# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: f4423_0_transfer_ArrayAccess, f3804_0_put_NULL, f3882_0_put_EQ, f3248_0_createMap_LE, f4328_0_transfer_GE, f517_0_createMap_Return, f1_0_main_Load, f3559_0_clear_GE, __init
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f3559_0_clear_GE: 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 ≤ _arg6P − 1 ∧ 0 ≤ _arg2 − 1 ∧ −1 ≤ _x7 − 1 ∧ _arg2P ≤ _arg1 ∧ 0 ≤ _arg1 − 1 ∧ 3 ≤ _arg1P − 1 ∧ 0 ≤ _arg2P − 1 ∧ 0 = _arg3P f517_0_createMap_Return 2 f3559_0_clear_GE: 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 ∧ 16 = _x19 ∧ 12 = _x18 ∧ _x2 = _x17 ∧ 0 = _x16 ∧ 12 = _x3 ∧ 16 = _x1 ∧ _x2 + 3 ≤ _x ∧ 0 ≤ _x15 − 1 ∧ 14 ≤ _x14 − 1 ∧ 14 ≤ _x − 1 ∧ _x15 + 14 ≤ _x ∧ _x14 ≤ _x f3559_0_clear_GE 3 f3559_0_clear_GE: x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ x4 = _x30 ∧ x5 = _x31 ∧ x6 = _x32 ∧ x7 = _x33 ∧ x8 = _x34 ∧ x9 = _x37 ∧ x10 = _x38 ∧ x11 = _x39 ∧ x12 = _x40 ∧ x13 = _x41 ∧ x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x4 = _x45 ∧ x5 = _x46 ∧ x6 = _x47 ∧ x7 = _x50 ∧ x8 = _x51 ∧ x9 = _x52 ∧ x10 = _x53 ∧ x11 = _x54 ∧ x12 = _x55 ∧ x13 = _x56 ∧ _x32 = _x47 ∧ _x31 = _x46 ∧ _x30 = _x45 ∧ _x29 + 1 = _x44 ∧ _x31 + 3 ≤ _x27 ∧ _x30 + 3 ≤ _x27 ∧ 0 ≤ _x43 − 1 ∧ 3 ≤ _x42 − 1 ∧ 0 ≤ _x28 − 1 ∧ 3 ≤ _x27 − 1 ∧ _x43 ≤ _x28 ∧ _x43 + 3 ≤ _x27 ∧ _x42 ≤ _x27 ∧ _x29 ≤ _x32 − 1 ∧ −1 ≤ _x32 − 1 f1_0_main_Load 4 f3248_0_createMap_LE: x1 = _x57 ∧ x2 = _x58 ∧ x3 = _x59 ∧ x4 = _x60 ∧ x5 = _x61 ∧ x6 = _x62 ∧ x7 = _x63 ∧ x8 = _x64 ∧ x9 = _x65 ∧ x10 = _x66 ∧ x11 = _x67 ∧ x12 = _x68 ∧ x13 = _x69 ∧ x1 = _x70 ∧ x2 = _x71 ∧ x3 = _x72 ∧ x4 = _x73 ∧ x5 = _x74 ∧ x6 = _x75 ∧ x7 = _x76 ∧ x8 = _x77 ∧ x9 = _x78 ∧ x10 = _x79 ∧ x11 = _x80 ∧ x12 = _x81 ∧ x13 = _x82 ∧ 12 = _x76 ∧ 0 = _x75 ∧ 16 = _x74 ∧ 1 = _x73 ∧ _x58 = _x72 ∧ 14 ≤ _x70 − 1 ∧ 0 ≤ _x57 − 1 ∧ _x70 − 14 ≤ _x57 ∧ 0 ≤ _x58 − 1 ∧ −1 ≤ _x71 − 1 f3248_0_createMap_LE 5 f3248_0_createMap_LE: x1 = _x83 ∧ x2 = _x84 ∧ x3 = _x85 ∧ x4 = _x86 ∧ x5 = _x88 ∧ x6 = _x89 ∧ x7 = _x90 ∧ x8 = _x91 ∧ x9 = _x92 ∧ x10 = _x93 ∧ x11 = _x94 ∧ x12 = _x95 ∧ x13 = _x96 ∧ x1 = _x97 ∧ x2 = _x98 ∧ x3 = _x99 ∧ x4 = _x100 ∧ x5 = _x101 ∧ x6 = _x102 ∧ x7 = _x103 ∧ x8 = _x104 ∧ x9 = _x105 ∧ x10 = _x106 ∧ x11 = _x107 ∧ x12 = _x108 ∧ x13 = _x109 ∧ 0 ≤ _x84 − 1 ∧ _x86 + 1 ≤ _x85 − 1 ∧ −1 ≤ _x85 − 1 ∧ −1 ≤ _x86 − 1 ∧ −1 ≤ _x110 − 1 ∧ −1 ≤ _x111 − 1 ∧ 1 ≤ _x88 − 1 ∧ 3 ≤ _x83 − 1 ∧ 3 ≤ _x97 − 1 ∧ _x90 + 3 ≤ _x83 ∧ _x89 + 3 ≤ _x83 ∧ _x84 − 1 = _x98 ∧ _x85 = _x99 ∧ _x86 + 2 = _x100 f3248_0_createMap_LE 6 f3804_0_put_NULL: x1 = _x112 ∧ x2 = _x113 ∧ x3 = _x114 ∧ x4 = _x115 ∧ x5 = _x116 ∧ x6 = _x117 ∧ x7 = _x118 ∧ x8 = _x119 ∧ x9 = _x120 ∧ x10 = _x121 ∧ x11 = _x122 ∧ x12 = _x123 ∧ x13 = _x124 ∧ x1 = _x125 ∧ x2 = _x126 ∧ x3 = _x127 ∧ x4 = _x128 ∧ x5 = _x129 ∧ x6 = _x130 ∧ x7 = _x131 ∧ x8 = _x132 ∧ x9 = _x133 ∧ x10 = _x134 ∧ x11 = _x135 ∧ x12 = _x136 ∧ x13 = _x137 ∧ _x115 + 1 ≤ _x114 − 1 ∧ 1 ≤ _x116 − 1 ∧ 0 ≤ _x113 − 1 ∧ −1 ≤ _x114 − 1 ∧ −1 ≤ _x115 − 1 ∧ −1 ≤ _x138 − 1 ∧ −1 ≤ _x139 − 1 ∧ _x127 ≤ _x116 − 1 ∧ _x125 ≤ _x112 ∧ 3 ≤ _x112 − 1 ∧ 3 ≤ _x125 − 1 ∧ −1 ≤ _x128 − 1 ∧ _x118 + 3 ≤ _x112 ∧ _x117 + 3 ≤ _x112 ∧ _x114 = _x129 ∧ _x115 + 2 = _x130 ∧ _x116 = _x131 ∧ _x117 = _x132 ∧ _x118 = _x133 f3804_0_put_NULL 7 f3882_0_put_EQ: x1 = _x140 ∧ x2 = _x141 ∧ x3 = _x142 ∧ x4 = _x143 ∧ x5 = _x144 ∧ x6 = _x145 ∧ x7 = _x146 ∧ x8 = _x147 ∧ x9 = _x148 ∧ x10 = _x149 ∧ x11 = _x150 ∧ x12 = _x151 ∧ x13 = _x152 ∧ x1 = _x153 ∧ x2 = _x154 ∧ x3 = _x155 ∧ x4 = _x156 ∧ x5 = _x157 ∧ x6 = _x158 ∧ x7 = _x159 ∧ x8 = _x160 ∧ x9 = _x161 ∧ x10 = _x162 ∧ x11 = _x163 ∧ x12 = _x164 ∧ x13 = _x165 ∧ _x141 = _x160 ∧ _x148 = _x159 ∧ _x147 = _x158 ∧ _x146 = _x157 ∧ 0 = _x156 ∧ _x142 = _x154 ∧ _x162 + 4 ≤ _x143 ∧ _x141 + 2 ≤ _x143 ∧ _x148 + 3 ≤ _x140 ∧ _x147 + 3 ≤ _x140 ∧ −1 ≤ _x161 − 1 ∧ 2 ≤ _x155 − 1 ∧ 3 ≤ _x153 − 1 ∧ 2 ≤ _x143 − 1 ∧ 3 ≤ _x140 − 1 ∧ _x161 + 2 ≤ _x143 ∧ _x155 ≤ _x143 ∧ 1 ≤ _x146 − 1 ∧ _x153 ≤ _x140 f3804_0_put_NULL 8 f3882_0_put_EQ: x1 = _x166 ∧ x2 = _x167 ∧ x3 = _x168 ∧ x4 = _x169 ∧ x5 = _x170 ∧ x6 = _x171 ∧ x7 = _x172 ∧ x8 = _x173 ∧ x9 = _x174 ∧ x10 = _x175 ∧ x11 = _x176 ∧ x12 = _x177 ∧ x13 = _x178 ∧ x1 = _x179 ∧ x2 = _x180 ∧ x3 = _x181 ∧ x4 = _x182 ∧ x5 = _x183 ∧ x6 = _x184 ∧ x7 = _x185 ∧ x8 = _x186 ∧ x9 = _x187 ∧ x10 = _x188 ∧ x11 = _x189 ∧ x12 = _x190 ∧ x13 = _x191 ∧ _x167 = _x186 ∧ _x174 = _x185 ∧ _x173 = _x184 ∧ _x172 = _x183 ∧ 1 = _x182 ∧ _x168 = _x180 ∧ _x188 + 4 ≤ _x169 ∧ _x167 + 2 ≤ _x169 ∧ _x174 + 3 ≤ _x166 ∧ _x173 + 3 ≤ _x166 ∧ −1 ≤ _x187 − 1 ∧ 2 ≤ _x181 − 1 ∧ 3 ≤ _x179 − 1 ∧ 2 ≤ _x169 − 1 ∧ 3 ≤ _x166 − 1 ∧ _x187 + 2 ≤ _x169 ∧ _x181 ≤ _x169 ∧ 1 ≤ _x172 − 1 ∧ _x179 ≤ _x166 f3804_0_put_NULL 9 f3804_0_put_NULL: x1 = _x192 ∧ x2 = _x193 ∧ x3 = _x194 ∧ x4 = _x195 ∧ x5 = _x196 ∧ x6 = _x197 ∧ x7 = _x198 ∧ x8 = _x199 ∧ x9 = _x200 ∧ x10 = _x201 ∧ x11 = _x202 ∧ x12 = _x203 ∧ x13 = _x204 ∧ x1 = _x205 ∧ x2 = _x206 ∧ x3 = _x207 ∧ x4 = _x208 ∧ x5 = _x209 ∧ x6 = _x210 ∧ x7 = _x211 ∧ x8 = _x212 ∧ x9 = _x213 ∧ x10 = _x214 ∧ x11 = _x215 ∧ x12 = _x216 ∧ x13 = _x217 ∧ _x205 ≤ _x192 ∧ _x218 ≤ _x193 − 1 ∧ _x208 + 1 ≤ _x195 ∧ 3 ≤ _x192 − 1 ∧ 0 ≤ _x195 − 1 ∧ 3 ≤ _x205 − 1 ∧ −1 ≤ _x208 − 1 ∧ _x199 + 3 ≤ _x192 ∧ _x200 + 3 ≤ _x192 ∧ _x193 = _x206 ∧ _x194 = _x207 ∧ _x196 = _x209 ∧ _x197 = _x210 ∧ _x198 = _x211 ∧ _x199 = _x212 ∧ _x200 = _x213 f3804_0_put_NULL 10 f3804_0_put_NULL: x1 = _x219 ∧ x2 = _x220 ∧ x3 = _x221 ∧ x4 = _x223 ∧ x5 = _x224 ∧ x6 = _x225 ∧ x7 = _x226 ∧ x8 = _x227 ∧ x9 = _x228 ∧ x10 = _x229 ∧ x11 = _x230 ∧ x12 = _x231 ∧ x13 = _x232 ∧ x1 = _x233 ∧ x2 = _x234 ∧ x3 = _x235 ∧ x4 = _x236 ∧ x5 = _x237 ∧ x6 = _x238 ∧ x7 = _x239 ∧ x8 = _x240 ∧ x9 = _x241 ∧ x10 = _x242 ∧ x11 = _x243 ∧ x12 = _x244 ∧ x13 = _x245 ∧ _x233 ≤ _x219 ∧ _x220 ≤ _x246 − 1 ∧ _x236 + 1 ≤ _x223 ∧ 3 ≤ _x219 − 1 ∧ 0 ≤ _x223 − 1 ∧ 3 ≤ _x233 − 1 ∧ −1 ≤ _x236 − 1 ∧ _x227 + 3 ≤ _x219 ∧ _x228 + 3 ≤ _x219 ∧ _x220 = _x234 ∧ _x221 = _x235 ∧ _x224 = _x237 ∧ _x225 = _x238 ∧ _x226 = _x239 ∧ _x227 = _x240 ∧ _x228 = _x241 f3804_0_put_NULL 11 f3804_0_put_NULL: x1 = _x247 ∧ x2 = _x248 ∧ x3 = _x249 ∧ x4 = _x250 ∧ x5 = _x251 ∧ x6 = _x252 ∧ x7 = _x253 ∧ x8 = _x254 ∧ x9 = _x255 ∧ x10 = _x256 ∧ x11 = _x257 ∧ x12 = _x258 ∧ x13 = _x259 ∧ x1 = _x260 ∧ x2 = _x261 ∧ x3 = _x262 ∧ x4 = _x263 ∧ x5 = _x264 ∧ x6 = _x265 ∧ x7 = _x266 ∧ x8 = _x267 ∧ x9 = _x268 ∧ x10 = _x269 ∧ x11 = _x270 ∧ x12 = _x271 ∧ x13 = _x272 ∧ _x255 = _x268 ∧ _x254 = _x267 ∧ _x253 = _x266 ∧ _x252 = _x265 ∧ _x251 = _x264 ∧ _x249 = _x262 ∧ _x248 = _x261 ∧ _x248 + 2 ≤ _x250 ∧ _x255 + 3 ≤ _x247 ∧ _x254 + 3 ≤ _x247 ∧ −1 ≤ _x263 − 1 ∧ 3 ≤ _x260 − 1 ∧ 1 ≤ _x250 − 1 ∧ 3 ≤ _x247 − 1 ∧ _x263 + 2 ≤ _x250 ∧ 1 ≤ _x253 − 1 ∧ _x260 ≤ _x247 f3804_0_put_NULL 12 f3804_0_put_NULL: x1 = _x273 ∧ x2 = _x274 ∧ x3 = _x275 ∧ x4 = _x276 ∧ x5 = _x277 ∧ x6 = _x278 ∧ x7 = _x279 ∧ x8 = _x280 ∧ x9 = _x281 ∧ x10 = _x282 ∧ x11 = _x283 ∧ x12 = _x284 ∧ x13 = _x285 ∧ 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 ∧ _x281 = _x294 ∧ _x280 = _x293 ∧ _x279 = _x292 ∧ _x278 = _x291 ∧ _x277 = _x290 ∧ _x275 = _x288 ∧ _x274 = _x287 ∧ _x274 + 2 ≤ _x276 ∧ _x281 + 3 ≤ _x273 ∧ _x280 + 3 ≤ _x273 ∧ −1 ≤ _x289 − 1 ∧ 3 ≤ _x286 − 1 ∧ 2 ≤ _x276 − 1 ∧ 3 ≤ _x273 − 1 ∧ _x289 + 2 ≤ _x276 ∧ 1 ≤ _x279 − 1 ∧ _x286 ≤ _x273 f3882_0_put_EQ 13 f3804_0_put_NULL: x1 = _x299 ∧ x2 = _x300 ∧ x3 = _x301 ∧ x4 = _x302 ∧ x5 = _x303 ∧ x6 = _x304 ∧ x7 = _x305 ∧ x8 = _x306 ∧ x9 = _x307 ∧ x10 = _x308 ∧ x11 = _x309 ∧ x12 = _x310 ∧ x13 = _x311 ∧ x1 = _x312 ∧ x2 = _x313 ∧ x3 = _x314 ∧ x4 = _x315 ∧ x5 = _x316 ∧ x6 = _x317 ∧ x7 = _x318 ∧ x8 = _x319 ∧ x9 = _x320 ∧ x10 = _x321 ∧ x11 = _x322 ∧ x12 = _x323 ∧ x13 = _x324 ∧ _x305 = _x320 ∧ _x304 = _x319 ∧ _x303 = _x318 ∧ _x300 = _x314 ∧ _x306 = _x313 ∧ 0 = _x302 ∧ _x308 + 4 ≤ _x301 ∧ _x306 + 2 ≤ _x301 ∧ _x305 + 3 ≤ _x299 ∧ _x304 + 3 ≤ _x299 ∧ −1 ≤ _x315 − 1 ∧ 3 ≤ _x312 − 1 ∧ −1 ≤ _x307 − 1 ∧ 2 ≤ _x301 − 1 ∧ 3 ≤ _x299 − 1 ∧ _x315 ≤ _x307 ∧ _x315 + 2 ≤ _x301 ∧ _x312 ≤ _x299 f3804_0_put_NULL 14 f4328_0_transfer_GE: x1 = _x325 ∧ x2 = _x326 ∧ x3 = _x327 ∧ x4 = _x328 ∧ x5 = _x329 ∧ x6 = _x330 ∧ x7 = _x331 ∧ x8 = _x332 ∧ x9 = _x333 ∧ x10 = _x334 ∧ x11 = _x335 ∧ x12 = _x336 ∧ x13 = _x337 ∧ x1 = _x338 ∧ x2 = _x339 ∧ x3 = _x340 ∧ x4 = _x341 ∧ x5 = _x342 ∧ x6 = _x343 ∧ x7 = _x344 ∧ x8 = _x345 ∧ x9 = _x346 ∧ x10 = _x347 ∧ x11 = _x348 ∧ x12 = _x349 ∧ x13 = _x350 ∧ _x331 = _x345 ∧ 2⋅_x331 = _x344 ∧ _x333 = _x343 ∧ _x332 + 1 = _x342 ∧ 0 = _x341 ∧ _x333 + 3 ≤ _x325 ∧ _x332 + 3 ≤ _x325 ∧ 0 ≤ _x340 − 1 ∧ 0 ≤ _x339 − 1 ∧ 3 ≤ _x338 − 1 ∧ −1 ≤ _x328 − 1 ∧ 3 ≤ _x325 − 1 ∧ _x340 − 1 ≤ _x328 ∧ _x340 + 3 ≤ _x325 ∧ _x339 − 1 ≤ _x328 ∧ _x339 + 3 ≤ _x325 ∧ _x338 − 1 ≤ _x325 ∧ _x331 ≤ 1073741823 ∧ 0 ≤ 2⋅_x331 ∧ _x333 ≤ _x332 ∧ 1 ≤ _x331 − 1 ∧ _x327 ≤ _x331 − 1 f3804_0_put_NULL 15 f4328_0_transfer_GE: x1 = _x351 ∧ x2 = _x352 ∧ x3 = _x353 ∧ x4 = _x354 ∧ x5 = _x355 ∧ x6 = _x356 ∧ x7 = _x357 ∧ x8 = _x358 ∧ x9 = _x359 ∧ x10 = _x360 ∧ x11 = _x361 ∧ x12 = _x362 ∧ x13 = _x363 ∧ x1 = _x364 ∧ x2 = _x365 ∧ x3 = _x366 ∧ x4 = _x367 ∧ x5 = _x368 ∧ x6 = _x369 ∧ x7 = _x370 ∧ x8 = _x371 ∧ x9 = _x372 ∧ x10 = _x373 ∧ x11 = _x374 ∧ x12 = _x375 ∧ x13 = _x376 ∧ _x357 = _x371 ∧ 2⋅_x357 = _x370 ∧ _x359 = _x369 ∧ _x358 + 1 = _x368 ∧ 0 = _x367 ∧ _x359 + 3 ≤ _x351 ∧ _x358 + 3 ≤ _x351 ∧ 0 ≤ _x366 − 1 ∧ 0 ≤ _x365 − 1 ∧ 3 ≤ _x364 − 1 ∧ −1 ≤ _x354 − 1 ∧ 3 ≤ _x351 − 1 ∧ _x366 − 1 ≤ _x354 ∧ _x366 + 3 ≤ _x351 ∧ _x365 − 1 ≤ _x354 ∧ _x365 + 3 ≤ _x351 ∧ _x364 − 1 ≤ _x351 ∧ _x359 ≤ _x358 ∧ 0 ≤ 2⋅_x357 ∧ 1073741824 ≤ _x357 − 1 ∧ _x353 ≤ _x357 − 1 f4328_0_transfer_GE 16 f4423_0_transfer_ArrayAccess: x1 = _x377 ∧ x2 = _x378 ∧ x3 = _x379 ∧ x4 = _x380 ∧ x5 = _x381 ∧ x6 = _x382 ∧ x7 = _x383 ∧ x8 = _x384 ∧ x9 = _x385 ∧ x10 = _x386 ∧ x11 = _x387 ∧ x12 = _x388 ∧ x13 = _x389 ∧ x1 = _x390 ∧ x2 = _x391 ∧ x3 = _x392 ∧ x4 = _x393 ∧ x5 = _x394 ∧ x6 = _x395 ∧ x7 = _x396 ∧ x8 = _x397 ∧ x9 = _x398 ∧ x10 = _x399 ∧ x11 = _x400 ∧ x12 = _x401 ∧ x13 = _x402 ∧ _x383 = _x402 ∧ _x384 = _x399 ∧ _x382 = _x398 ∧ _x381 = _x397 ∧ _x380 = _x392 ∧ _x382 + 3 ≤ _x377 ∧ _x381 + 3 ≤ _x377 ∧ 0 ≤ _x395 − 1 ∧ 0 ≤ _x394 − 1 ∧ −1 ≤ _x393 − 1 ∧ 0 ≤ _x391 − 1 ∧ 3 ≤ _x390 − 1 ∧ 0 ≤ _x379 − 1 ∧ 0 ≤ _x378 − 1 ∧ 3 ≤ _x377 − 1 ∧ _x395 ≤ _x379 ∧ _x395 ≤ _x378 ∧ _x395 + 3 ≤ _x377 ∧ _x391 ≤ _x379 ∧ _x391 ≤ _x378 ∧ _x391 + 3 ≤ _x377 ∧ _x390 ≤ _x377 ∧ _x380 ≤ _x384 − 1 ∧ 0 ≤ _x383 − 1 f4423_0_transfer_ArrayAccess 17 f4423_0_transfer_ArrayAccess: 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 ∧ x1 = _x416 ∧ x2 = _x417 ∧ x3 = _x418 ∧ x4 = _x419 ∧ x5 = _x420 ∧ x6 = _x421 ∧ x7 = _x422 ∧ x8 = _x423 ∧ x9 = _x424 ∧ x10 = _x425 ∧ x11 = _x426 ∧ x12 = _x427 ∧ x13 = _x428 ∧ _x415 = _x428 ∧ _x412 = _x425 ∧ _x411 = _x424 ∧ _x410 = _x423 ∧ _x405 = _x418 ∧ _x414 + 2 ≤ _x407 ∧ _x427 + 4 ≤ _x407 ∧ _x426 + 4 ≤ _x407 ∧ _x413 + 2 ≤ _x407 ∧ _x427 + 2 ≤ _x406 ∧ _x426 + 2 ≤ _x406 ∧ _x411 + 3 ≤ _x403 ∧ _x410 + 3 ≤ _x403 ∧ 0 ≤ _x421 − 1 ∧ 0 ≤ _x420 − 1 ∧ −1 ≤ _x419 − 1 ∧ 0 ≤ _x417 − 1 ∧ 3 ≤ _x416 − 1 ∧ 0 ≤ _x408 − 1 ∧ 2 ≤ _x407 − 1 ∧ 0 ≤ _x406 − 1 ∧ 0 ≤ _x404 − 1 ∧ 3 ≤ _x403 − 1 ∧ _x421 ≤ _x408 ∧ _x421 + 2 ≤ _x407 ∧ _x421 ≤ _x406 ∧ _x421 ≤ _x404 ∧ _x421 + 3 ≤ _x403 ∧ _x420 + 2 ≤ _x407 ∧ _x420 ≤ _x406 ∧ _x419 + 3 ≤ _x407 ∧ _x419 + 1 ≤ _x406 ∧ _x417 ≤ _x408 ∧ _x417 + 2 ≤ _x407 ∧ _x417 ≤ _x406 ∧ _x417 ≤ _x404 ∧ _x417 + 3 ≤ _x403 ∧ _x416 ≤ _x403 ∧ 0 ≤ _x415 − 1 ∧ _x409 ≤ _x415 − 1 f4328_0_transfer_GE 18 f4328_0_transfer_GE: x1 = _x429 ∧ x2 = _x430 ∧ x3 = _x431 ∧ x4 = _x432 ∧ x5 = _x433 ∧ x6 = _x434 ∧ x7 = _x435 ∧ x8 = _x436 ∧ x9 = _x437 ∧ x10 = _x438 ∧ x11 = _x439 ∧ x12 = _x440 ∧ x13 = _x441 ∧ x1 = _x442 ∧ x2 = _x443 ∧ x3 = _x444 ∧ x4 = _x445 ∧ x5 = _x446 ∧ x6 = _x447 ∧ x7 = _x448 ∧ x8 = _x449 ∧ x9 = _x450 ∧ x10 = _x451 ∧ x11 = _x452 ∧ x12 = _x453 ∧ x13 = _x454 ∧ _x436 = _x449 ∧ _x435 = _x448 ∧ _x434 = _x447 ∧ _x433 = _x446 ∧ _x432 + 1 = _x445 ∧ _x434 + 3 ≤ _x429 ∧ _x433 + 3 ≤ _x429 ∧ 0 ≤ _x444 − 1 ∧ 0 ≤ _x443 − 1 ∧ 3 ≤ _x442 − 1 ∧ 0 ≤ _x431 − 1 ∧ 0 ≤ _x430 − 1 ∧ 3 ≤ _x429 − 1 ∧ _x444 ≤ _x431 ∧ _x444 ≤ _x430 ∧ _x444 + 3 ≤ _x429 ∧ _x443 ≤ _x431 ∧ _x443 ≤ _x430 ∧ _x443 + 3 ≤ _x429 ∧ _x442 ≤ _x429 ∧ _x432 ≤ _x436 − 1 ∧ −1 ≤ _x436 − 1 f4423_0_transfer_ArrayAccess 19 f4328_0_transfer_GE: x1 = _x455 ∧ x2 = _x456 ∧ x3 = _x457 ∧ x4 = _x458 ∧ x5 = _x459 ∧ x6 = _x460 ∧ x7 = _x461 ∧ x8 = _x462 ∧ x9 = _x463 ∧ x10 = _x464 ∧ x11 = _x465 ∧ x12 = _x466 ∧ x13 = _x467 ∧ x1 = _x468 ∧ x2 = _x469 ∧ x3 = _x470 ∧ x4 = _x471 ∧ x5 = _x472 ∧ x6 = _x473 ∧ x7 = _x474 ∧ x8 = _x475 ∧ x9 = _x476 ∧ x10 = _x477 ∧ x11 = _x478 ∧ x12 = _x479 ∧ x13 = _x480 ∧ _x464 = _x475 ∧ _x467 = _x474 ∧ _x463 = _x473 ∧ _x462 = _x472 ∧ _x457 + 1 = _x471 ∧ _x466 + 2 ≤ _x459 ∧ _x465 + 2 ≤ _x459 ∧ _x463 + 3 ≤ _x455 ∧ _x462 + 3 ≤ _x455 ∧ 0 ≤ _x470 − 1 ∧ 0 ≤ _x469 − 1 ∧ 3 ≤ _x468 − 1 ∧ 0 ≤ _x460 − 1 ∧ 1 ≤ _x459 − 1 ∧ −1 ≤ _x458 − 1 ∧ 0 ≤ _x456 − 1 ∧ 3 ≤ _x455 − 1 ∧ _x470 ≤ _x460 ∧ _x470 + 1 ≤ _x459 ∧ _x470 − 1 ≤ _x458 ∧ _x470 ≤ _x456 ∧ _x470 + 3 ≤ _x455 ∧ _x469 ≤ _x460 ∧ _x469 + 1 ≤ _x459 ∧ _x469 − 1 ≤ _x458 ∧ _x469 ≤ _x456 ∧ _x469 + 3 ≤ _x455 ∧ _x468 ≤ _x455 ∧ _x461 ≤ _x467 − 1 ∧ −1 ≤ _x464 − 1 __init 20 f1_0_main_Load: x1 = _x481 ∧ x2 = _x482 ∧ x3 = _x483 ∧ x4 = _x484 ∧ x5 = _x485 ∧ x6 = _x486 ∧ x7 = _x487 ∧ x8 = _x488 ∧ x9 = _x489 ∧ x10 = _x490 ∧ x11 = _x491 ∧ x12 = _x492 ∧ x13 = _x493 ∧ x1 = _x494 ∧ x2 = _x495 ∧ x3 = _x496 ∧ x4 = _x497 ∧ x5 = _x498 ∧ x6 = _x499 ∧ x7 = _x500 ∧ x8 = _x501 ∧ x9 = _x502 ∧ x10 = _x503 ∧ x11 = _x504 ∧ x12 = _x505 ∧ x13 = _x506 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f4423_0_transfer_ArrayAccess f4423_0_transfer_ArrayAccess f4423_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 f3804_0_put_NULL f3804_0_put_NULL f3804_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 f3882_0_put_EQ f3882_0_put_EQ f3882_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 f3248_0_createMap_LE f3248_0_createMap_LE f3248_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 f4328_0_transfer_GE f4328_0_transfer_GE f4328_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 f517_0_createMap_Return f517_0_createMap_Return f517_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 f3559_0_clear_GE f3559_0_clear_GE f3559_0_clear_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 __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
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 { f3248_0_createMap_LE }.

### 2.1.1 Transition Removal

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

 f3248_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 { f3804_0_put_NULL, f3882_0_put_EQ }.

### 2.2.1 Transition Removal

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

 f3804_0_put_NULL: 1 + x4 f3882_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 { f4423_0_transfer_ArrayAccess, f4328_0_transfer_GE }.

### 2.3.1 Transition Removal

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

 f4328_0_transfer_GE: −1 − x4 + 2⋅x8 f4423_0_transfer_ArrayAccess: −1 − x3 + 2⋅x10

### 2.3.2 Transition Removal

We remove transition 16 using the following ranking functions, which are bounded by 0.

 f4328_0_transfer_GE: −1 − x4 + x7 + x8 f4423_0_transfer_ArrayAccess: −2 − x3 + x10 + x13

### 2.3.3 Transition Removal

We remove transitions 19, 17 using the following ranking functions, which are bounded by 0.

 f4423_0_transfer_ArrayAccess: x4 f4328_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 { f3559_0_clear_GE }.

### 2.4.1 Transition Removal

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

 f3559_0_clear_GE: − x3 + x6

### 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)