = 0 ∧ 1 + _x158 ≤ _x162 l13 10 l14: x1 = _x176 ∧ x2 = _x177 ∧ x3 = _x178 ∧ x4 = _x179 ∧ x5 = _x180 ∧ x6 = _x181 ∧ x7 = _x182 ∧ x8 = _x183 ∧ x9 = _x184 ∧ x10 = _x185 ∧ x11 = _x186 ∧ x1 = _x187 ∧ x2 = _x188 ∧ x3 = _x189 ∧ x4 = _x190 ∧ x5 = _x191 ∧ x6 = _x192 ∧ x7 = _x193 ∧ x8 = _x194 ∧ x9 = _x195 ∧ x10 = _x196 ∧ x11 = _x197 ∧ _x186 = _x197 ∧ _x185 = _x196 ∧ _x184 = _x195 ∧ _x183 = _x194 ∧ _x182 = _x193 ∧ _x181 = _x192 ∧ _x180 = _x191 ∧ _x179 = _x190 ∧ _x178 = _x189 ∧ _x177 = _x188 ∧ _x176 = _x187 l10 11 l11: x1 = _x198 ∧ x2 = _x199 ∧ x3 = _x200 ∧ x4 = _x201 ∧ x5 = _x202 ∧ x6 = _x203 ∧ x7 = _x204 ∧ x8 = _x205 ∧ x9 = _x206 ∧ x10 = _x207 ∧ x11 = _x208 ∧ x1 = _x209 ∧ x2 = _x210 ∧ x3 = _x211 ∧ x4 = _x212 ∧ x5 = _x213 ∧ x6 = _x214 ∧ x7 = _x215 ∧ x8 = _x216 ∧ x9 = _x217 ∧ x10 = _x218 ∧ x11 = _x219 ∧ _x208 = _x219 ∧ _x207 = _x218 ∧ _x206 = _x217 ∧ _x205 = _x216 ∧ _x204 = _x215 ∧ _x203 = _x214 ∧ _x202 = _x213 ∧ _x201 = _x212 ∧ _x200 = _x211 ∧ _x199 = _x210 ∧ _x198 = _x209 l14 12 l4: x1 = _x220 ∧ x2 = _x221 ∧ x3 = _x222 ∧ x4 = _x223 ∧ x5 = _x224 ∧ x6 = _x225 ∧ x7 = _x226 ∧ x8 = _x227 ∧ x9 = _x228 ∧ x10 = _x229 ∧ x11 = _x230 ∧ x1 = _x231 ∧ x2 = _x232 ∧ x3 = _x233 ∧ x4 = _x234 ∧ x5 = _x235 ∧ x6 = _x236 ∧ x7 = _x237 ∧ x8 = _x238 ∧ x9 = _x239 ∧ x10 = _x240 ∧ x11 = _x241 ∧ _x230 = _x241 ∧ _x229 = _x240 ∧ _x228 = _x239 ∧ _x227 = _x238 ∧ _x225 = _x236 ∧ _x224 = _x235 ∧ _x223 = _x234 ∧ _x222 = _x233 ∧ _x221 = _x232 ∧ _x220 = _x231 ∧ _x237 = 1 + _x226 ∧ _x228 ≤ _x223 l14 13 l13: x1 = _x242 ∧ x2 = _x243 ∧ x3 = _x244 ∧ x4 = _x245 ∧ x5 = _x246 ∧ x6 = _x247 ∧ x7 = _x248 ∧ x8 = _x249 ∧ x9 = _x250 ∧ x10 = _x251 ∧ x11 = _x252 ∧ x1 = _x253 ∧ x2 = _x254 ∧ x3 = _x255 ∧ x4 = _x256 ∧ x5 = _x257 ∧ x6 = _x258 ∧ x7 = _x259 ∧ x8 = _x260 ∧ x9 = _x261 ∧ x10 = _x262 ∧ x11 = _x263 ∧ _x251 = _x262 ∧ _x250 = _x261 ∧ _x248 = _x259 ∧ _x247 = _x258 ∧ _x246 = _x257 ∧ _x244 = _x255 ∧ _x243 = _x254 ∧ _x242 = _x253 ∧ _x256 = 1 + _x245 ∧ _x263 = _x260 ∧ _x260 = _x260 ∧ 1 + _x245 ≤ _x250 l5 14 l10: x1 = _x264 ∧ x2 = _x265 ∧ x3 = _x266 ∧ x4 = _x267 ∧ x5 = _x268 ∧ x6 = _x269 ∧ x7 = _x270 ∧ x8 = _x271 ∧ x9 = _x272 ∧ x10 = _x273 ∧ x11 = _x274 ∧ x1 = _x275 ∧ x2 = _x276 ∧ x3 = _x277 ∧ x4 = _x278 ∧ x5 = _x279 ∧ x6 = _x280 ∧ x7 = _x281 ∧ x8 = _x282 ∧ x9 = _x283 ∧ x10 = _x284 ∧ x11 = _x285 ∧ _x274 = _x285 ∧ _x273 = _x284 ∧ _x272 = _x283 ∧ _x271 = _x282 ∧ _x270 = _x281 ∧ _x269 = _x280 ∧ _x267 = _x278 ∧ _x266 = _x277 ∧ _x265 = _x276 ∧ _x264 = _x275 ∧ _x279 = 0 ∧ _x272 ≤ _x270 l5 15 l13: x1 = _x286 ∧ x2 = _x287 ∧ x3 = _x288 ∧ x4 = _x289 ∧ x5 = _x290 ∧ x6 = _x291 ∧ x7 = _x292 ∧ x8 = _x293 ∧ x9 = _x294 ∧ x10 = _x295 ∧ x11 = _x296 ∧ x1 = _x297 ∧ x2 = _x298 ∧ x3 = _x299 ∧ x4 = _x300 ∧ x5 = _x301 ∧ x6 = _x302 ∧ x7 = _x303 ∧ x8 = _x304 ∧ x9 = _x305 ∧ x10 = _x306 ∧ x11 = _x307 ∧ _x296 = _x307 ∧ _x295 = _x306 ∧ _x294 = _x305 ∧ _x293 = _x304 ∧ _x292 = _x303 ∧ _x291 = _x302 ∧ _x290 = _x301 ∧ _x288 = _x299 ∧ _x287 = _x298 ∧ _x286 = _x297 ∧ _x300 = 0 ∧ 1 + _x292 ≤ _x294 l7 16 l9: x1 = _x308 ∧ x2 = _x309 ∧ x3 = _x310 ∧ x4 = _x311 ∧ x5 = _x312 ∧ x6 = _x313 ∧ x7 = _x314 ∧ x8 = _x315 ∧ x9 = _x316 ∧ x10 = _x317 ∧ x11 = _x318 ∧ x1 = _x319 ∧ x2 = _x320 ∧ x3 = _x321 ∧ x4 = _x322 ∧ x5 = _x323 ∧ x6 = _x324 ∧ x7 = _x325 ∧ x8 = _x326 ∧ x9 = _x327 ∧ x10 = _x328 ∧ x11 = _x329 ∧ _x318 = _x329 ∧ _x317 = _x328 ∧ _x316 = _x327 ∧ _x315 = _x326 ∧ _x314 = _x325 ∧ _x313 = _x324 ∧ _x312 = _x323 ∧ _x311 = _x322 ∧ _x310 = _x321 ∧ _x309 = _x320 ∧ _x308 = _x319 l8 17 l6: x1 = _x330 ∧ x2 = _x331 ∧ x3 = _x332 ∧ x4 = _x333 ∧ x5 = _x334 ∧ x6 = _x335 ∧ x7 = _x336 ∧ x8 = _x337 ∧ x9 = _x338 ∧ x10 = _x339 ∧ x11 = _x340 ∧ x1 = _x341 ∧ x2 = _x342 ∧ x3 = _x343 ∧ x4 = _x344 ∧ x5 = _x345 ∧ x6 = _x346 ∧ x7 = _x347 ∧ x8 = _x348 ∧ x9 = _x349 ∧ x10 = _x350 ∧ x11 = _x351 ∧ _x340 = _x351 ∧ _x339 = _x350 ∧ _x338 = _x349 ∧ _x337 = _x348 ∧ _x336 = _x347 ∧ _x335 = _x346 ∧ _x334 = _x345 ∧ _x333 = _x344 ∧ _x332 = _x343 ∧ _x331 = _x342 ∧ _x330 = _x341 l3 18 l0: x1 = _x352 ∧ x2 = _x353 ∧ x3 = _x354 ∧ x4 = _x355 ∧ x5 = _x356 ∧ x6 = _x357 ∧ x7 = _x358 ∧ x8 = _x359 ∧ x9 = _x360 ∧ x10 = _x361 ∧ x11 = _x362 ∧ x1 = _x363 ∧ x2 = _x364 ∧ x3 = _x365 ∧ x4 = _x366 ∧ x5 = _x367 ∧ x6 = _x368 ∧ x7 = _x369 ∧ x8 = _x370 ∧ x9 = _x371 ∧ x10 = _x372 ∧ x11 = _x373 ∧ _x362 = _x373 ∧ _x361 = _x372 ∧ _x360 = _x371 ∧ _x359 = _x370 ∧ _x358 = _x369 ∧ _x356 = _x367 ∧ _x355 = _x366 ∧ _x354 = _x365 ∧ _x353 = _x364 ∧ _x352 = _x363 ∧ _x368 = 1 + _x357 ∧ _x360 ≤ _x354 l3 19 l2: x1 = _x374 ∧ x2 = _x375 ∧ x3 = _x376 ∧ x4 = _x377 ∧ x5 = _x378 ∧ x6 = _x379 ∧ x7 = _x380 ∧ x8 = _x381 ∧ x9 = _x382 ∧ x10 = _x383 ∧ x11 = _x384 ∧ x1 = _x385 ∧ x2 = _x386 ∧ x3 = _x387 ∧ x4 = _x388 ∧ x5 = _x389 ∧ x6 = _x390 ∧ x7 = _x391 ∧ x8 = _x392 ∧ x9 = _x393 ∧ x10 = _x394 ∧ x11 = _x395 ∧ _x384 = _x395 ∧ _x382 = _x393 ∧ _x380 = _x391 ∧ _x379 = _x390 ∧ _x378 = _x389 ∧ _x377 = _x388 ∧ _x375 = _x386 ∧ _x374 = _x385 ∧ _x387 = 1 + _x376 ∧ _x394 = _x392 ∧ _x392 = _x392 ∧ 1 + _x376 ≤ _x382 l1 20 l4: x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x5 = _x400 ∧ x6 = _x401 ∧ x7 = _x402 ∧ x8 = _x403 ∧ x9 = _x404 ∧ x10 = _x405 ∧ x11 = _x406 ∧ x1 = _x407 ∧ x2 = _x408 ∧ x3 = _x409 ∧ x4 = _x410 ∧ x5 = _x411 ∧ x6 = _x412 ∧ x7 = _x413 ∧ x8 = _x414 ∧ x9 = _x415 ∧ x10 = _x416 ∧ x11 = _x417 ∧ _x406 = _x417 ∧ _x405 = _x416 ∧ _x404 = _x415 ∧ _x403 = _x414 ∧ _x401 = _x412 ∧ _x400 = _x411 ∧ _x399 = _x410 ∧ _x398 = _x409 ∧ _x397 = _x408 ∧ _x396 = _x407 ∧ _x413 = 0 ∧ _x404 ≤ _x401 l1 21 l2: x1 = _x418 ∧ x2 = _x419 ∧ x3 = _x420 ∧ x4 = _x421 ∧ x5 = _x422 ∧ x6 = _x423 ∧ x7 = _x424 ∧ x8 = _x425 ∧ x9 = _x426 ∧ x10 = _x427 ∧ x11 = _x428 ∧ x1 = _x429 ∧ x2 = _x430 ∧ x3 = _x431 ∧ x4 = _x432 ∧ x5 = _x433 ∧ x6 = _x434 ∧ x7 = _x435 ∧ x8 = _x436 ∧ x9 = _x437 ∧ x10 = _x438 ∧ x11 = _x439 ∧ _x428 = _x439 ∧ _x427 = _x438 ∧ _x426 = _x437 ∧ _x425 = _x436 ∧ _x424 = _x435 ∧ _x423 = _x434 ∧ _x422 = _x433 ∧ _x421 = _x432 ∧ _x419 = _x430 ∧ _x418 = _x429 ∧ _x431 = 0 ∧ 1 + _x423 ≤ _x426 l15 22 l0: x1 = _x440 ∧ x2 = _x441 ∧ x3 = _x442 ∧ x4 = _x443 ∧ x5 = _x444 ∧ x6 = _x445 ∧ x7 = _x446 ∧ x8 = _x447 ∧ x9 = _x448 ∧ x10 = _x449 ∧ x11 = _x450 ∧ x1 = _x451 ∧ x2 = _x452 ∧ x3 = _x453 ∧ x4 = _x454 ∧ x5 = _x455 ∧ x6 = _x456 ∧ x7 = _x457 ∧ x8 = _x458 ∧ x9 = _x459 ∧ x10 = _x460 ∧ x11 = _x461 ∧ _x450 = _x461 ∧ _x449 = _x460 ∧ _x448 = _x459 ∧ _x446 = _x457 ∧ _x444 = _x455 ∧ _x443 = _x454 ∧ _x442 = _x453 ∧ _x441 = _x452 ∧ _x440 = _x451 ∧ _x456 = 0 ∧ _x458 = 0 l16 23 l15: x1 = _x462 ∧ x2 = _x463 ∧ x3 = _x464 ∧ x4 = _x465 ∧ x5 = _x466 ∧ x6 = _x467 ∧ x7 = _x468 ∧ x8 = _x469 ∧ x9 = _x470 ∧ x10 = _x471 ∧ x11 = _x472 ∧ x1 = _x473 ∧ x2 = _x474 ∧ x3 = _x475 ∧ x4 = _x476 ∧ x5 = _x477 ∧ x6 = _x478 ∧ x7 = _x479 ∧ x8 = _x480 ∧ x9 = _x481 ∧ x10 = _x482 ∧ x11 = _x483 ∧ _x472 = _x483 ∧ _x471 = _x482 ∧ _x470 = _x481 ∧ _x469 = _x480 ∧ _x468 = _x479 ∧ _x467 = _x478 ∧ _x466 = _x477 ∧ _x465 = _x476 ∧ _x464 = _x475 ∧ _x463 = _x474 ∧ _x462 = _x473

## 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 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 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 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 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 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 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 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 l14 l14 l14: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 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 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 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 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 l15 l15 l15: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 l16 l16 l16: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 ∧ x11 = x11 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
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, l3, l0, l2 }.

### 2.1.1 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by 0.

 l0: −1 − x6 + x9 l1: −1 − x6 + x9 l3: −2 − x6 + x9 l2: −2 − x6 + x9

### 2.1.2 Transition Removal

We remove transitions 1, 18 using the following ranking functions, which are bounded by 0.

 l0: 0 l1: −1 l3: 1 l2: 1

### 2.1.3 Transition Removal

We remove transition 19 using the following ranking functions, which are bounded by 0.

 l2: −2⋅x3 + 2⋅x9 + 1 l3: −2⋅x3 + 2⋅x9

### 2.1.4 Transition Removal

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

 l2: 0 l3: −1

### 2.1.5 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, l4, l13, l14 }.

### 2.2.1 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by 0.

 l4: −1 − x7 + x9 l5: −1 − x7 + x9 l14: −2 − x7 + x9 l13: −2 − x7 + x9

### 2.2.2 Transition Removal

We remove transitions 3, 12 using the following ranking functions, which are bounded by 0.

 l4: 0 l5: −1 l14: 1 l13: 1

### 2.2.3 Transition Removal

We remove transition 13 using the following ranking functions, which are bounded by 0.

 l13: −2⋅x4 + 2⋅x9 + 1 l14: −2⋅x4 + 2⋅x9

### 2.2.4 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 0.

 l13: 0 l14: −1

### 2.2.5 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 { l7, l10, l6, l11, l8, l9 }.

### 2.3.1 Transition Removal

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

 l10: −1 − x5 + x9 l11: −1 − x5 + x9 l9: −2 − x5 + x9 l7: −2 − x5 + x9 l6: −2 − x5 + x9 l8: −2 − x5 + x9

### 2.3.2 Transition Removal

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

 l10: −1 l11: −2 l9: 0 l7: 0 l6: 0 l8: 0

### 2.3.3 Transition Removal

We remove transition 11 using the following ranking functions, which are bounded by 0.

 l10: 0 l11: −1 l7: −3⋅x2 + 2⋅x3 + 2⋅x4 + 2⋅x5 + 2⋅x6 + 2⋅x7 + 2⋅x8 + 4⋅x9 + 2⋅x10 + 2⋅x11 + 3 l9: −3⋅x2 + 2⋅x3 + 2⋅x4 + 2⋅x5 + 2⋅x6 + 2⋅x7 + 2⋅x8 + 4⋅x9 + 2⋅x10 + 2⋅x11 + 2 l6: 4⋅x9 − 3⋅x2 + 2⋅x3 + 2⋅x4 + 2⋅x5 + 2⋅x6 + 2⋅x7 + 2⋅x8 + 2⋅x10 + 2⋅x11 + 1 l8: −3⋅x2 + 2⋅x3 + 2⋅x4 + 2⋅x5 + 2⋅x6 + 2⋅x7 + 2⋅x8 + 4⋅x9 + 2⋅x10 + 2⋅x11 + 1

### 2.3.4 Transition Removal

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

 l7: −1 − x2 + x9 l9: −1 − x2 + x9 l6: −2 − x2 + x9 l8: −2 − x2 + x9

### 2.3.5 Transition Removal

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

 l7: −1 − x1 + x9 l9: −1 − x1 + x9 l6: −1 − x1 + x9 l8: −1 − x1 + x9

### 2.3.6 Transition Removal

We remove transitions 16, 4, 17 using the following ranking functions, which are bounded by 0.

 l7: 0 l9: −1 l6: 1 l8: 2

### 2.3.7 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 % (22 real / 0 unknown / 0 assumptions / 22 total proof steps)