LTS Termination Proof

by AProVE

Input

• Initial Location: f349_0_createList_Return, f1264_0_createList_LE, f1293_0_clear_FieldAccess, f716_0_createList_Load, f337_0_createList_Load, f1_0_main_Load, f1543_0_clear_EQ, __init
• Transitions: (pre-variables and post-variables)

  f337_0_createList_Load	1	f716_0_createList_Load:		x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x7 = _arg7 ∧ x8 = _arg8 ∧ x9 = _arg9 ∧ x10 = _arg10 ∧ x11 = _arg11 ∧ x12 = _arg12 ∧ x13 = _arg13 ∧ x14 = _arg14 ∧ x15 = _arg15 ∧ x16 = _arg16 ∧ x17 = _arg17 ∧ x18 = _arg18 ∧ x19 = _arg19 ∧ x20 = _arg20 ∧ x21 = _arg21 ∧ x22 = _arg22 ∧ x23 = _arg23 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ x7 = _arg7P ∧ x8 = _arg8P ∧ x9 = _arg9P ∧ x10 = _arg10P ∧ x11 = _arg11P ∧ x12 = _arg12P ∧ x13 = _arg13P ∧ x14 = _arg14P ∧ x15 = _arg15P ∧ x16 = _arg16P ∧ x17 = _arg17P ∧ x18 = _arg18P ∧ x19 = _arg19P ∧ x20 = _arg20P ∧ x21 = _arg21P ∧ x22 = _arg22P ∧ x23 = _arg23P ∧ _arg7 = _arg21P ∧ _arg6 = _arg20P ∧ _arg5 = _arg19P ∧ _arg4 = _arg17P ∧ _arg3 = _arg16P ∧ _arg3 = _arg15P ∧ 0 = _arg10P ∧ 0 = _arg9P ∧ 0 = _arg8P ∧ _arg6P = _arg7P ∧ _arg4 = _arg5P ∧ 0 = _arg4P ∧ 0 = _arg3P ∧ _arg1 = _arg1P ∧ _arg6 + 5 ≤ _arg2 ∧ _arg7 + 3 ≤ _arg2 ∧ 9 ≤ _arg2P − 1 ∧ 9 ≤ _arg2 − 1 ∧ _arg2P ≤ _arg2
  f1_0_main_Load	2	f1293_0_clear_FieldAccess:		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 = _x21 ∧ x20 = _x22 ∧ x21 = _x23 ∧ x22 = _x24 ∧ x23 = _x25 ∧ x1 = _x26 ∧ x2 = _x27 ∧ x3 = _x28 ∧ x4 = _x29 ∧ x5 = _x30 ∧ x6 = _x31 ∧ x7 = _x32 ∧ x8 = _x33 ∧ x9 = _x34 ∧ x10 = _x35 ∧ x11 = _x36 ∧ x12 = _x37 ∧ x13 = _x38 ∧ x14 = _x39 ∧ x15 = _x40 ∧ x16 = _x41 ∧ x17 = _x42 ∧ x18 = _x43 ∧ x19 = _x44 ∧ x20 = _x45 ∧ x21 = _x46 ∧ x22 = _x47 ∧ x23 = _x48 ∧ −1 ≤ _x49 − 1 ∧ 0 ≤ _x1 − 1 ∧ −1 ≤ _x50 − 1 ∧ _x26 ≤ _x50 − 1 ∧ −1 ≤ _x51 − 1 ∧ _x27 ≤ _x51 − 1 ∧ 0 ≤ _x − 1
  f349_0_createList_Return	3	f1293_0_clear_FieldAccess:		x1 = _x52 ∧ x2 = _x53 ∧ x3 = _x54 ∧ x4 = _x55 ∧ x5 = _x56 ∧ x6 = _x57 ∧ x7 = _x58 ∧ x8 = _x59 ∧ x9 = _x60 ∧ x10 = _x61 ∧ x11 = _x62 ∧ x12 = _x63 ∧ x13 = _x65 ∧ x14 = _x66 ∧ x15 = _x67 ∧ x16 = _x68 ∧ x17 = _x69 ∧ x18 = _x70 ∧ x19 = _x71 ∧ x20 = _x72 ∧ x21 = _x73 ∧ x22 = _x74 ∧ x23 = _x75 ∧ 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 ∧ x20 = _x95 ∧ x21 = _x96 ∧ x22 = _x97 ∧ x23 = _x98 ∧ −1 ≤ _x53 − 1 ∧ _x77 ≤ _x53 − 1 ∧ −1 ≤ _x52 − 1 ∧ _x76 ≤ _x52 − 1
  f1293_0_clear_FieldAccess	4	f1543_0_clear_EQ:		x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x103 ∧ x4 = _x104 ∧ x5 = _x105 ∧ x6 = _x106 ∧ x7 = _x107 ∧ x8 = _x108 ∧ x9 = _x109 ∧ x10 = _x110 ∧ x11 = _x111 ∧ x12 = _x112 ∧ x13 = _x113 ∧ x14 = _x114 ∧ x15 = _x115 ∧ x16 = _x116 ∧ x17 = _x117 ∧ x18 = _x118 ∧ x19 = _x119 ∧ x20 = _x120 ∧ x21 = _x121 ∧ x22 = _x122 ∧ x23 = _x123 ∧ x1 = _x124 ∧ x2 = _x125 ∧ x3 = _x126 ∧ x4 = _x127 ∧ x5 = _x128 ∧ x6 = _x129 ∧ x7 = _x130 ∧ x8 = _x131 ∧ x9 = _x132 ∧ x10 = _x134 ∧ x11 = _x135 ∧ x12 = _x136 ∧ x13 = _x137 ∧ x14 = _x138 ∧ x15 = _x139 ∧ x16 = _x140 ∧ x17 = _x141 ∧ x18 = _x142 ∧ x19 = _x143 ∧ x20 = _x144 ∧ x21 = _x145 ∧ x22 = _x146 ∧ x23 = _x147 ∧ _x99 = _x126 ∧ 0 = _x125 ∧ 0 = _x124 ∧ 0 ≤ _x100 − 1 ∧ 0 ≤ _x99 − 1
  f1293_0_clear_FieldAccess	5	f1543_0_clear_EQ:		x1 = _x148 ∧ x2 = _x149 ∧ x3 = _x150 ∧ x4 = _x151 ∧ x5 = _x152 ∧ x6 = _x153 ∧ x7 = _x154 ∧ x8 = _x155 ∧ x9 = _x156 ∧ x10 = _x157 ∧ x11 = _x158 ∧ x12 = _x159 ∧ x13 = _x160 ∧ x14 = _x161 ∧ x15 = _x162 ∧ x16 = _x163 ∧ x17 = _x164 ∧ x18 = _x165 ∧ x19 = _x166 ∧ x20 = _x167 ∧ x21 = _x168 ∧ x22 = _x169 ∧ x23 = _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 ∧ x20 = _x190 ∧ x21 = _x191 ∧ x22 = _x192 ∧ x23 = _x193 ∧ _x148 = _x173 ∧ 1 = _x171 ∧ 0 ≤ _x148 − 1
  f1543_0_clear_EQ	6	f1543_0_clear_EQ:		x1 = _x194 ∧ x2 = _x195 ∧ x3 = _x196 ∧ x4 = _x197 ∧ x5 = _x198 ∧ x6 = _x199 ∧ x7 = _x200 ∧ x8 = _x201 ∧ x9 = _x202 ∧ x10 = _x203 ∧ x11 = _x204 ∧ x12 = _x205 ∧ x13 = _x206 ∧ x14 = _x207 ∧ x15 = _x208 ∧ x16 = _x209 ∧ x17 = _x210 ∧ x18 = _x211 ∧ x19 = _x212 ∧ x20 = _x213 ∧ x21 = _x214 ∧ x22 = _x215 ∧ x23 = _x216 ∧ x1 = _x217 ∧ x2 = _x218 ∧ x3 = _x219 ∧ x4 = _x220 ∧ x5 = _x221 ∧ x6 = _x222 ∧ x7 = _x223 ∧ x8 = _x224 ∧ x9 = _x225 ∧ x10 = _x226 ∧ x11 = _x227 ∧ x12 = _x228 ∧ x13 = _x229 ∧ x14 = _x230 ∧ x15 = _x231 ∧ x16 = _x232 ∧ x17 = _x233 ∧ x18 = _x234 ∧ x19 = _x235 ∧ x20 = _x236 ∧ x21 = _x237 ∧ x22 = _x238 ∧ x23 = _x239 ∧ _x195 = _x218 ∧ _x194 = _x217 ∧ _x219 ≤ _x196 − 1 ∧ 0 ≤ _x194 − 1 ∧ 0 ≤ _x196 − 1 ∧ 0 ≤ _x195 − 1
  f1_0_main_Load	7	f337_0_createList_Load:		x1 = _x240 ∧ x2 = _x241 ∧ x3 = _x242 ∧ x4 = _x243 ∧ x5 = _x244 ∧ x6 = _x245 ∧ x7 = _x246 ∧ x8 = _x247 ∧ x9 = _x248 ∧ x10 = _x249 ∧ x11 = _x250 ∧ x12 = _x251 ∧ x13 = _x252 ∧ x14 = _x253 ∧ x15 = _x254 ∧ x16 = _x255 ∧ x17 = _x256 ∧ x18 = _x257 ∧ x19 = _x258 ∧ x20 = _x259 ∧ x21 = _x260 ∧ x22 = _x261 ∧ x23 = _x262 ∧ x1 = _x263 ∧ x2 = _x264 ∧ x3 = _x265 ∧ x4 = _x266 ∧ x5 = _x267 ∧ x6 = _x268 ∧ x7 = _x269 ∧ x8 = _x270 ∧ x9 = _x271 ∧ x10 = _x272 ∧ x11 = _x273 ∧ x12 = _x274 ∧ x13 = _x275 ∧ x14 = _x276 ∧ x15 = _x277 ∧ x16 = _x278 ∧ x17 = _x279 ∧ x18 = _x280 ∧ x19 = _x281 ∧ x20 = _x282 ∧ x21 = _x283 ∧ x22 = _x284 ∧ x23 = _x285 ∧ 0 = _x269 ∧ 0 = _x268 ∧ 1 = _x267 ∧ 7 ≤ _x264 − 1 ∧ 0 ≤ _x240 − 1 ∧ _x264 − 7 ≤ _x240 ∧ 0 ≤ _x241 − 1 ∧ −1 ≤ _x263 − 1
  f716_0_createList_Load	8	f1264_0_createList_LE:		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 ∧ x23 = _x308 ∧ x1 = _x309 ∧ x2 = _x310 ∧ x3 = _x311 ∧ x4 = _x312 ∧ x5 = _x313 ∧ x6 = _x314 ∧ x7 = _x315 ∧ x8 = _x316 ∧ x9 = _x317 ∧ x10 = _x318 ∧ x11 = _x319 ∧ x12 = _x320 ∧ x13 = _x321 ∧ x14 = _x322 ∧ x15 = _x323 ∧ x16 = _x324 ∧ x17 = _x325 ∧ x18 = _x326 ∧ x19 = _x327 ∧ x20 = _x328 ∧ x21 = _x329 ∧ x22 = _x330 ∧ x23 = _x331 ∧ _x306 = _x331 ∧ _x305 = _x330 ∧ _x304 = _x328 ∧ _x302 = _x327 ∧ _x301 = _x326 ∧ _x300 = _x325 ∧ _x295 = _x324 ∧ _x294 = _x323 ∧ _x293 = _x322 ∧ _x289 = _x321 ∧ 0 = _x320 ∧ _x290 = _x319 ∧ _x299 = _x318 ∧ _x288 = _x317 ∧ _x291 = _x315 ∧ _x297 = _x314 ∧ _x292 = _x313 ∧ _x296 = _x312 ∧ _x298 = _x311 ∧ _x286 = _x310 ∧ _x305 + 5 ≤ _x287 ∧ _x306 + 3 ≤ _x287 ∧ 11 ≤ _x309 − 1 ∧ 11 ≤ _x287 − 1
  f1264_0_createList_LE	9	f1264_0_createList_LE:		x1 = _x332 ∧ x2 = _x333 ∧ x3 = _x334 ∧ x4 = _x335 ∧ x5 = _x336 ∧ x6 = _x337 ∧ x7 = _x338 ∧ x8 = _x339 ∧ x9 = _x340 ∧ x10 = _x341 ∧ x11 = _x342 ∧ x12 = _x343 ∧ x13 = _x344 ∧ x14 = _x345 ∧ x15 = _x346 ∧ x16 = _x347 ∧ x17 = _x348 ∧ x18 = _x349 ∧ x19 = _x350 ∧ x20 = _x351 ∧ x21 = _x352 ∧ x22 = _x353 ∧ x23 = _x354 ∧ x1 = _x355 ∧ x2 = _x356 ∧ x3 = _x357 ∧ x4 = _x358 ∧ x5 = _x359 ∧ x6 = _x360 ∧ x7 = _x361 ∧ x8 = _x362 ∧ x9 = _x363 ∧ x10 = _x364 ∧ x11 = _x365 ∧ x12 = _x366 ∧ x13 = _x367 ∧ x14 = _x368 ∧ x15 = _x369 ∧ x16 = _x370 ∧ x17 = _x371 ∧ x18 = _x372 ∧ x19 = _x373 ∧ x20 = _x374 ∧ x21 = _x375 ∧ x22 = _x376 ∧ x23 = _x377 ∧ 0 ≤ _x333 − 1 ∧ −1 ≤ _x378 − 1 ∧ 0 ≤ _x337 − 1 ∧ 0 ≤ _x334 − 1 ∧ −1 ≤ _x351 − 1 ∧ _x351 ≤ _x378 − 1 ∧ 0 ≤ _x341 − 1 ∧ 0 ≤ _x335 − 1 ∧ 0 ≤ _x344 − 1 ∧ 0 ≤ _x342 − 1 ∧ 0 ≤ _x343 − 1 ∧ −1 ≤ _x379 − 1 ∧ 0 ≤ _x340 − 1 ∧ 0 ≤ _x336 − 1 ∧ 0 ≤ _x349 − 1 ∧ 0 ≤ _x345 − 1 ∧ 0 ≤ _x350 − 1 ∧ 0 ≤ _x348 − 1 ∧ 0 ≤ _x346 − 1 ∧ 0 ≤ _x347 − 1 ∧ −1 ≤ _x354 − 1 ∧ −1 ≤ _x353 − 1 ∧ 9 ≤ _x332 − 1 ∧ 9 ≤ _x355 − 1 ∧ _x352 + 9 ≤ _x332 ∧ _x354 + 3 ≤ _x332 ∧ _x353 + 5 ≤ _x332 ∧ _x333 − 1 = _x356 ∧ _x334 = _x357 ∧ _x337 = _x360 ∧ _x338 = _x361 ∧ _x339 = _x362 ∧ _x341 = _x364 ∧ _x343 = _x366 ∧ _x351 + 1 = _x374 ∧ _x353 + 1 = _x376 ∧ _x354 + 1 = _x377
  f1264_0_createList_LE	10	f1264_0_createList_LE:		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 ∧ x20 = _x399 ∧ x21 = _x400 ∧ x22 = _x401 ∧ x23 = _x402 ∧ x1 = _x403 ∧ x2 = _x404 ∧ x3 = _x405 ∧ x4 = _x406 ∧ x5 = _x407 ∧ x6 = _x408 ∧ x7 = _x409 ∧ x8 = _x410 ∧ x9 = _x411 ∧ x10 = _x412 ∧ x11 = _x413 ∧ x12 = _x414 ∧ x13 = _x415 ∧ x14 = _x416 ∧ x15 = _x417 ∧ x16 = _x418 ∧ x17 = _x419 ∧ x18 = _x420 ∧ x19 = _x421 ∧ x20 = _x422 ∧ x21 = _x423 ∧ x22 = _x424 ∧ x23 = _x425 ∧ 0 ≤ _x381 − 1 ∧ −1 ≤ _x426 − 1 ∧ 0 ≤ _x385 − 1 ∧ 0 ≤ _x382 − 1 ∧ −1 ≤ _x399 − 1 ∧ _x399 ≤ _x426 − 1 ∧ 0 ≤ _x389 − 1 ∧ 0 ≤ _x391 − 1 ∧ −1 ≤ _x427 − 1 ∧ 0 ≤ _x397 − 1 ∧ 0 ≤ _x398 − 1 ∧ 0 ≤ _x396 − 1 ∧ 0 ≤ _x387 − 1 ∧ −1 ≤ _x402 − 1 ∧ −1 ≤ _x401 − 1 ∧ 11 ≤ _x380 − 1 ∧ 13 ≤ _x403 − 1 ∧ _x400 + 9 ≤ _x380 ∧ _x402 + 3 ≤ _x380 ∧ _x401 + 5 ≤ _x380 ∧ _x387 = _x388 ∧ _x389 = _x390 ∧ _x391 = _x392 ∧ _x386 = _x395 ∧ _x381 − 1 = _x404 ∧ 0 = _x405 ∧ 1 = _x406 ∧ 1 = _x407 ∧ _x387 = _x410 ∧ _x389 = _x412 ∧ _x391 = _x414 ∧ 0 = _x415 ∧ 2 = _x416 ∧ _x399 + 1 = _x422 ∧ _x401 + 1 = _x424 ∧ _x402 + 1 = _x425
  __init	11	f1_0_main_Load:		x1 = _x428 ∧ x2 = _x429 ∧ x3 = _x430 ∧ x4 = _x431 ∧ x5 = _x432 ∧ x6 = _x433 ∧ x7 = _x434 ∧ x8 = _x435 ∧ x9 = _x436 ∧ x10 = _x437 ∧ x11 = _x438 ∧ x12 = _x439 ∧ x13 = _x440 ∧ x14 = _x441 ∧ x15 = _x442 ∧ x16 = _x443 ∧ x17 = _x444 ∧ x18 = _x445 ∧ x19 = _x446 ∧ x20 = _x447 ∧ x21 = _x448 ∧ x22 = _x449 ∧ x23 = _x450 ∧ x1 = _x451 ∧ x2 = _x452 ∧ x3 = _x453 ∧ x4 = _x454 ∧ x5 = _x455 ∧ x6 = _x456 ∧ x7 = _x457 ∧ x8 = _x458 ∧ x9 = _x459 ∧ x10 = _x460 ∧ x11 = _x461 ∧ x12 = _x462 ∧ x13 = _x463 ∧ x14 = _x464 ∧ x15 = _x465 ∧ x16 = _x466 ∧ x17 = _x467 ∧ x18 = _x468 ∧ x19 = _x469 ∧ x20 = _x470 ∧ x21 = _x471 ∧ x22 = _x472 ∧ x23 = _x473 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

2 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

2.1 SCC Subproblem 1/2

Here we consider the SCC { f1543_0_clear_EQ }.

2.1.1 Transition Removal

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

2.1.2 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.2 SCC Subproblem 2/2

Here we consider the SCC { f1264_0_createList_LE }.

2.2.1 Transition Removal

We remove transitions 9, 10 using the following ranking functions, which are bounded by 0.

2.2.2 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 % (7 real / 0 unknown / 0 assumptions / 7 total proof steps)