LTS Termination Proof

by AProVE

Input

Integer Transition System
• Initial Location: f1596_0_createTree_LE, f97_0_createTree_NE, f1014_0_mirror_InvokeMethod, f179_0_createNode_Return, f674_0_createTree_Return, __init, f101_0_main_InvokeMethod, f1562_0_createTree_FieldAccess, f1475_0_main_InvokeMethod, f727_0_mirror_NONNULL, f1_0_main_Load, f1514_0_createTree_NONNULL, f1650_0_createTree_FieldAccess, f1458_0_createTree_LE
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f101_0_main_InvokeMethod: x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x7 = _arg7 ∧ x8 = _arg8 ∧ x9 = _arg9 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ x7 = _arg7P ∧ x8 = _arg8P ∧ x9 = _arg9P ∧ 0 = _arg3P ∧ 0 = _arg2P ∧ 0 = _arg2 ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg1P ≤ _arg1 f1_0_main_Load 2 f101_0_main_InvokeMethod: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ x4 = _x12 ∧ x5 = _x13 ∧ x6 = _x14 ∧ x7 = _x15 ∧ x8 = _x16 ∧ x9 = _x17 ∧ _x1 = _x11 ∧ 1 = _x10 ∧ 0 ≤ _x9 − 1 ∧ 0 ≤ _x − 1 ∧ _x9 ≤ _x f101_0_main_InvokeMethod 3 f727_0_mirror_NONNULL: x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x4 = _x21 ∧ x5 = _x22 ∧ x6 = _x23 ∧ x7 = _x24 ∧ x8 = _x25 ∧ x9 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ x4 = _x30 ∧ x5 = _x31 ∧ x6 = _x32 ∧ x7 = _x33 ∧ x8 = _x34 ∧ x9 = _x35 ∧ −1 ≤ _x27 − 1 ∧ 0 ≤ _x18 − 1 ∧ _x19 ≤ 1 ∧ _x27 + 1 ≤ _x18 f1_0_main_Load 4 f1475_0_main_InvokeMethod: x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x4 = _x39 ∧ x5 = _x40 ∧ x6 = _x41 ∧ x7 = _x42 ∧ x8 = _x43 ∧ x9 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ x4 = _x48 ∧ x5 = _x49 ∧ x6 = _x50 ∧ x7 = _x51 ∧ x8 = _x52 ∧ x9 = _x53 ∧ 0 ≤ _x46 − 1 ∧ 0 ≤ _x45 − 1 ∧ 0 ≤ _x36 − 1 ∧ _x45 ≤ _x36 f674_0_createTree_Return 5 f1475_0_main_InvokeMethod: x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x4 = _x57 ∧ x5 = _x58 ∧ x6 = _x59 ∧ x7 = _x60 ∧ x8 = _x61 ∧ x9 = _x62 ∧ x1 = _x63 ∧ x2 = _x64 ∧ x3 = _x65 ∧ x4 = _x66 ∧ x5 = _x67 ∧ x6 = _x68 ∧ x7 = _x69 ∧ x8 = _x70 ∧ x9 = _x71 ∧ _x56 = _x65 ∧ _x56 + 2 ≤ _x55 ∧ 1 ≤ _x64 − 1 ∧ 0 ≤ _x63 − 1 ∧ 1 ≤ _x55 − 1 ∧ 0 ≤ _x54 − 1 ∧ _x64 ≤ _x55 ∧ _x63 + 1 ≤ _x55 ∧ _x63 ≤ _x54 f1475_0_main_InvokeMethod 6 f727_0_mirror_NONNULL: x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x6 = _x77 ∧ x7 = _x78 ∧ x8 = _x79 ∧ x9 = _x80 ∧ x1 = _x81 ∧ x2 = _x82 ∧ x3 = _x83 ∧ x4 = _x84 ∧ x5 = _x85 ∧ x6 = _x86 ∧ x7 = _x87 ∧ x8 = _x88 ∧ x9 = _x89 ∧ _x74 + 2 ≤ _x73 ∧ 0 ≤ _x81 − 1 ∧ 0 ≤ _x73 − 1 ∧ 0 ≤ _x72 − 1 ∧ _x81 ≤ _x73 f1_0_main_Load 7 f97_0_createTree_NE: x1 = _x90 ∧ x2 = _x91 ∧ x3 = _x92 ∧ x4 = _x93 ∧ x5 = _x94 ∧ x6 = _x95 ∧ x7 = _x96 ∧ x8 = _x97 ∧ x9 = _x98 ∧ x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x101 ∧ x4 = _x102 ∧ x5 = _x103 ∧ x6 = _x104 ∧ x7 = _x105 ∧ x8 = _x106 ∧ x9 = _x107 ∧ _x91 = _x100 ∧ 0 = _x99 ∧ 0 ≤ _x91 − 1 ∧ 0 ≤ _x90 − 1 f1_0_main_Load 8 f97_0_createTree_NE: x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x4 = _x111 ∧ x5 = _x112 ∧ x6 = _x113 ∧ x7 = _x114 ∧ x8 = _x115 ∧ x9 = _x116 ∧ x1 = _x117 ∧ x2 = _x118 ∧ x3 = _x119 ∧ x4 = _x120 ∧ x5 = _x121 ∧ x6 = _x122 ∧ x7 = _x123 ∧ x8 = _x124 ∧ x9 = _x125 ∧ _x109 = _x118 ∧ 0 ≤ _x108 − 1 ∧ 0 ≤ _x109 − 1 ∧ −1 ≤ _x117 − 1 f97_0_createTree_NE 9 f1458_0_createTree_LE: x1 = _x126 ∧ x2 = _x127 ∧ x3 = _x128 ∧ x4 = _x129 ∧ x5 = _x130 ∧ x6 = _x131 ∧ x7 = _x132 ∧ x8 = _x133 ∧ x9 = _x134 ∧ x1 = _x135 ∧ x2 = _x136 ∧ x3 = _x137 ∧ x4 = _x138 ∧ x5 = _x139 ∧ x6 = _x140 ∧ x7 = _x141 ∧ x8 = _x142 ∧ x9 = _x143 ∧ 1 = _x139 ∧ _x127 = _x138 ∧ _x126 = _x137 ∧ 1 ≤ _x135 − 1 ∧ 1 ≤ _x136 − 1 ∧ 0 ≤ _x127 − 1 ∧ 0 ≤ _x126 − 1 f97_0_createTree_NE 10 f1458_0_createTree_LE: x1 = _x144 ∧ x2 = _x145 ∧ x3 = _x146 ∧ x4 = _x147 ∧ x5 = _x148 ∧ x6 = _x149 ∧ x7 = _x150 ∧ x8 = _x151 ∧ x9 = _x152 ∧ x1 = _x153 ∧ x2 = _x154 ∧ x3 = _x155 ∧ x4 = _x156 ∧ x5 = _x157 ∧ x6 = _x158 ∧ x7 = _x159 ∧ x8 = _x160 ∧ x9 = _x161 ∧ _x145 = _x156 ∧ _x144 = _x155 ∧ 1 ≤ _x153 − 1 ∧ 1 ≤ _x154 − 1 ∧ 0 ≤ _x145 − 1 ∧ 0 ≤ _x144 − 1 f179_0_createNode_Return 11 f1458_0_createTree_LE: x1 = _x162 ∧ x2 = _x163 ∧ x3 = _x164 ∧ x4 = _x165 ∧ x5 = _x166 ∧ x6 = _x167 ∧ x7 = _x168 ∧ x8 = _x169 ∧ x9 = _x170 ∧ x1 = _x171 ∧ x2 = _x172 ∧ x3 = _x173 ∧ x4 = _x174 ∧ x5 = _x175 ∧ x6 = _x176 ∧ x7 = _x177 ∧ x8 = _x178 ∧ x9 = _x179 ∧ _x164 = _x175 ∧ _x163 = _x174 ∧ _x162 = _x173 ∧ 1 ≤ _x171 − 1 ∧ 1 ≤ _x172 − 1 f1458_0_createTree_LE 12 f1514_0_createTree_NONNULL: x1 = _x180 ∧ x2 = _x181 ∧ x3 = _x182 ∧ x4 = _x183 ∧ x5 = _x184 ∧ x6 = _x185 ∧ x7 = _x186 ∧ x8 = _x187 ∧ x9 = _x188 ∧ x1 = _x189 ∧ x2 = _x190 ∧ x3 = _x191 ∧ x4 = _x192 ∧ x5 = _x193 ∧ x6 = _x194 ∧ x7 = _x195 ∧ x8 = _x196 ∧ x9 = _x197 ∧ _x184 = _x194 ∧ _x183 = _x193 ∧ _x182 = _x189 ∧ _x197 + 2 ≤ _x181 ∧ _x196 + 2 ≤ _x180 ∧ _x195 + 2 ≤ _x180 ∧ −1 ≤ _x192 − 1 ∧ 0 ≤ _x191 − 1 ∧ 0 ≤ _x190 − 1 ∧ 0 ≤ _x181 − 1 ∧ 0 ≤ _x180 − 1 ∧ _x192 + 1 ≤ _x181 ∧ _x191 ≤ _x181 ∧ _x190 ≤ _x180 ∧ 0 ≤ _x182 − 1 ∧ −1 ≤ _x183 − 1 ∧ _x183 ≤ _x184 f1514_0_createTree_NONNULL 13 f1458_0_createTree_LE: x1 = _x198 ∧ x2 = _x199 ∧ x3 = _x200 ∧ x4 = _x201 ∧ x5 = _x202 ∧ x6 = _x203 ∧ x7 = _x204 ∧ x8 = _x205 ∧ x9 = _x206 ∧ x1 = _x207 ∧ x2 = _x208 ∧ x3 = _x209 ∧ x4 = _x210 ∧ x5 = _x211 ∧ x6 = _x212 ∧ x7 = _x213 ∧ x8 = _x214 ∧ x9 = _x215 ∧ _x203 = _x211 ∧ _x202 = _x210 ∧ _x198 − 1 = _x209 ∧ _x206 + 2 ≤ _x200 ∧ _x205 + 2 ≤ _x199 ∧ _x204 + 2 ≤ _x199 ∧ 0 ≤ _x208 − 1 ∧ 0 ≤ _x207 − 1 ∧ 0 ≤ _x201 − 1 ∧ 2 ≤ _x200 − 1 ∧ 0 ≤ _x199 − 1 ∧ _x208 ≤ _x201 ∧ _x208 + 2 ≤ _x200 ∧ _x207 ≤ _x199 f1514_0_createTree_NONNULL 14 f1562_0_createTree_FieldAccess: x1 = _x216 ∧ x2 = _x217 ∧ x3 = _x218 ∧ x4 = _x219 ∧ x5 = _x220 ∧ x6 = _x221 ∧ x7 = _x222 ∧ x8 = _x223 ∧ x9 = _x224 ∧ x1 = _x225 ∧ x2 = _x226 ∧ x3 = _x227 ∧ x4 = _x228 ∧ x5 = _x229 ∧ x6 = _x230 ∧ x7 = _x231 ∧ x8 = _x232 ∧ x9 = _x233 ∧ _x224 = _x231 ∧ _x223 = _x230 ∧ _x221 = _x229 ∧ _x220 = _x228 ∧ _x216 = _x225 ∧ _x224 + 2 ≤ _x218 ∧ _x223 + 2 ≤ _x217 ∧ _x222 + 2 ≤ _x217 ∧ 1 ≤ _x227 − 1 ∧ 0 ≤ _x226 − 1 ∧ −1 ≤ _x219 − 1 ∧ 1 ≤ _x218 − 1 ∧ 0 ≤ _x217 − 1 ∧ _x227 ≤ _x218 ∧ _x226 ≤ _x217 ∧ 0 ≤ _x216 − 1 ∧ _x220 ≤ _x221 f1514_0_createTree_NONNULL 15 f1562_0_createTree_FieldAccess: x1 = _x234 ∧ x2 = _x235 ∧ x3 = _x236 ∧ x4 = _x237 ∧ x5 = _x238 ∧ x6 = _x239 ∧ x7 = _x240 ∧ x8 = _x241 ∧ x9 = _x242 ∧ x1 = _x243 ∧ x2 = _x244 ∧ x3 = _x245 ∧ x4 = _x246 ∧ x5 = _x247 ∧ x6 = _x248 ∧ x7 = _x249 ∧ x8 = _x250 ∧ x9 = _x251 ∧ _x242 = _x249 ∧ _x241 = _x248 ∧ _x238 = _x246 ∧ _x234 = _x243 ∧ _x242 + 2 ≤ _x236 ∧ _x241 + 2 ≤ _x235 ∧ _x240 + 2 ≤ _x235 ∧ 1 ≤ _x245 − 1 ∧ 0 ≤ _x244 − 1 ∧ −1 ≤ _x237 − 1 ∧ 1 ≤ _x236 − 1 ∧ 0 ≤ _x235 − 1 ∧ _x245 ≤ _x236 ∧ _x244 ≤ _x235 ∧ 0 ≤ _x234 − 1 ∧ _x238 ≤ _x239 f1458_0_createTree_LE 16 f1596_0_createTree_LE: x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ x8 = _x259 ∧ x9 = _x260 ∧ x1 = _x261 ∧ x2 = _x262 ∧ x3 = _x263 ∧ x4 = _x264 ∧ x5 = _x265 ∧ x6 = _x266 ∧ x7 = _x267 ∧ x8 = _x268 ∧ x9 = _x269 ∧ _x256 + 1 = _x266 ∧ _x255 = _x265 ∧ 0 = _x264 ∧ _x254 = _x261 ∧ _x268 + 2 ≤ _x252 ∧ _x267 + 2 ≤ _x252 ∧ 0 ≤ _x263 − 1 ∧ 0 ≤ _x262 − 1 ∧ 0 ≤ _x253 − 1 ∧ 0 ≤ _x252 − 1 ∧ _x263 ≤ _x253 ∧ _x262 ≤ _x252 ∧ −1 ≤ _x256 − 1 ∧ _x256 ≤ _x255 − 1 ∧ −1 ≤ _x255 − 1 ∧ 0 ≤ _x254 − 1 f1458_0_createTree_LE 17 f1596_0_createTree_LE: x1 = _x270 ∧ x2 = _x271 ∧ x3 = _x272 ∧ x4 = _x273 ∧ x5 = _x274 ∧ x6 = _x275 ∧ x7 = _x276 ∧ x8 = _x277 ∧ x9 = _x278 ∧ x1 = _x279 ∧ x2 = _x280 ∧ x3 = _x281 ∧ x4 = _x282 ∧ x5 = _x283 ∧ x6 = _x284 ∧ x7 = _x285 ∧ x8 = _x286 ∧ x9 = _x287 ∧ _x274 + 1 = _x284 ∧ _x273 = _x283 ∧ _x272 = _x279 ∧ _x286 + 2 ≤ _x270 ∧ _x285 + 2 ≤ _x270 ∧ 0 ≤ _x281 − 1 ∧ 0 ≤ _x280 − 1 ∧ 0 ≤ _x271 − 1 ∧ 0 ≤ _x270 − 1 ∧ _x281 ≤ _x271 ∧ _x280 ≤ _x270 ∧ −1 ≤ _x282 − 1 ∧ −1 ≤ _x274 − 1 ∧ _x274 ≤ _x273 − 1 ∧ −1 ≤ _x273 − 1 ∧ 0 ≤ _x272 − 1 f1562_0_createTree_FieldAccess 18 f1458_0_createTree_LE: x1 = _x288 ∧ x2 = _x289 ∧ x3 = _x290 ∧ x4 = _x291 ∧ x5 = _x292 ∧ x6 = _x293 ∧ x7 = _x294 ∧ x8 = _x295 ∧ x9 = _x296 ∧ x1 = _x297 ∧ x2 = _x298 ∧ x3 = _x299 ∧ x4 = _x300 ∧ x5 = _x301 ∧ x6 = _x302 ∧ x7 = _x303 ∧ x8 = _x304 ∧ x9 = _x305 ∧ _x292 = _x301 ∧ _x291 = _x300 ∧ _x288 − 1 = _x299 ∧ _x294 + 2 ≤ _x290 ∧ _x293 + 2 ≤ _x289 ∧ 0 ≤ _x298 − 1 ∧ 0 ≤ _x297 − 1 ∧ 1 ≤ _x290 − 1 ∧ 0 ≤ _x289 − 1 f1562_0_createTree_FieldAccess 19 f1458_0_createTree_LE: x1 = _x306 ∧ x2 = _x307 ∧ x3 = _x308 ∧ x4 = _x309 ∧ x5 = _x310 ∧ x6 = _x311 ∧ x7 = _x312 ∧ x8 = _x313 ∧ x9 = _x314 ∧ x1 = _x315 ∧ x2 = _x316 ∧ x3 = _x317 ∧ x4 = _x318 ∧ x5 = _x319 ∧ x6 = _x320 ∧ x7 = _x321 ∧ x8 = _x322 ∧ x9 = _x323 ∧ _x310 = _x319 ∧ _x309 = _x318 ∧ _x306 − 1 = _x317 ∧ _x311 = _x312 ∧ _x311 + 2 ≤ _x308 ∧ _x311 + 2 ≤ _x307 ∧ 3 ≤ _x316 − 1 ∧ 3 ≤ _x315 − 1 ∧ 1 ≤ _x308 − 1 ∧ 1 ≤ _x307 − 1 ∧ _x316 − 2 ≤ _x308 ∧ _x316 − 2 ≤ _x307 ∧ _x315 − 2 ≤ _x308 ∧ _x315 − 2 ≤ _x307 f1596_0_createTree_LE 20 f1514_0_createTree_NONNULL: x1 = _x324 ∧ x2 = _x325 ∧ x3 = _x326 ∧ x4 = _x327 ∧ x5 = _x328 ∧ x6 = _x329 ∧ x7 = _x330 ∧ x8 = _x331 ∧ x9 = _x332 ∧ x1 = _x333 ∧ x2 = _x334 ∧ x3 = _x335 ∧ x4 = _x336 ∧ x5 = _x337 ∧ x6 = _x338 ∧ x7 = _x339 ∧ x8 = _x340 ∧ x9 = _x341 ∧ _x331 = _x340 ∧ _x330 = _x339 ∧ _x329 = _x338 ∧ _x328 = _x337 ∧ _x324 = _x333 ∧ 0 = _x327 ∧ _x341 + 2 ≤ _x326 ∧ _x331 + 2 ≤ _x325 ∧ _x330 + 2 ≤ _x325 ∧ −1 ≤ _x336 − 1 ∧ 0 ≤ _x335 − 1 ∧ 0 ≤ _x334 − 1 ∧ 0 ≤ _x326 − 1 ∧ 0 ≤ _x325 − 1 ∧ _x336 + 1 ≤ _x326 ∧ _x335 ≤ _x326 ∧ _x334 ≤ _x325 f1596_0_createTree_LE 21 f1458_0_createTree_LE: x1 = _x342 ∧ x2 = _x343 ∧ x3 = _x344 ∧ x4 = _x345 ∧ x5 = _x346 ∧ x6 = _x347 ∧ x7 = _x348 ∧ x8 = _x349 ∧ x9 = _x350 ∧ x1 = _x351 ∧ x2 = _x352 ∧ x3 = _x353 ∧ x4 = _x354 ∧ x5 = _x355 ∧ x6 = _x356 ∧ x7 = _x357 ∧ x8 = _x358 ∧ x9 = _x359 ∧ _x347 = _x355 ∧ _x346 = _x354 ∧ _x342 − 1 = _x353 ∧ _x349 + 2 ≤ _x343 ∧ _x348 + 2 ≤ _x343 ∧ 0 ≤ _x352 − 1 ∧ 0 ≤ _x351 − 1 ∧ 2 ≤ _x344 − 1 ∧ 0 ≤ _x343 − 1 ∧ _x352 + 2 ≤ _x344 ∧ 0 ≤ _x345 − 1 ∧ _x351 ≤ _x343 f1596_0_createTree_LE 22 f1650_0_createTree_FieldAccess: x1 = _x360 ∧ x2 = _x361 ∧ x3 = _x362 ∧ x4 = _x363 ∧ x5 = _x364 ∧ x6 = _x365 ∧ x7 = _x366 ∧ x8 = _x367 ∧ x9 = _x368 ∧ x1 = _x369 ∧ x2 = _x370 ∧ x3 = _x371 ∧ x4 = _x372 ∧ x5 = _x373 ∧ x6 = _x374 ∧ x7 = _x375 ∧ x8 = _x376 ∧ x9 = _x377 ∧ _x366 = _x374 ∧ _x365 = _x373 ∧ _x364 = _x372 ∧ _x360 = _x369 ∧ _x375 + 2 ≤ _x362 ∧ _x367 + 2 ≤ _x361 ∧ _x366 + 2 ≤ _x361 ∧ 1 ≤ _x371 − 1 ∧ 0 ≤ _x370 − 1 ∧ 1 ≤ _x362 − 1 ∧ 0 ≤ _x361 − 1 ∧ _x371 ≤ _x362 ∧ _x370 ≤ _x361 ∧ 0 ≤ _x360 − 1 ∧ 0 ≤ _x365 − 1 ∧ 0 ≤ _x363 − 1 f1596_0_createTree_LE 23 f1650_0_createTree_FieldAccess: x1 = _x378 ∧ x2 = _x379 ∧ x3 = _x380 ∧ x4 = _x381 ∧ x5 = _x382 ∧ x6 = _x383 ∧ x7 = _x384 ∧ x8 = _x385 ∧ x9 = _x386 ∧ x1 = _x387 ∧ x2 = _x388 ∧ x3 = _x389 ∧ x4 = _x390 ∧ x5 = _x391 ∧ x6 = _x392 ∧ x7 = _x393 ∧ x8 = _x394 ∧ x9 = _x395 ∧ _x384 = _x392 ∧ _x382 = _x390 ∧ _x378 = _x387 ∧ _x393 + 2 ≤ _x380 ∧ _x385 + 2 ≤ _x379 ∧ _x384 + 2 ≤ _x379 ∧ 1 ≤ _x389 − 1 ∧ 0 ≤ _x388 − 1 ∧ 1 ≤ _x380 − 1 ∧ 0 ≤ _x379 − 1 ∧ _x389 ≤ _x380 ∧ _x388 ≤ _x379 ∧ 0 ≤ _x378 − 1 ∧ 0 ≤ _x383 − 1 ∧ 0 ≤ _x381 − 1 f1650_0_createTree_FieldAccess 24 f1458_0_createTree_LE: x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x5 = _x400 ∧ x6 = _x401 ∧ x7 = _x402 ∧ x8 = _x403 ∧ x9 = _x404 ∧ x1 = _x405 ∧ x2 = _x406 ∧ x3 = _x407 ∧ x4 = _x408 ∧ x5 = _x409 ∧ x6 = _x410 ∧ x7 = _x411 ∧ x8 = _x412 ∧ x9 = _x413 ∧ _x400 = _x409 ∧ _x399 = _x408 ∧ _x396 − 1 = _x407 ∧ _x402 + 2 ≤ _x398 ∧ _x401 + 2 ≤ _x397 ∧ 0 ≤ _x406 − 1 ∧ 0 ≤ _x405 − 1 ∧ 1 ≤ _x398 − 1 ∧ 0 ≤ _x397 − 1 f1650_0_createTree_FieldAccess 25 f1458_0_createTree_LE: x1 = _x414 ∧ x2 = _x415 ∧ x3 = _x416 ∧ x4 = _x417 ∧ x5 = _x418 ∧ x6 = _x419 ∧ x7 = _x420 ∧ x8 = _x421 ∧ x9 = _x422 ∧ x1 = _x423 ∧ x2 = _x424 ∧ x3 = _x425 ∧ x4 = _x426 ∧ x5 = _x427 ∧ x6 = _x428 ∧ x7 = _x429 ∧ x8 = _x430 ∧ x9 = _x431 ∧ _x418 = _x427 ∧ _x417 = _x426 ∧ _x414 − 1 = _x425 ∧ _x419 = _x420 ∧ _x419 + 2 ≤ _x416 ∧ _x419 + 2 ≤ _x415 ∧ 3 ≤ _x424 − 1 ∧ 3 ≤ _x423 − 1 ∧ 1 ≤ _x416 − 1 ∧ 1 ≤ _x415 − 1 ∧ _x424 − 2 ≤ _x416 ∧ _x424 − 2 ≤ _x415 ∧ _x423 − 2 ≤ _x416 ∧ _x423 − 2 ≤ _x415 f727_0_mirror_NONNULL 26 f727_0_mirror_NONNULL: x1 = _x432 ∧ x2 = _x433 ∧ x3 = _x434 ∧ x4 = _x435 ∧ x5 = _x436 ∧ x6 = _x437 ∧ x7 = _x438 ∧ x8 = _x439 ∧ x9 = _x440 ∧ x1 = _x441 ∧ x2 = _x442 ∧ x3 = _x443 ∧ x4 = _x444 ∧ x5 = _x445 ∧ x6 = _x446 ∧ x7 = _x447 ∧ x8 = _x448 ∧ x9 = _x449 ∧ −1 ≤ _x441 − 1 ∧ 0 ≤ _x432 − 1 ∧ _x441 + 1 ≤ _x432 f727_0_mirror_NONNULL 27 f727_0_mirror_NONNULL: x1 = _x450 ∧ x2 = _x451 ∧ x3 = _x452 ∧ x4 = _x453 ∧ x5 = _x454 ∧ x6 = _x455 ∧ x7 = _x456 ∧ x8 = _x457 ∧ x9 = _x458 ∧ x1 = _x459 ∧ x2 = _x460 ∧ x3 = _x461 ∧ x4 = _x462 ∧ x5 = _x463 ∧ x6 = _x464 ∧ x7 = _x465 ∧ x8 = _x466 ∧ x9 = _x467 ∧ −1 ≤ _x459 − 1 ∧ 1 ≤ _x450 − 1 ∧ _x459 + 2 ≤ _x450 f727_0_mirror_NONNULL 28 f1014_0_mirror_InvokeMethod: x1 = _x468 ∧ x2 = _x469 ∧ x3 = _x470 ∧ x4 = _x471 ∧ x5 = _x472 ∧ x6 = _x473 ∧ x7 = _x474 ∧ x8 = _x475 ∧ x9 = _x476 ∧ x1 = _x477 ∧ x2 = _x478 ∧ x3 = _x479 ∧ x4 = _x480 ∧ x5 = _x481 ∧ x6 = _x482 ∧ x7 = _x483 ∧ x8 = _x484 ∧ x9 = _x485 ∧ −1 ≤ _x480 − 1 ∧ −1 ≤ _x478 − 1 ∧ 4 ≤ _x477 − 1 ∧ 0 ≤ _x468 − 1 ∧ _x480 + 1 ≤ _x468 ∧ _x478 + 1 ≤ _x468 f727_0_mirror_NONNULL 29 f1014_0_mirror_InvokeMethod: x1 = _x486 ∧ x2 = _x487 ∧ x3 = _x488 ∧ x4 = _x489 ∧ x5 = _x490 ∧ x6 = _x491 ∧ x7 = _x492 ∧ x8 = _x493 ∧ x9 = _x494 ∧ x1 = _x495 ∧ x2 = _x496 ∧ x3 = _x497 ∧ x4 = _x498 ∧ x5 = _x499 ∧ x6 = _x500 ∧ x7 = _x501 ∧ x8 = _x502 ∧ x9 = _x503 ∧ −1 ≤ _x498 − 1 ∧ −1 ≤ _x496 − 1 ∧ 3 ≤ _x495 − 1 ∧ 0 ≤ _x486 − 1 ∧ _x498 + 1 ≤ _x486 ∧ _x496 + 1 ≤ _x486 ∧ _x495 − 3 ≤ _x486 f1014_0_mirror_InvokeMethod 30 f727_0_mirror_NONNULL: x1 = _x504 ∧ x2 = _x505 ∧ x3 = _x506 ∧ x4 = _x507 ∧ x5 = _x508 ∧ x6 = _x509 ∧ x7 = _x510 ∧ x8 = _x511 ∧ x9 = _x512 ∧ x1 = _x513 ∧ x2 = _x514 ∧ x3 = _x515 ∧ x4 = _x516 ∧ x5 = _x517 ∧ x6 = _x518 ∧ x7 = _x519 ∧ x8 = _x520 ∧ x9 = _x521 ∧ −1 ≤ _x513 − 1 ∧ −1 ≤ _x507 − 1 ∧ −1 ≤ _x505 − 1 ∧ 2 ≤ _x504 − 1 ∧ _x513 ≤ _x507 ∧ _x513 ≤ _x505 ∧ _x513 + 2 ≤ _x504 f97_0_createTree_NE 31 f554_0_random_GT: x1 = _x522 ∧ x2 = _x523 ∧ x3 = _x524 ∧ x4 = _x525 ∧ x5 = _x526 ∧ x6 = _x527 ∧ x7 = _x528 ∧ x8 = _x529 ∧ x9 = _x530 ∧ x1 = _x531 ∧ x2 = _x532 ∧ x3 = _x533 ∧ x4 = _x534 ∧ x5 = _x535 ∧ x6 = _x536 ∧ x7 = _x537 ∧ x8 = _x538 ∧ x9 = _x539 ∧ 1 = _x533 ∧ _x523 = _x532 ∧ 0 ≤ _x522 − 1 ∧ 0 ≤ _x523 − 1 f1514_0_createTree_NONNULL 32 f554_0_random_GT: x1 = _x540 ∧ x2 = _x541 ∧ x3 = _x542 ∧ x4 = _x543 ∧ x5 = _x544 ∧ x6 = _x545 ∧ x7 = _x546 ∧ x8 = _x547 ∧ x9 = _x548 ∧ x1 = _x549 ∧ x2 = _x550 ∧ x3 = _x551 ∧ x4 = _x552 ∧ x5 = _x553 ∧ x6 = _x554 ∧ x7 = _x555 ∧ x8 = _x556 ∧ x9 = _x557 ∧ _x545 = _x551 ∧ _x544 = _x550 ∧ _x548 + 2 ≤ _x542 ∧ _x547 + 2 ≤ _x541 ∧ _x546 + 2 ≤ _x541 ∧ −1 ≤ _x543 − 1 ∧ 1 ≤ _x542 − 1 ∧ 0 ≤ _x541 − 1 ∧ 0 ≤ _x540 − 1 ∧ _x544 ≤ _x545 ∧ −1 ≤ _x544 − 1 f1596_0_createTree_LE 33 f554_0_random_GT: x1 = _x558 ∧ x2 = _x559 ∧ x3 = _x560 ∧ x4 = _x561 ∧ x5 = _x562 ∧ x6 = _x563 ∧ x7 = _x564 ∧ x8 = _x565 ∧ x9 = _x566 ∧ x1 = _x567 ∧ x2 = _x568 ∧ x3 = _x569 ∧ x4 = _x570 ∧ x5 = _x571 ∧ x6 = _x572 ∧ x7 = _x573 ∧ x8 = _x574 ∧ x9 = _x575 ∧ _x563 = _x569 ∧ _x562 = _x568 ∧ _x565 + 2 ≤ _x559 ∧ _x564 + 2 ≤ _x559 ∧ 1 ≤ _x560 − 1 ∧ 0 ≤ _x559 − 1 ∧ 0 ≤ _x561 − 1 ∧ −1 ≤ _x562 − 1 ∧ 0 ≤ _x563 − 1 ∧ 0 ≤ _x558 − 1 __init 34 f1_0_main_Load: x1 = _x576 ∧ x2 = _x577 ∧ x3 = _x578 ∧ x4 = _x579 ∧ x5 = _x580 ∧ x6 = _x581 ∧ x7 = _x582 ∧ x8 = _x583 ∧ x9 = _x584 ∧ x1 = _x585 ∧ x2 = _x586 ∧ x3 = _x587 ∧ x4 = _x588 ∧ x5 = _x589 ∧ x6 = _x590 ∧ x7 = _x591 ∧ x8 = _x592 ∧ x9 = _x593 ∧ 0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f1596_0_createTree_LE f1596_0_createTree_LE f1596_0_createTree_LE: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f97_0_createTree_NE f97_0_createTree_NE f97_0_createTree_NE: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f1014_0_mirror_InvokeMethod f1014_0_mirror_InvokeMethod f1014_0_mirror_InvokeMethod: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f179_0_createNode_Return f179_0_createNode_Return f179_0_createNode_Return: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f674_0_createTree_Return f674_0_createTree_Return f674_0_createTree_Return: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 __init __init __init: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f101_0_main_InvokeMethod f101_0_main_InvokeMethod f101_0_main_InvokeMethod: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f1562_0_createTree_FieldAccess f1562_0_createTree_FieldAccess f1562_0_createTree_FieldAccess: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f1475_0_main_InvokeMethod f1475_0_main_InvokeMethod f1475_0_main_InvokeMethod: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f727_0_mirror_NONNULL f727_0_mirror_NONNULL f727_0_mirror_NONNULL: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 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 f1514_0_createTree_NONNULL f1514_0_createTree_NONNULL f1514_0_createTree_NONNULL: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f1650_0_createTree_FieldAccess f1650_0_createTree_FieldAccess f1650_0_createTree_FieldAccess: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 f1458_0_createTree_LE f1458_0_createTree_LE f1458_0_createTree_LE: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
and for every transition t, a duplicate t is considered.

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 { f1596_0_createTree_LE, f1514_0_createTree_NONNULL, f1650_0_createTree_FieldAccess, f1458_0_createTree_LE, f1562_0_createTree_FieldAccess }.

2.1.1 Transition Removal

We remove transitions 12, 16, 17 using the following ranking functions, which are bounded by 0.

 f1458_0_createTree_LE: −1 + x3 + x4 f1514_0_createTree_NONNULL: −2 + x1 + x5 f1596_0_createTree_LE: −2 + x1 + x5 f1650_0_createTree_FieldAccess: −2 + x1 + x4 f1562_0_createTree_FieldAccess: −2 + x1 + x4

2.1.2 Transition Removal

We remove transitions 13, 20, 21, 25, 24, 23, 22, 19, 18, 15, 14 using the following ranking functions, which are bounded by 0.

 f1514_0_createTree_NONNULL: 2 f1458_0_createTree_LE: 0 f1596_0_createTree_LE: 3 f1650_0_createTree_FieldAccess: 1 f1562_0_createTree_FieldAccess: 1

2.1.3 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 { f1014_0_mirror_InvokeMethod, f727_0_mirror_NONNULL }.

2.2.1 Transition Removal

We remove transitions 26, 27, 30, 29, 28 using the following ranking functions, which are bounded by 0.

 f727_0_mirror_NONNULL: 2⋅x1 f1014_0_mirror_InvokeMethod: 2⋅x2 + 1

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 % (9 real / 0 unknown / 0 assumptions / 9 total proof steps)