# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: f3797_0_createMap_LE, f4358_0_put_InvokeMethod, f3875_0_random_ArrayAccess, f4529_0_put_EQ, f5087_0_transfer_ArrayAccess, f1_0_main_Load, f617_0_createMap_Return, __init, f4448_0_put_NULL, f4991_0_transfer_GE
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f3875_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 f617_0_createMap_Return 2 f3875_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 f3797_0_createMap_LE: x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x31 ∧ x4 = _x33 ∧ x5 = _x34 ∧ x6 = _x35 ∧ x7 = _x36 ∧ x8 = _x37 ∧ x9 = _x40 ∧ x10 = _x41 ∧ x11 = _x42 ∧ x12 = _x43 ∧ x13 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ x4 = _x50 ∧ x5 = _x51 ∧ x6 = _x52 ∧ x7 = _x53 ∧ x8 = _x54 ∧ x9 = _x55 ∧ x10 = _x56 ∧ x11 = _x57 ∧ x12 = _x58 ∧ x13 = _x59 ∧ 12 = _x53 ∧ 0 = _x52 ∧ 16 = _x51 ∧ 1 = _x50 ∧ _x28 = _x47 ∧ 14 ≤ _x45 − 1 ∧ 0 ≤ _x27 − 1 ∧ _x45 − 14 ≤ _x27 ∧ 0 ≤ _x28 − 1 ∧ −1 ≤ _x46 − 1 f3797_0_createMap_LE 4 f3797_0_createMap_LE: 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 ∧ 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 ≤ _x61 − 1 ∧ _x63 + 1 ≤ _x62 − 1 ∧ −1 ≤ _x62 − 1 ∧ −1 ≤ _x63 − 1 ∧ −1 ≤ _x86 − 1 ∧ −1 ≤ _x87 − 1 ∧ 1 ≤ _x64 − 1 ∧ 3 ≤ _x60 − 1 ∧ 3 ≤ _x73 − 1 ∧ _x66 + 3 ≤ _x60 ∧ _x65 + 3 ≤ _x60 ∧ _x61 − 1 = _x74 ∧ _x62 = _x75 ∧ _x63 + 2 = _x76 f3875_0_random_ArrayAccess 5 f4358_0_put_InvokeMethod: x1 = _x88 ∧ x2 = _x89 ∧ x3 = _x91 ∧ x4 = _x92 ∧ x5 = _x93 ∧ x6 = _x94 ∧ x7 = _x95 ∧ x8 = _x96 ∧ x9 = _x97 ∧ x10 = _x98 ∧ x11 = _x99 ∧ x12 = _x100 ∧ x13 = _x101 ∧ x1 = _x102 ∧ x2 = _x103 ∧ x3 = _x104 ∧ x4 = _x105 ∧ x5 = _x106 ∧ x6 = _x107 ∧ x7 = _x108 ∧ x8 = _x109 ∧ x9 = _x110 ∧ x10 = _x111 ∧ x11 = _x112 ∧ x12 = _x113 ∧ x13 = _x114 ∧ −1 ≤ _x115 − 1 ∧ _x115 + 1 ≤ _x89 − 1 ∧ −1 ≤ _x116 − 1 ∧ −1 ≤ _x117 − 1 ∧ 0 ≤ _x89 − 1 ∧ 1 ≤ _x91 − 1 ∧ _x102 ≤ _x88 ∧ 3 ≤ _x88 − 1 ∧ 3 ≤ _x102 − 1 ∧ _x93 + 3 ≤ _x88 ∧ _x92 + 3 ≤ _x88 ∧ _x91 = _x103 ∧ _x92 = _x104 ∧ _x93 = _x105 f3797_0_createMap_LE 6 f4358_0_put_InvokeMethod: x1 = _x118 ∧ x2 = _x119 ∧ x3 = _x120 ∧ x4 = _x121 ∧ x5 = _x122 ∧ x6 = _x123 ∧ x7 = _x124 ∧ x8 = _x125 ∧ x9 = _x126 ∧ x10 = _x127 ∧ x11 = _x128 ∧ x12 = _x129 ∧ x13 = _x130 ∧ 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 ∧ 0 ≤ _x119 − 1 ∧ _x121 + 1 ≤ _x120 − 1 ∧ −1 ≤ _x120 − 1 ∧ −1 ≤ _x121 − 1 ∧ −1 ≤ _x144 − 1 ∧ −1 ≤ _x145 − 1 ∧ 1 ≤ _x122 − 1 ∧ _x131 ≤ _x118 ∧ 3 ≤ _x118 − 1 ∧ 3 ≤ _x131 − 1 ∧ _x124 + 3 ≤ _x118 ∧ _x123 + 3 ≤ _x118 ∧ _x122 = _x132 ∧ _x123 = _x133 ∧ _x124 = _x134 f4358_0_put_InvokeMethod 7 f4448_0_put_NULL: 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 ∧ _x149 = _x165 ∧ _x148 = _x164 ∧ _x147 = _x163 ∧ _x148 + 3 ≤ _x146 ∧ _x149 + 3 ≤ _x146 ∧ −1 ≤ _x162 − 1 ∧ 3 ≤ _x159 − 1 ∧ 3 ≤ _x146 − 1 ∧ _x159 ≤ _x146 ∧ 1 ≤ _x147 − 1 ∧ _x161 ≤ _x147 − 1 f4448_0_put_NULL 8 f4529_0_put_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 ∧ _x173 = _x192 ∧ _x178 = _x191 ∧ _x177 = _x190 ∧ _x176 = _x189 ∧ 0 = _x188 ∧ _x174 = _x186 ∧ _x194 + 4 ≤ _x175 ∧ _x173 + 2 ≤ _x175 ∧ _x178 + 3 ≤ _x172 ∧ _x177 + 3 ≤ _x172 ∧ −1 ≤ _x193 − 1 ∧ 2 ≤ _x187 − 1 ∧ 3 ≤ _x185 − 1 ∧ 2 ≤ _x175 − 1 ∧ 3 ≤ _x172 − 1 ∧ _x193 + 2 ≤ _x175 ∧ _x187 ≤ _x175 ∧ 1 ≤ _x176 − 1 ∧ _x185 ≤ _x172 f4448_0_put_NULL 9 f4529_0_put_EQ: 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 = _x212 ∧ x2 = _x213 ∧ x3 = _x214 ∧ x4 = _x215 ∧ x5 = _x216 ∧ x6 = _x217 ∧ x7 = _x218 ∧ x8 = _x219 ∧ x9 = _x220 ∧ x10 = _x221 ∧ x11 = _x222 ∧ x12 = _x223 ∧ x13 = _x224 ∧ _x199 = _x219 ∧ _x204 = _x218 ∧ _x203 = _x217 ∧ _x202 = _x216 ∧ 1 = _x215 ∧ _x200 = _x213 ∧ _x221 + 4 ≤ _x201 ∧ _x199 + 2 ≤ _x201 ∧ _x204 + 3 ≤ _x198 ∧ _x203 + 3 ≤ _x198 ∧ −1 ≤ _x220 − 1 ∧ 2 ≤ _x214 − 1 ∧ 3 ≤ _x212 − 1 ∧ 2 ≤ _x201 − 1 ∧ 3 ≤ _x198 − 1 ∧ _x220 + 2 ≤ _x201 ∧ _x214 ≤ _x201 ∧ 1 ≤ _x202 − 1 ∧ _x212 ≤ _x198 f4448_0_put_NULL 10 f4448_0_put_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 ∧ _x238 ≤ _x225 ∧ _x251 ≤ _x226 − 1 ∧ _x241 + 1 ≤ _x228 ∧ 3 ≤ _x225 − 1 ∧ 0 ≤ _x228 − 1 ∧ 3 ≤ _x238 − 1 ∧ −1 ≤ _x241 − 1 ∧ _x230 + 3 ≤ _x225 ∧ _x231 + 3 ≤ _x225 ∧ _x226 = _x239 ∧ _x227 = _x240 ∧ _x229 = _x242 ∧ _x230 = _x243 ∧ _x231 = _x244 f4448_0_put_NULL 11 f4448_0_put_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 = _x264 ∧ x1 = _x265 ∧ x2 = _x266 ∧ x3 = _x267 ∧ x4 = _x268 ∧ x5 = _x269 ∧ x6 = _x270 ∧ x7 = _x271 ∧ x8 = _x272 ∧ x9 = _x273 ∧ x10 = _x274 ∧ x11 = _x275 ∧ x12 = _x276 ∧ x13 = _x277 ∧ _x265 ≤ _x252 ∧ _x253 ≤ _x278 − 1 ∧ _x268 + 1 ≤ _x255 ∧ 3 ≤ _x252 − 1 ∧ 0 ≤ _x255 − 1 ∧ 3 ≤ _x265 − 1 ∧ −1 ≤ _x268 − 1 ∧ _x257 + 3 ≤ _x252 ∧ _x258 + 3 ≤ _x252 ∧ _x253 = _x266 ∧ _x254 = _x267 ∧ _x256 = _x269 ∧ _x257 = _x270 ∧ _x258 = _x271 f4448_0_put_NULL 12 f4448_0_put_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 ∧ _x285 = _x298 ∧ _x284 = _x297 ∧ _x283 = _x296 ∧ _x281 = _x294 ∧ _x280 = _x293 ∧ _x280 + 2 ≤ _x282 ∧ _x285 + 3 ≤ _x279 ∧ _x284 + 3 ≤ _x279 ∧ −1 ≤ _x295 − 1 ∧ 3 ≤ _x292 − 1 ∧ 1 ≤ _x282 − 1 ∧ 3 ≤ _x279 − 1 ∧ _x295 + 2 ≤ _x282 ∧ 1 ≤ _x283 − 1 ∧ _x292 ≤ _x279 f4448_0_put_NULL 13 f4448_0_put_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 ∧ _x311 = _x324 ∧ _x310 = _x323 ∧ _x309 = _x322 ∧ _x307 = _x320 ∧ _x306 = _x319 ∧ _x306 + 2 ≤ _x308 ∧ _x311 + 3 ≤ _x305 ∧ _x310 + 3 ≤ _x305 ∧ −1 ≤ _x321 − 1 ∧ 3 ≤ _x318 − 1 ∧ 2 ≤ _x308 − 1 ∧ 3 ≤ _x305 − 1 ∧ _x321 + 2 ≤ _x308 ∧ 1 ≤ _x309 − 1 ∧ _x318 ≤ _x305 f4529_0_put_EQ 14 f4448_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 ∧ _x337 = _x350 ∧ _x336 = _x349 ∧ _x335 = _x348 ∧ _x332 = _x346 ∧ _x338 = _x345 ∧ 0 = _x334 ∧ _x340 + 4 ≤ _x333 ∧ _x338 + 2 ≤ _x333 ∧ _x337 + 3 ≤ _x331 ∧ _x336 + 3 ≤ _x331 ∧ −1 ≤ _x347 − 1 ∧ 3 ≤ _x344 − 1 ∧ −1 ≤ _x339 − 1 ∧ 2 ≤ _x333 − 1 ∧ 3 ≤ _x331 − 1 ∧ _x347 ≤ _x339 ∧ _x347 + 2 ≤ _x333 ∧ _x344 ≤ _x331 f4448_0_put_NULL 15 f4991_0_transfer_GE: x1 = _x357 ∧ x2 = _x358 ∧ x3 = _x359 ∧ x4 = _x360 ∧ x5 = _x361 ∧ x6 = _x362 ∧ x7 = _x363 ∧ x8 = _x364 ∧ x9 = _x365 ∧ x10 = _x366 ∧ x11 = _x367 ∧ x12 = _x368 ∧ x13 = _x369 ∧ x1 = _x370 ∧ x2 = _x371 ∧ x3 = _x372 ∧ x4 = _x373 ∧ x5 = _x374 ∧ x6 = _x375 ∧ x7 = _x376 ∧ x8 = _x377 ∧ x9 = _x378 ∧ x10 = _x379 ∧ x11 = _x380 ∧ x12 = _x381 ∧ x13 = _x382 ∧ _x361 = _x377 ∧ 2⋅_x361 = _x376 ∧ _x363 = _x375 ∧ _x362 + 1 = _x374 ∧ 0 = _x373 ∧ _x363 + 3 ≤ _x357 ∧ _x362 + 3 ≤ _x357 ∧ 0 ≤ _x372 − 1 ∧ 0 ≤ _x371 − 1 ∧ 3 ≤ _x370 − 1 ∧ −1 ≤ _x360 − 1 ∧ 3 ≤ _x357 − 1 ∧ _x372 − 1 ≤ _x360 ∧ _x372 + 3 ≤ _x357 ∧ _x371 − 1 ≤ _x360 ∧ _x371 + 3 ≤ _x357 ∧ _x370 − 1 ≤ _x357 ∧ _x361 ≤ 1073741823 ∧ 0 ≤ 2⋅_x361 ∧ _x363 ≤ _x362 ∧ 1 ≤ _x361 − 1 ∧ _x359 ≤ _x361 − 1 f4448_0_put_NULL 16 f4991_0_transfer_GE: x1 = _x383 ∧ x2 = _x384 ∧ x3 = _x385 ∧ x4 = _x386 ∧ x5 = _x387 ∧ x6 = _x388 ∧ x7 = _x389 ∧ x8 = _x390 ∧ x9 = _x391 ∧ x10 = _x392 ∧ x11 = _x393 ∧ x12 = _x394 ∧ x13 = _x395 ∧ x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x5 = _x400 ∧ x6 = _x401 ∧ x7 = _x402 ∧ x8 = _x403 ∧ x9 = _x404 ∧ x10 = _x405 ∧ x11 = _x406 ∧ x12 = _x407 ∧ x13 = _x408 ∧ _x387 = _x403 ∧ 2⋅_x387 = _x402 ∧ _x389 = _x401 ∧ _x388 + 1 = _x400 ∧ 0 = _x399 ∧ _x389 + 3 ≤ _x383 ∧ _x388 + 3 ≤ _x383 ∧ 0 ≤ _x398 − 1 ∧ 0 ≤ _x397 − 1 ∧ 3 ≤ _x396 − 1 ∧ −1 ≤ _x386 − 1 ∧ 3 ≤ _x383 − 1 ∧ _x398 − 1 ≤ _x386 ∧ _x398 + 3 ≤ _x383 ∧ _x397 − 1 ≤ _x386 ∧ _x397 + 3 ≤ _x383 ∧ _x396 − 1 ≤ _x383 ∧ _x389 ≤ _x388 ∧ 0 ≤ 2⋅_x387 ∧ 1073741824 ≤ _x387 − 1 ∧ _x385 ≤ _x387 − 1 f4991_0_transfer_GE 17 f5087_0_transfer_ArrayAccess: x1 = _x409 ∧ x2 = _x410 ∧ x3 = _x411 ∧ x4 = _x412 ∧ x5 = _x413 ∧ x6 = _x414 ∧ x7 = _x415 ∧ x8 = _x416 ∧ x9 = _x417 ∧ x10 = _x418 ∧ x11 = _x419 ∧ x12 = _x420 ∧ x13 = _x421 ∧ x1 = _x422 ∧ x2 = _x423 ∧ x3 = _x424 ∧ x4 = _x425 ∧ x5 = _x426 ∧ x6 = _x427 ∧ x7 = _x428 ∧ x8 = _x429 ∧ x9 = _x430 ∧ x10 = _x431 ∧ x11 = _x432 ∧ x12 = _x433 ∧ x13 = _x434 ∧ _x415 = _x434 ∧ _x416 = _x431 ∧ _x414 = _x430 ∧ _x413 = _x429 ∧ _x412 = _x424 ∧ _x414 + 3 ≤ _x409 ∧ _x413 + 3 ≤ _x409 ∧ 0 ≤ _x427 − 1 ∧ 0 ≤ _x426 − 1 ∧ −1 ≤ _x425 − 1 ∧ 0 ≤ _x423 − 1 ∧ 3 ≤ _x422 − 1 ∧ 0 ≤ _x411 − 1 ∧ 0 ≤ _x410 − 1 ∧ 3 ≤ _x409 − 1 ∧ _x427 ≤ _x411 ∧ _x427 ≤ _x410 ∧ _x427 + 3 ≤ _x409 ∧ _x423 ≤ _x411 ∧ _x423 ≤ _x410 ∧ _x423 + 3 ≤ _x409 ∧ _x422 ≤ _x409 ∧ _x412 ≤ _x416 − 1 ∧ 0 ≤ _x415 − 1 f5087_0_transfer_ArrayAccess 18 f5087_0_transfer_ArrayAccess: x1 = _x435 ∧ x2 = _x436 ∧ x3 = _x437 ∧ x4 = _x438 ∧ x5 = _x439 ∧ x6 = _x440 ∧ x7 = _x441 ∧ x8 = _x442 ∧ x9 = _x443 ∧ x10 = _x444 ∧ x11 = _x445 ∧ x12 = _x446 ∧ x13 = _x447 ∧ x1 = _x448 ∧ x2 = _x449 ∧ x3 = _x450 ∧ x4 = _x451 ∧ x5 = _x452 ∧ x6 = _x453 ∧ x7 = _x454 ∧ x8 = _x455 ∧ x9 = _x456 ∧ x10 = _x457 ∧ x11 = _x458 ∧ x12 = _x459 ∧ x13 = _x460 ∧ _x447 = _x460 ∧ _x444 = _x457 ∧ _x443 = _x456 ∧ _x442 = _x455 ∧ _x437 = _x450 ∧ _x446 + 2 ≤ _x439 ∧ _x459 + 4 ≤ _x439 ∧ _x458 + 4 ≤ _x439 ∧ _x445 + 2 ≤ _x439 ∧ _x459 + 2 ≤ _x438 ∧ _x458 + 2 ≤ _x438 ∧ _x443 + 3 ≤ _x435 ∧ _x442 + 3 ≤ _x435 ∧ 0 ≤ _x453 − 1 ∧ 0 ≤ _x452 − 1 ∧ −1 ≤ _x451 − 1 ∧ 0 ≤ _x449 − 1 ∧ 3 ≤ _x448 − 1 ∧ 0 ≤ _x440 − 1 ∧ 2 ≤ _x439 − 1 ∧ 0 ≤ _x438 − 1 ∧ 0 ≤ _x436 − 1 ∧ 3 ≤ _x435 − 1 ∧ _x453 ≤ _x440 ∧ _x453 + 2 ≤ _x439 ∧ _x453 ≤ _x438 ∧ _x453 ≤ _x436 ∧ _x453 + 3 ≤ _x435 ∧ _x452 + 2 ≤ _x439 ∧ _x452 ≤ _x438 ∧ _x451 + 3 ≤ _x439 ∧ _x451 + 1 ≤ _x438 ∧ _x449 ≤ _x440 ∧ _x449 + 2 ≤ _x439 ∧ _x449 ≤ _x438 ∧ _x449 ≤ _x436 ∧ _x449 + 3 ≤ _x435 ∧ _x448 ≤ _x435 ∧ 0 ≤ _x447 − 1 ∧ _x441 ≤ _x447 − 1 f4991_0_transfer_GE 19 f4991_0_transfer_GE: x1 = _x461 ∧ x2 = _x462 ∧ x3 = _x463 ∧ x4 = _x464 ∧ x5 = _x465 ∧ x6 = _x466 ∧ x7 = _x467 ∧ x8 = _x468 ∧ x9 = _x469 ∧ x10 = _x470 ∧ x11 = _x471 ∧ x12 = _x472 ∧ x13 = _x473 ∧ x1 = _x474 ∧ x2 = _x475 ∧ x3 = _x476 ∧ x4 = _x477 ∧ x5 = _x478 ∧ x6 = _x479 ∧ x7 = _x480 ∧ x8 = _x481 ∧ x9 = _x482 ∧ x10 = _x483 ∧ x11 = _x484 ∧ x12 = _x485 ∧ x13 = _x486 ∧ _x468 = _x481 ∧ _x467 = _x480 ∧ _x466 = _x479 ∧ _x465 = _x478 ∧ _x464 + 1 = _x477 ∧ _x466 + 3 ≤ _x461 ∧ _x465 + 3 ≤ _x461 ∧ 0 ≤ _x476 − 1 ∧ 0 ≤ _x475 − 1 ∧ 3 ≤ _x474 − 1 ∧ 0 ≤ _x463 − 1 ∧ 0 ≤ _x462 − 1 ∧ 3 ≤ _x461 − 1 ∧ _x476 ≤ _x463 ∧ _x476 ≤ _x462 ∧ _x476 + 3 ≤ _x461 ∧ _x475 ≤ _x463 ∧ _x475 ≤ _x462 ∧ _x475 + 3 ≤ _x461 ∧ _x474 ≤ _x461 ∧ _x464 ≤ _x468 − 1 ∧ −1 ≤ _x468 − 1 f5087_0_transfer_ArrayAccess 20 f4991_0_transfer_GE: x1 = _x487 ∧ x2 = _x488 ∧ x3 = _x489 ∧ x4 = _x490 ∧ x5 = _x491 ∧ x6 = _x492 ∧ x7 = _x493 ∧ x8 = _x494 ∧ x9 = _x495 ∧ x10 = _x496 ∧ x11 = _x497 ∧ x12 = _x498 ∧ x13 = _x499 ∧ x1 = _x500 ∧ x2 = _x501 ∧ x3 = _x502 ∧ x4 = _x503 ∧ x5 = _x504 ∧ x6 = _x505 ∧ x7 = _x506 ∧ x8 = _x507 ∧ x9 = _x508 ∧ x10 = _x509 ∧ x11 = _x510 ∧ x12 = _x511 ∧ x13 = _x512 ∧ _x496 = _x507 ∧ _x499 = _x506 ∧ _x495 = _x505 ∧ _x494 = _x504 ∧ _x489 + 1 = _x503 ∧ _x498 + 2 ≤ _x491 ∧ _x497 + 2 ≤ _x491 ∧ _x495 + 3 ≤ _x487 ∧ _x494 + 3 ≤ _x487 ∧ 0 ≤ _x502 − 1 ∧ 0 ≤ _x501 − 1 ∧ 3 ≤ _x500 − 1 ∧ 0 ≤ _x492 − 1 ∧ 1 ≤ _x491 − 1 ∧ −1 ≤ _x490 − 1 ∧ 0 ≤ _x488 − 1 ∧ 3 ≤ _x487 − 1 ∧ _x502 ≤ _x492 ∧ _x502 + 1 ≤ _x491 ∧ _x502 − 1 ≤ _x490 ∧ _x502 ≤ _x488 ∧ _x502 + 3 ≤ _x487 ∧ _x501 ≤ _x492 ∧ _x501 + 1 ≤ _x491 ∧ _x501 − 1 ≤ _x490 ∧ _x501 ≤ _x488 ∧ _x501 + 3 ≤ _x487 ∧ _x500 ≤ _x487 ∧ _x493 ≤ _x499 − 1 ∧ −1 ≤ _x496 − 1 __init 21 f1_0_main_Load: 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 ∧ x1 = _x526 ∧ x2 = _x527 ∧ x3 = _x528 ∧ x4 = _x529 ∧ x5 = _x530 ∧ x6 = _x531 ∧ x7 = _x532 ∧ x8 = _x533 ∧ x9 = _x534 ∧ x10 = _x535 ∧ x11 = _x536 ∧ x12 = _x537 ∧ x13 = _x538 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f3797_0_createMap_LE f3797_0_createMap_LE f3797_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 f4358_0_put_InvokeMethod f4358_0_put_InvokeMethod f4358_0_put_InvokeMethod: 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 f3875_0_random_ArrayAccess f3875_0_random_ArrayAccess f3875_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 f4529_0_put_EQ f4529_0_put_EQ f4529_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 f5087_0_transfer_ArrayAccess f5087_0_transfer_ArrayAccess f5087_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 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 f617_0_createMap_Return f617_0_createMap_Return f617_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 __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 f4448_0_put_NULL f4448_0_put_NULL f4448_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 f4991_0_transfer_GE f4991_0_transfer_GE f4991_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
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 { f3797_0_createMap_LE }.

### 2.1.1 Transition Removal

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

 f3797_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 2/3

Here we consider the SCC { f4529_0_put_EQ, f4448_0_put_NULL }.

### 2.2.1 Transition Removal

We remove transitions 8, 10, 11, 12, 13, 14, 9 using the following ranking functions, which are bounded by 0.

 f4448_0_put_NULL: 1 + x4 f4529_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 3/3

Here we consider the SCC { f5087_0_transfer_ArrayAccess, f4991_0_transfer_GE }.

### 2.3.1 Transition Removal

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

 f4991_0_transfer_GE: −1 − x4 + 2⋅x8 f5087_0_transfer_ArrayAccess: −1 − x3 + 2⋅x10

### 2.3.2 Transition Removal

We remove transition 17 using the following ranking functions, which are bounded by 0.

 f4991_0_transfer_GE: −1 − x4 + x7 + x8 f5087_0_transfer_ArrayAccess: −2 − x3 + x10 + x13

### 2.3.3 Transition Removal

We remove transitions 20, 18 using the following ranking functions, which are bounded by 0.

 f5087_0_transfer_ArrayAccess: 4⋅x4 f4991_0_transfer_GE: − x1

### 2.3.4 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 % (13 real / 0 unknown / 0 assumptions / 13 total proof steps)