# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: f4644_0_put_NULL, f4725_0_put_EQ, f3994_0_random_ArrayAccess, f3916_0_createMap_LE, f606_0_createMap_Return, f1_0_main_Load, f5171_0_transfer_GE, f4480_0_getEntry_NULL, __init, f4575_0_getEntry_EQ, f5266_0_transfer_ArrayAccess
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f3994_0_random_ArrayAccess: 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 ∧ 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 ∧ −1 ≤ _x7 − 1 ∧ 0 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1 ∧ 3 ≤ _arg1P − 1 ∧ _arg2 = _arg2P f606_0_createMap_Return 2 f3994_0_random_ArrayAccess: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x8 ∧ x9 = _x9 ∧ x10 = _x10 ∧ x11 = _x11 ∧ x12 = _x12 ∧ x13 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ x3 = _x16 ∧ x4 = _x17 ∧ x5 = _x18 ∧ x6 = _x19 ∧ x7 = _x20 ∧ x8 = _x21 ∧ x9 = _x22 ∧ x10 = _x23 ∧ x11 = _x24 ∧ x12 = _x25 ∧ x13 = _x26 ∧ 12 = _x18 ∧ _x4 = _x17 ∧ 16 = _x16 ∧ 12 = _x5 ∧ 16 = _x3 ∧ _x4 + 3 ≤ _x1 ∧ 14 ≤ _x14 − 1 ∧ 14 ≤ _x1 − 1 ∧ 0 ≤ _x − 1 ∧ _x14 ≤ _x1 f1_0_main_Load 3 f3916_0_createMap_LE: x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x31 ∧ x4 = _x33 ∧ x5 = _x34 ∧ x6 = _x35 ∧ x7 = _x36 ∧ x8 = _x37 ∧ x9 = _x38 ∧ x10 = _x41 ∧ x11 = _x42 ∧ x12 = _x43 ∧ x13 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ x4 = _x48 ∧ x5 = _x49 ∧ x6 = _x50 ∧ x7 = _x51 ∧ x8 = _x52 ∧ x9 = _x53 ∧ x10 = _x54 ∧ x11 = _x55 ∧ x12 = _x56 ∧ x13 = _x57 ∧ 12 = _x51 ∧ 0 = _x50 ∧ 16 = _x49 ∧ 1 = _x48 ∧ _x28 = _x47 ∧ 14 ≤ _x45 − 1 ∧ 0 ≤ _x27 − 1 ∧ _x45 − 14 ≤ _x27 ∧ 0 ≤ _x28 − 1 ∧ −1 ≤ _x46 − 1 f3916_0_createMap_LE 4 f3916_0_createMap_LE: x1 = _x58 ∧ x2 = _x59 ∧ x3 = _x61 ∧ x4 = _x62 ∧ x5 = _x63 ∧ x6 = _x65 ∧ x7 = _x66 ∧ x8 = _x67 ∧ x9 = _x68 ∧ x10 = _x69 ∧ x11 = _x70 ∧ x12 = _x71 ∧ x13 = _x72 ∧ x1 = _x73 ∧ x2 = _x74 ∧ x3 = _x75 ∧ x4 = _x76 ∧ x5 = _x77 ∧ x6 = _x78 ∧ x7 = _x79 ∧ x8 = _x80 ∧ x9 = _x81 ∧ x10 = _x82 ∧ x11 = _x83 ∧ x12 = _x84 ∧ x13 = _x85 ∧ 0 ≤ _x59 − 1 ∧ _x62 + 1 ≤ _x61 − 1 ∧ −1 ≤ _x61 − 1 ∧ −1 ≤ _x62 − 1 ∧ −1 ≤ _x86 − 1 ∧ −1 ≤ _x87 − 1 ∧ 1 ≤ _x63 − 1 ∧ 3 ≤ _x58 − 1 ∧ 3 ≤ _x73 − 1 ∧ _x66 + 3 ≤ _x58 ∧ _x65 + 3 ≤ _x58 ∧ _x59 − 1 = _x74 ∧ _x61 = _x75 ∧ _x62 + 2 = _x76 f3994_0_random_ArrayAccess 5 f4480_0_getEntry_NULL: x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x92 ∧ x4 = _x93 ∧ x5 = _x94 ∧ x6 = _x95 ∧ x7 = _x96 ∧ x8 = _x97 ∧ x9 = _x98 ∧ x10 = _x99 ∧ x11 = _x100 ∧ x12 = _x101 ∧ x13 = _x102 ∧ x1 = _x103 ∧ x2 = _x104 ∧ x3 = _x105 ∧ x4 = _x106 ∧ x5 = _x107 ∧ x6 = _x108 ∧ x7 = _x109 ∧ x8 = _x110 ∧ x9 = _x111 ∧ x10 = _x112 ∧ x11 = _x113 ∧ x12 = _x114 ∧ x13 = _x115 ∧ _x116 ≤ _x89 − 1 ∧ 1 ≤ _x92 − 1 ∧ −1 ≤ _x116 − 1 ∧ −1 ≤ _x117 − 1 ∧ 0 ≤ _x89 − 1 ∧ _x118 ≤ _x92 − 1 ∧ 3 ≤ _x88 − 1 ∧ −1 ≤ _x104 − 1 ∧ _x94 + 3 ≤ _x88 ∧ _x93 + 3 ≤ _x88 f4480_0_getEntry_NULL 6 f1738_0_equals_CheckCast: x1 = _x119 ∧ x2 = _x120 ∧ x3 = _x121 ∧ x4 = _x122 ∧ x5 = _x123 ∧ x6 = _x124 ∧ x7 = _x125 ∧ x8 = _x126 ∧ x9 = _x127 ∧ x10 = _x128 ∧ x11 = _x129 ∧ x12 = _x130 ∧ x13 = _x131 ∧ x1 = _x132 ∧ x2 = _x133 ∧ x3 = _x134 ∧ x4 = _x135 ∧ x5 = _x136 ∧ x6 = _x137 ∧ x7 = _x139 ∧ x8 = _x140 ∧ x9 = _x141 ∧ x10 = _x142 ∧ x11 = _x143 ∧ x12 = _x144 ∧ x13 = _x145 ∧ _x119 + 2 ≤ _x120 ∧ _x134 + 2 ≤ _x120 ∧ 0 ≤ _x133 − 1 ∧ 0 ≤ _x120 − 1 f4480_0_getEntry_NULL 7 f4575_0_getEntry_EQ: x1 = _x146 ∧ x2 = _x147 ∧ x3 = _x148 ∧ x4 = _x149 ∧ x5 = _x150 ∧ x6 = _x151 ∧ x7 = _x152 ∧ x8 = _x153 ∧ x9 = _x154 ∧ x10 = _x155 ∧ x11 = _x156 ∧ x12 = _x157 ∧ x13 = _x158 ∧ x1 = _x159 ∧ x2 = _x160 ∧ x3 = _x161 ∧ x4 = _x162 ∧ x5 = _x163 ∧ x6 = _x164 ∧ x7 = _x165 ∧ x8 = _x166 ∧ x9 = _x167 ∧ x10 = _x168 ∧ x11 = _x169 ∧ x12 = _x170 ∧ x13 = _x171 ∧ _x146 = _x162 ∧ 0 = _x160 ∧ _x164 + 4 ≤ _x147 ∧ _x146 + 2 ≤ _x147 ∧ −1 ≤ _x163 − 1 ∧ 2 ≤ _x159 − 1 ∧ 2 ≤ _x147 − 1 ∧ _x163 + 2 ≤ _x147 ∧ _x159 ≤ _x147 f4480_0_getEntry_NULL 8 f4575_0_getEntry_EQ: x1 = _x172 ∧ x2 = _x173 ∧ x3 = _x174 ∧ x4 = _x175 ∧ x5 = _x176 ∧ x6 = _x177 ∧ x7 = _x178 ∧ x8 = _x179 ∧ x9 = _x180 ∧ x10 = _x181 ∧ x11 = _x182 ∧ x12 = _x183 ∧ x13 = _x184 ∧ x1 = _x185 ∧ x2 = _x186 ∧ x3 = _x187 ∧ x4 = _x188 ∧ x5 = _x189 ∧ x6 = _x190 ∧ x7 = _x191 ∧ x8 = _x192 ∧ x9 = _x193 ∧ x10 = _x194 ∧ x11 = _x195 ∧ x12 = _x196 ∧ x13 = _x197 ∧ _x172 = _x188 ∧ 1 = _x186 ∧ _x190 + 4 ≤ _x173 ∧ _x172 + 2 ≤ _x173 ∧ −1 ≤ _x189 − 1 ∧ 2 ≤ _x185 − 1 ∧ 2 ≤ _x173 − 1 ∧ _x189 + 2 ≤ _x173 ∧ _x185 ≤ _x173 f4480_0_getEntry_NULL 9 f4480_0_getEntry_NULL: 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 ∧ 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 ∧ _x212 + 1 ≤ _x199 ∧ _x224 ≤ _x198 − 1 ∧ 0 ≤ _x199 − 1 ∧ −1 ≤ _x212 − 1 ∧ _x198 = _x211 f4480_0_getEntry_NULL 10 f4480_0_getEntry_NULL: x1 = _x225 ∧ x2 = _x226 ∧ x3 = _x227 ∧ x4 = _x228 ∧ x5 = _x229 ∧ x6 = _x230 ∧ x7 = _x231 ∧ x8 = _x232 ∧ x9 = _x233 ∧ x10 = _x234 ∧ x11 = _x235 ∧ x12 = _x236 ∧ x13 = _x237 ∧ x1 = _x238 ∧ x2 = _x239 ∧ x3 = _x240 ∧ x4 = _x241 ∧ x5 = _x242 ∧ x6 = _x243 ∧ x7 = _x244 ∧ x8 = _x245 ∧ x9 = _x246 ∧ x10 = _x247 ∧ x11 = _x248 ∧ x12 = _x249 ∧ x13 = _x250 ∧ _x239 + 1 ≤ _x226 ∧ _x225 ≤ _x251 − 1 ∧ 0 ≤ _x226 − 1 ∧ −1 ≤ _x239 − 1 ∧ _x225 = _x238 f4480_0_getEntry_NULL 11 f4480_0_getEntry_NULL: 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 = _x265 ∧ 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 ∧ _x252 = _x266 ∧ _x252 + 2 ≤ _x253 ∧ −1 ≤ _x267 − 1 ∧ 1 ≤ _x253 − 1 ∧ _x267 + 2 ≤ _x253 f4480_0_getEntry_NULL 12 f4480_0_getEntry_NULL: x1 = _x279 ∧ x2 = _x280 ∧ x3 = _x281 ∧ x4 = _x282 ∧ x5 = _x283 ∧ x6 = _x284 ∧ x7 = _x285 ∧ x8 = _x286 ∧ x9 = _x287 ∧ x10 = _x288 ∧ x11 = _x289 ∧ x12 = _x290 ∧ x13 = _x291 ∧ x1 = _x292 ∧ x2 = _x293 ∧ x3 = _x294 ∧ x4 = _x295 ∧ x5 = _x296 ∧ x6 = _x297 ∧ x7 = _x298 ∧ x8 = _x299 ∧ x9 = _x300 ∧ x10 = _x301 ∧ x11 = _x302 ∧ x12 = _x303 ∧ x13 = _x304 ∧ _x279 = _x292 ∧ _x279 + 2 ≤ _x280 ∧ −1 ≤ _x293 − 1 ∧ 2 ≤ _x280 − 1 ∧ _x293 + 2 ≤ _x280 f4575_0_getEntry_EQ 13 f4480_0_getEntry_NULL: x1 = _x305 ∧ x2 = _x306 ∧ x3 = _x307 ∧ x4 = _x308 ∧ x5 = _x309 ∧ x6 = _x310 ∧ x7 = _x311 ∧ x8 = _x312 ∧ x9 = _x313 ∧ x10 = _x314 ∧ x11 = _x315 ∧ x12 = _x316 ∧ x13 = _x317 ∧ x1 = _x318 ∧ x2 = _x319 ∧ x3 = _x320 ∧ x4 = _x321 ∧ x5 = _x322 ∧ x6 = _x323 ∧ x7 = _x324 ∧ x8 = _x325 ∧ x9 = _x326 ∧ x10 = _x327 ∧ x11 = _x328 ∧ x12 = _x329 ∧ x13 = _x330 ∧ _x308 = _x318 ∧ 0 = _x306 ∧ _x310 + 4 ≤ _x305 ∧ _x308 + 2 ≤ _x305 ∧ −1 ≤ _x319 − 1 ∧ −1 ≤ _x309 − 1 ∧ 2 ≤ _x305 − 1 ∧ _x319 ≤ _x309 ∧ _x319 + 2 ≤ _x305 f3916_0_createMap_LE 14 f4644_0_put_NULL: x1 = _x331 ∧ x2 = _x332 ∧ x3 = _x333 ∧ x4 = _x334 ∧ x5 = _x335 ∧ x6 = _x336 ∧ x7 = _x337 ∧ x8 = _x338 ∧ x9 = _x339 ∧ x10 = _x340 ∧ x11 = _x341 ∧ x12 = _x342 ∧ x13 = _x343 ∧ x1 = _x344 ∧ x2 = _x345 ∧ x3 = _x346 ∧ x4 = _x347 ∧ x5 = _x348 ∧ x6 = _x349 ∧ x7 = _x350 ∧ x8 = _x351 ∧ x9 = _x352 ∧ x10 = _x353 ∧ x11 = _x354 ∧ x12 = _x355 ∧ x13 = _x356 ∧ _x334 + 1 ≤ _x333 − 1 ∧ 1 ≤ _x335 − 1 ∧ 0 ≤ _x332 − 1 ∧ −1 ≤ _x333 − 1 ∧ −1 ≤ _x334 − 1 ∧ −1 ≤ _x357 − 1 ∧ −1 ≤ _x358 − 1 ∧ _x346 ≤ _x335 − 1 ∧ _x344 ≤ _x331 ∧ 3 ≤ _x331 − 1 ∧ 3 ≤ _x344 − 1 ∧ −1 ≤ _x347 − 1 ∧ _x337 + 3 ≤ _x331 ∧ _x336 + 3 ≤ _x331 ∧ _x334 + 2 = _x348 ∧ _x335 = _x349 ∧ _x336 = _x350 ∧ _x337 = _x351 f4644_0_put_NULL 15 f1738_0_equals_CheckCast: x1 = _x359 ∧ x2 = _x360 ∧ x3 = _x361 ∧ x4 = _x362 ∧ x5 = _x363 ∧ x6 = _x364 ∧ x7 = _x365 ∧ x8 = _x366 ∧ x9 = _x367 ∧ x10 = _x368 ∧ x11 = _x369 ∧ x12 = _x370 ∧ x13 = _x371 ∧ x1 = _x372 ∧ x2 = _x373 ∧ x3 = _x374 ∧ x4 = _x375 ∧ x5 = _x376 ∧ x6 = _x377 ∧ x7 = _x378 ∧ x8 = _x379 ∧ x9 = _x380 ∧ x10 = _x381 ∧ x11 = _x382 ∧ x12 = _x383 ∧ x13 = _x384 ∧ _x360 + 2 ≤ _x362 ∧ _x374 + 2 ≤ _x362 ∧ _x366 + 3 ≤ _x359 ∧ _x365 + 3 ≤ _x359 ∧ 0 ≤ _x373 − 1 ∧ 0 ≤ _x362 − 1 ∧ 3 ≤ _x359 − 1 ∧ 1 ≤ _x363 − 1 ∧ 1 ≤ _x364 − 1 f4644_0_put_NULL 16 f4725_0_put_EQ: x1 = _x385 ∧ x2 = _x386 ∧ x3 = _x387 ∧ x4 = _x388 ∧ x5 = _x389 ∧ x6 = _x390 ∧ x7 = _x391 ∧ x8 = _x392 ∧ x9 = _x393 ∧ x10 = _x394 ∧ x11 = _x395 ∧ x12 = _x396 ∧ x13 = _x397 ∧ x1 = _x398 ∧ x2 = _x399 ∧ x3 = _x400 ∧ x4 = _x401 ∧ x5 = _x402 ∧ x6 = _x403 ∧ x7 = _x404 ∧ x8 = _x405 ∧ x9 = _x406 ∧ x10 = _x407 ∧ x11 = _x408 ∧ x12 = _x409 ∧ x13 = _x410 ∧ _x386 = _x406 ∧ _x392 = _x405 ∧ _x391 = _x404 ∧ _x390 = _x403 ∧ _x389 = _x402 ∧ 0 = _x401 ∧ _x387 = _x399 ∧ _x408 + 4 ≤ _x388 ∧ _x386 + 2 ≤ _x388 ∧ _x392 + 3 ≤ _x385 ∧ _x391 + 3 ≤ _x385 ∧ −1 ≤ _x407 − 1 ∧ 2 ≤ _x400 − 1 ∧ 3 ≤ _x398 − 1 ∧ 2 ≤ _x388 − 1 ∧ 3 ≤ _x385 − 1 ∧ _x407 + 2 ≤ _x388 ∧ _x400 ≤ _x388 ∧ _x398 ≤ _x385 ∧ 1 ≤ _x389 − 1 ∧ 1 ≤ _x390 − 1 f4644_0_put_NULL 17 f4725_0_put_EQ: x1 = _x411 ∧ x2 = _x412 ∧ x3 = _x413 ∧ x4 = _x414 ∧ x5 = _x415 ∧ x6 = _x416 ∧ x7 = _x417 ∧ x8 = _x418 ∧ x9 = _x419 ∧ x10 = _x420 ∧ x11 = _x421 ∧ x12 = _x422 ∧ x13 = _x423 ∧ x1 = _x424 ∧ x2 = _x425 ∧ x3 = _x426 ∧ x4 = _x427 ∧ x5 = _x428 ∧ x6 = _x429 ∧ x7 = _x430 ∧ x8 = _x431 ∧ x9 = _x432 ∧ x10 = _x433 ∧ x11 = _x434 ∧ x12 = _x435 ∧ x13 = _x436 ∧ _x412 = _x432 ∧ _x418 = _x431 ∧ _x417 = _x430 ∧ _x416 = _x429 ∧ _x415 = _x428 ∧ 1 = _x427 ∧ _x413 = _x425 ∧ _x434 + 4 ≤ _x414 ∧ _x412 + 2 ≤ _x414 ∧ _x418 + 3 ≤ _x411 ∧ _x417 + 3 ≤ _x411 ∧ −1 ≤ _x433 − 1 ∧ 2 ≤ _x426 − 1 ∧ 3 ≤ _x424 − 1 ∧ 2 ≤ _x414 − 1 ∧ 3 ≤ _x411 − 1 ∧ _x433 + 2 ≤ _x414 ∧ _x426 ≤ _x414 ∧ _x424 ≤ _x411 ∧ 1 ≤ _x415 − 1 ∧ 1 ≤ _x416 − 1 f4644_0_put_NULL 18 f4644_0_put_NULL: 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 ∧ 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 ∧ _x450 ≤ _x437 ∧ _x463 ≤ _x438 − 1 ∧ _x453 + 1 ≤ _x440 ∧ 3 ≤ _x437 − 1 ∧ 0 ≤ _x440 − 1 ∧ 3 ≤ _x450 − 1 ∧ −1 ≤ _x453 − 1 ∧ _x443 + 3 ≤ _x437 ∧ _x444 + 3 ≤ _x437 ∧ _x438 = _x451 ∧ _x439 = _x452 ∧ _x441 = _x454 ∧ _x442 = _x455 ∧ _x443 = _x456 ∧ _x444 = _x457 f4644_0_put_NULL 19 f4644_0_put_NULL: x1 = _x464 ∧ x2 = _x465 ∧ x3 = _x466 ∧ x4 = _x467 ∧ x5 = _x468 ∧ x6 = _x469 ∧ x7 = _x470 ∧ x8 = _x471 ∧ x9 = _x472 ∧ x10 = _x473 ∧ x11 = _x474 ∧ x12 = _x475 ∧ x13 = _x476 ∧ x1 = _x477 ∧ x2 = _x478 ∧ x3 = _x479 ∧ x4 = _x480 ∧ x5 = _x481 ∧ x6 = _x482 ∧ x7 = _x483 ∧ x8 = _x484 ∧ x9 = _x485 ∧ x10 = _x486 ∧ x11 = _x487 ∧ x12 = _x488 ∧ x13 = _x489 ∧ _x477 ≤ _x464 ∧ _x465 ≤ _x490 − 1 ∧ _x480 + 1 ≤ _x467 ∧ 3 ≤ _x464 − 1 ∧ 0 ≤ _x467 − 1 ∧ 3 ≤ _x477 − 1 ∧ −1 ≤ _x480 − 1 ∧ _x470 + 3 ≤ _x464 ∧ _x471 + 3 ≤ _x464 ∧ _x465 = _x478 ∧ _x466 = _x479 ∧ _x468 = _x481 ∧ _x469 = _x482 ∧ _x470 = _x483 ∧ _x471 = _x484 f4644_0_put_NULL 20 f4644_0_put_NULL: x1 = _x491 ∧ x2 = _x492 ∧ x3 = _x493 ∧ x4 = _x494 ∧ x5 = _x495 ∧ x6 = _x496 ∧ x7 = _x497 ∧ x8 = _x498 ∧ x9 = _x499 ∧ x10 = _x500 ∧ x11 = _x501 ∧ x12 = _x502 ∧ x13 = _x503 ∧ 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 ∧ _x498 = _x511 ∧ _x497 = _x510 ∧ _x496 = _x509 ∧ _x495 = _x508 ∧ _x493 = _x506 ∧ _x492 = _x505 ∧ _x492 + 2 ≤ _x494 ∧ _x498 + 3 ≤ _x491 ∧ _x497 + 3 ≤ _x491 ∧ −1 ≤ _x507 − 1 ∧ 3 ≤ _x504 − 1 ∧ 1 ≤ _x494 − 1 ∧ 3 ≤ _x491 − 1 ∧ _x507 + 2 ≤ _x494 ∧ _x504 ≤ _x491 ∧ 1 ≤ _x495 − 1 ∧ 1 ≤ _x496 − 1 f4644_0_put_NULL 21 f4644_0_put_NULL: x1 = _x517 ∧ x2 = _x518 ∧ x3 = _x519 ∧ x4 = _x520 ∧ x5 = _x521 ∧ x6 = _x522 ∧ x7 = _x523 ∧ x8 = _x524 ∧ x9 = _x525 ∧ x10 = _x526 ∧ x11 = _x527 ∧ x12 = _x528 ∧ x13 = _x529 ∧ x1 = _x530 ∧ x2 = _x531 ∧ x3 = _x532 ∧ x4 = _x533 ∧ x5 = _x534 ∧ x6 = _x535 ∧ x7 = _x536 ∧ x8 = _x537 ∧ x9 = _x538 ∧ x10 = _x539 ∧ x11 = _x540 ∧ x12 = _x541 ∧ x13 = _x542 ∧ _x524 = _x537 ∧ _x523 = _x536 ∧ _x522 = _x535 ∧ _x521 = _x534 ∧ _x519 = _x532 ∧ _x518 = _x531 ∧ _x518 + 2 ≤ _x520 ∧ _x524 + 3 ≤ _x517 ∧ _x523 + 3 ≤ _x517 ∧ −1 ≤ _x533 − 1 ∧ 3 ≤ _x530 − 1 ∧ 2 ≤ _x520 − 1 ∧ 3 ≤ _x517 − 1 ∧ _x533 + 2 ≤ _x520 ∧ _x530 ≤ _x517 ∧ 1 ≤ _x521 − 1 ∧ 1 ≤ _x522 − 1 f4725_0_put_EQ 22 f4644_0_put_NULL: x1 = _x543 ∧ x2 = _x544 ∧ x3 = _x545 ∧ x4 = _x546 ∧ x5 = _x547 ∧ x6 = _x548 ∧ x7 = _x549 ∧ x8 = _x550 ∧ x9 = _x551 ∧ x10 = _x552 ∧ x11 = _x553 ∧ x12 = _x554 ∧ x13 = _x555 ∧ x1 = _x556 ∧ x2 = _x557 ∧ x3 = _x558 ∧ x4 = _x559 ∧ x5 = _x560 ∧ x6 = _x561 ∧ x7 = _x562 ∧ x8 = _x563 ∧ x9 = _x564 ∧ x10 = _x565 ∧ x11 = _x566 ∧ x12 = _x567 ∧ x13 = _x568 ∧ _x550 = _x563 ∧ _x549 = _x562 ∧ _x548 = _x561 ∧ _x547 = _x560 ∧ _x544 = _x558 ∧ _x551 = _x557 ∧ 0 = _x546 ∧ _x553 + 4 ≤ _x545 ∧ _x551 + 2 ≤ _x545 ∧ _x550 + 3 ≤ _x543 ∧ _x549 + 3 ≤ _x543 ∧ −1 ≤ _x559 − 1 ∧ 3 ≤ _x556 − 1 ∧ −1 ≤ _x552 − 1 ∧ 2 ≤ _x545 − 1 ∧ 3 ≤ _x543 − 1 ∧ _x559 ≤ _x552 ∧ _x559 + 2 ≤ _x545 ∧ _x556 ≤ _x543 f4644_0_put_NULL 23 f5171_0_transfer_GE: x1 = _x569 ∧ x2 = _x570 ∧ x3 = _x571 ∧ x4 = _x572 ∧ x5 = _x573 ∧ x6 = _x574 ∧ x7 = _x575 ∧ x8 = _x576 ∧ x9 = _x577 ∧ x10 = _x578 ∧ x11 = _x579 ∧ x12 = _x580 ∧ x13 = _x581 ∧ x1 = _x582 ∧ x2 = _x583 ∧ x3 = _x584 ∧ x4 = _x585 ∧ x5 = _x586 ∧ x6 = _x587 ∧ x7 = _x588 ∧ x8 = _x589 ∧ x9 = _x590 ∧ x10 = _x591 ∧ x11 = _x592 ∧ x12 = _x593 ∧ x13 = _x594 ∧ _x574 = _x589 ∧ 2⋅_x574 = _x588 ∧ _x576 = _x587 ∧ _x575 + 1 = _x586 ∧ 0 = _x585 ∧ _x576 + 3 ≤ _x569 ∧ _x575 + 3 ≤ _x569 ∧ 0 ≤ _x584 − 1 ∧ 0 ≤ _x583 − 1 ∧ 3 ≤ _x582 − 1 ∧ −1 ≤ _x572 − 1 ∧ 3 ≤ _x569 − 1 ∧ _x584 − 1 ≤ _x572 ∧ _x584 + 3 ≤ _x569 ∧ _x583 − 1 ≤ _x572 ∧ _x583 + 3 ≤ _x569 ∧ _x582 − 1 ≤ _x569 ∧ _x574 ≤ 1073741823 ∧ 0 ≤ 2⋅_x574 ∧ _x576 ≤ _x575 ∧ 1 ≤ _x574 − 1 ∧ _x571 ≤ _x574 − 1 f4644_0_put_NULL 24 f5171_0_transfer_GE: x1 = _x595 ∧ x2 = _x596 ∧ x3 = _x597 ∧ x4 = _x598 ∧ x5 = _x599 ∧ x6 = _x600 ∧ x7 = _x601 ∧ x8 = _x602 ∧ x9 = _x603 ∧ x10 = _x604 ∧ x11 = _x605 ∧ x12 = _x606 ∧ x13 = _x607 ∧ 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 ∧ _x600 = _x615 ∧ 2⋅_x600 = _x614 ∧ _x602 = _x613 ∧ _x601 + 1 = _x612 ∧ 0 = _x611 ∧ _x602 + 3 ≤ _x595 ∧ _x601 + 3 ≤ _x595 ∧ 0 ≤ _x610 − 1 ∧ 0 ≤ _x609 − 1 ∧ 3 ≤ _x608 − 1 ∧ −1 ≤ _x598 − 1 ∧ 3 ≤ _x595 − 1 ∧ _x610 − 1 ≤ _x598 ∧ _x610 + 3 ≤ _x595 ∧ _x609 − 1 ≤ _x598 ∧ _x609 + 3 ≤ _x595 ∧ _x608 − 1 ≤ _x595 ∧ _x602 ≤ _x601 ∧ 0 ≤ 2⋅_x600 ∧ 1073741824 ≤ _x600 − 1 ∧ _x597 ≤ _x600 − 1 f5171_0_transfer_GE 25 f5266_0_transfer_ArrayAccess: x1 = _x621 ∧ x2 = _x622 ∧ x3 = _x623 ∧ x4 = _x624 ∧ x5 = _x625 ∧ x6 = _x626 ∧ x7 = _x627 ∧ x8 = _x628 ∧ x9 = _x629 ∧ x10 = _x630 ∧ x11 = _x631 ∧ x12 = _x632 ∧ x13 = _x633 ∧ x1 = _x634 ∧ x2 = _x635 ∧ x3 = _x636 ∧ x4 = _x637 ∧ x5 = _x638 ∧ x6 = _x639 ∧ x7 = _x640 ∧ x8 = _x641 ∧ x9 = _x642 ∧ x10 = _x643 ∧ x11 = _x644 ∧ x12 = _x645 ∧ x13 = _x646 ∧ _x627 = _x646 ∧ _x628 = _x643 ∧ _x626 = _x642 ∧ _x625 = _x641 ∧ _x624 = _x636 ∧ _x626 + 3 ≤ _x621 ∧ _x625 + 3 ≤ _x621 ∧ 0 ≤ _x639 − 1 ∧ 0 ≤ _x638 − 1 ∧ −1 ≤ _x637 − 1 ∧ 0 ≤ _x635 − 1 ∧ 3 ≤ _x634 − 1 ∧ 0 ≤ _x623 − 1 ∧ 0 ≤ _x622 − 1 ∧ 3 ≤ _x621 − 1 ∧ _x639 ≤ _x623 ∧ _x639 ≤ _x622 ∧ _x639 + 3 ≤ _x621 ∧ _x635 ≤ _x623 ∧ _x635 ≤ _x622 ∧ _x635 + 3 ≤ _x621 ∧ _x634 ≤ _x621 ∧ _x624 ≤ _x628 − 1 ∧ 0 ≤ _x627 − 1 f5266_0_transfer_ArrayAccess 26 f5266_0_transfer_ArrayAccess: x1 = _x647 ∧ x2 = _x648 ∧ x3 = _x649 ∧ x4 = _x650 ∧ x5 = _x651 ∧ x6 = _x652 ∧ x7 = _x653 ∧ x8 = _x654 ∧ x9 = _x655 ∧ x10 = _x656 ∧ x11 = _x657 ∧ x12 = _x658 ∧ x13 = _x659 ∧ x1 = _x660 ∧ x2 = _x661 ∧ x3 = _x662 ∧ x4 = _x663 ∧ x5 = _x664 ∧ x6 = _x665 ∧ x7 = _x666 ∧ x8 = _x667 ∧ x9 = _x668 ∧ x10 = _x669 ∧ x11 = _x670 ∧ x12 = _x671 ∧ x13 = _x672 ∧ _x659 = _x672 ∧ _x656 = _x669 ∧ _x655 = _x668 ∧ _x654 = _x667 ∧ _x649 = _x662 ∧ _x658 + 2 ≤ _x651 ∧ _x671 + 4 ≤ _x651 ∧ _x670 + 4 ≤ _x651 ∧ _x657 + 2 ≤ _x651 ∧ _x671 + 2 ≤ _x650 ∧ _x670 + 2 ≤ _x650 ∧ _x655 + 3 ≤ _x647 ∧ _x654 + 3 ≤ _x647 ∧ 0 ≤ _x665 − 1 ∧ 0 ≤ _x664 − 1 ∧ −1 ≤ _x663 − 1 ∧ 0 ≤ _x661 − 1 ∧ 3 ≤ _x660 − 1 ∧ 0 ≤ _x652 − 1 ∧ 2 ≤ _x651 − 1 ∧ 0 ≤ _x650 − 1 ∧ 0 ≤ _x648 − 1 ∧ 3 ≤ _x647 − 1 ∧ _x665 ≤ _x652 ∧ _x665 + 2 ≤ _x651 ∧ _x665 ≤ _x650 ∧ _x665 ≤ _x648 ∧ _x665 + 3 ≤ _x647 ∧ _x664 + 2 ≤ _x651 ∧ _x664 ≤ _x650 ∧ _x663 + 3 ≤ _x651 ∧ _x663 + 1 ≤ _x650 ∧ _x661 ≤ _x652 ∧ _x661 + 2 ≤ _x651 ∧ _x661 ≤ _x650 ∧ _x661 ≤ _x648 ∧ _x661 + 3 ≤ _x647 ∧ _x660 ≤ _x647 ∧ 0 ≤ _x659 − 1 ∧ _x653 ≤ _x659 − 1 f5171_0_transfer_GE 27 f5171_0_transfer_GE: x1 = _x673 ∧ x2 = _x674 ∧ x3 = _x675 ∧ x4 = _x676 ∧ x5 = _x677 ∧ x6 = _x678 ∧ x7 = _x679 ∧ x8 = _x680 ∧ x9 = _x681 ∧ x10 = _x682 ∧ x11 = _x683 ∧ x12 = _x684 ∧ x13 = _x685 ∧ x1 = _x686 ∧ x2 = _x687 ∧ x3 = _x688 ∧ x4 = _x689 ∧ x5 = _x690 ∧ x6 = _x691 ∧ x7 = _x692 ∧ x8 = _x693 ∧ x9 = _x694 ∧ x10 = _x695 ∧ x11 = _x696 ∧ x12 = _x697 ∧ x13 = _x698 ∧ _x680 = _x693 ∧ _x679 = _x692 ∧ _x678 = _x691 ∧ _x677 = _x690 ∧ _x676 + 1 = _x689 ∧ _x678 + 3 ≤ _x673 ∧ _x677 + 3 ≤ _x673 ∧ 0 ≤ _x688 − 1 ∧ 0 ≤ _x687 − 1 ∧ 3 ≤ _x686 − 1 ∧ 0 ≤ _x675 − 1 ∧ 0 ≤ _x674 − 1 ∧ 3 ≤ _x673 − 1 ∧ _x688 ≤ _x675 ∧ _x688 ≤ _x674 ∧ _x688 + 3 ≤ _x673 ∧ _x687 ≤ _x675 ∧ _x687 ≤ _x674 ∧ _x687 + 3 ≤ _x673 ∧ _x686 ≤ _x673 ∧ _x676 ≤ _x680 − 1 ∧ −1 ≤ _x680 − 1 f5266_0_transfer_ArrayAccess 28 f5171_0_transfer_GE: x1 = _x699 ∧ x2 = _x700 ∧ x3 = _x701 ∧ x4 = _x702 ∧ x5 = _x703 ∧ x6 = _x704 ∧ x7 = _x705 ∧ x8 = _x706 ∧ x9 = _x707 ∧ x10 = _x708 ∧ x11 = _x709 ∧ x12 = _x710 ∧ x13 = _x711 ∧ x1 = _x712 ∧ x2 = _x713 ∧ x3 = _x714 ∧ x4 = _x715 ∧ x5 = _x716 ∧ x6 = _x717 ∧ x7 = _x718 ∧ x8 = _x719 ∧ x9 = _x720 ∧ x10 = _x721 ∧ x11 = _x722 ∧ x12 = _x723 ∧ x13 = _x724 ∧ _x708 = _x719 ∧ _x711 = _x718 ∧ _x707 = _x717 ∧ _x706 = _x716 ∧ _x701 + 1 = _x715 ∧ _x710 + 2 ≤ _x703 ∧ _x709 + 2 ≤ _x703 ∧ _x707 + 3 ≤ _x699 ∧ _x706 + 3 ≤ _x699 ∧ 0 ≤ _x714 − 1 ∧ 0 ≤ _x713 − 1 ∧ 3 ≤ _x712 − 1 ∧ 0 ≤ _x704 − 1 ∧ 1 ≤ _x703 − 1 ∧ −1 ≤ _x702 − 1 ∧ 0 ≤ _x700 − 1 ∧ 3 ≤ _x699 − 1 ∧ _x714 ≤ _x704 ∧ _x714 + 1 ≤ _x703 ∧ _x714 − 1 ≤ _x702 ∧ _x714 ≤ _x700 ∧ _x714 + 3 ≤ _x699 ∧ _x713 ≤ _x704 ∧ _x713 + 1 ≤ _x703 ∧ _x713 − 1 ≤ _x702 ∧ _x713 ≤ _x700 ∧ _x713 + 3 ≤ _x699 ∧ _x712 ≤ _x699 ∧ _x705 ≤ _x711 − 1 ∧ −1 ≤ _x708 − 1 __init 29 f1_0_main_Load: x1 = _x725 ∧ x2 = _x726 ∧ x3 = _x727 ∧ x4 = _x728 ∧ x5 = _x729 ∧ x6 = _x730 ∧ x7 = _x731 ∧ x8 = _x732 ∧ x9 = _x733 ∧ x10 = _x734 ∧ x11 = _x735 ∧ x12 = _x736 ∧ x13 = _x737 ∧ x1 = _x738 ∧ x2 = _x739 ∧ x3 = _x740 ∧ x4 = _x741 ∧ x5 = _x742 ∧ x6 = _x743 ∧ x7 = _x744 ∧ x8 = _x745 ∧ x9 = _x746 ∧ x10 = _x747 ∧ x11 = _x748 ∧ x12 = _x749 ∧ x13 = _x750 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f4644_0_put_NULL f4644_0_put_NULL f4644_0_put_NULL: 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 f4725_0_put_EQ f4725_0_put_EQ f4725_0_put_EQ: 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 f3994_0_random_ArrayAccess f3994_0_random_ArrayAccess f3994_0_random_ArrayAccess: 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 f3916_0_createMap_LE f3916_0_createMap_LE f3916_0_createMap_LE: 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 f606_0_createMap_Return f606_0_createMap_Return f606_0_createMap_Return: 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 f1_0_main_Load f1_0_main_Load f1_0_main_Load: 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 f5171_0_transfer_GE f5171_0_transfer_GE f5171_0_transfer_GE: 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 f4480_0_getEntry_NULL f4480_0_getEntry_NULL f4480_0_getEntry_NULL: 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 __init __init __init: 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 f4575_0_getEntry_EQ f4575_0_getEntry_EQ f4575_0_getEntry_EQ: 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 f5266_0_transfer_ArrayAccess f5266_0_transfer_ArrayAccess f5266_0_transfer_ArrayAccess: 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
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 4 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/4

Here we consider the SCC { f3916_0_createMap_LE }.

### 2.1.1 Transition Removal

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

 f3916_0_createMap_LE: x2

### 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 2/4

Here we consider the SCC { f4644_0_put_NULL, f4725_0_put_EQ }.

### 2.2.1 Transition Removal

We remove transitions 16, 18, 19, 20, 21, 22, 17 using the following ranking functions, which are bounded by 0.

 f4644_0_put_NULL: 1 + x4 f4725_0_put_EQ: x3

### 2.2.2 Trivial Cooperation Program

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

### 2.3 SCC Subproblem 3/4

Here we consider the SCC { f5171_0_transfer_GE, f5266_0_transfer_ArrayAccess }.

### 2.3.1 Transition Removal

We remove transition 27 using the following ranking functions, which are bounded by 0.

 f5171_0_transfer_GE: −2⋅x4 + 2⋅x8 + 1 f5266_0_transfer_ArrayAccess: −2⋅x3 + 2⋅x10

### 2.3.2 Transition Removal

We remove transition 25 using the following ranking functions, which are bounded by 0.

 f5171_0_transfer_GE: −2⋅x4 + 2⋅x8 + 2 f5266_0_transfer_ArrayAccess: −2⋅x3 + 2⋅x10 + 1

### 2.3.3 Transition Removal

We remove transitions 28, 26 using the following ranking functions, which are bounded by 0.

 f5266_0_transfer_ArrayAccess: x4 f5171_0_transfer_GE: −1

### 2.3.4 Trivial Cooperation Program

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

### 2.4 SCC Subproblem 4/4

Here we consider the SCC { f4480_0_getEntry_NULL, f4575_0_getEntry_EQ }.

### 2.4.1 Transition Removal

We remove transitions 7, 9, 10, 11, 12, 13, 8 using the following ranking functions, which are bounded by 0.

 f4480_0_getEntry_NULL: x2 + 1 f4575_0_getEntry_EQ: x1

### 2.4.2 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 % (16 real / 0 unknown / 0 assumptions / 16 total proof steps)