# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: f532_0_createMap_Return, f5950_0_nextEntry_GE, f5790_0_hasNext_NULL, f4279_0_createMap_LE, f5935_0_transfer_ArrayAccess, f4729_0__init__LE, f5797_0_transfer_GE, f4900_0_put_NULL, f1_0_main_Load, f4935_0__init__GE, __init, f5022_0_put_EQ
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f4729_0__init__LE: 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 ∧ 5 ≤ _arg1P − 1 ∧ 3 ≤ _arg2P − 1 ∧ 0 = _arg3P f532_0_createMap_Return 2 f4729_0__init__LE: 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 = _x19 ∧ 16 = _x18 ∧ _x1 = _x17 ∧ 0 = _x16 ∧ 12 = _x3 ∧ 16 = _x2 ∧ _x1 + 3 ≤ _x ∧ 14 ≤ _x15 − 1 ∧ 16 ≤ _x14 − 1 ∧ 14 ≤ _x − 1 ∧ _x15 ≤ _x ∧ _x14 − 2 ≤ _x f4729_0__init__LE 3 f4935_0__init__GE: x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ x4 = _x30 ∧ x5 = _x31 ∧ x6 = _x32 ∧ x7 = _x33 ∧ x8 = _x34 ∧ x9 = _x35 ∧ x10 = _x36 ∧ x11 = _x37 ∧ x12 = _x38 ∧ x13 = _x39 ∧ x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x7 = _x46 ∧ x8 = _x47 ∧ x9 = _x48 ∧ x10 = _x49 ∧ x11 = _x50 ∧ x12 = _x51 ∧ x13 = _x52 ∧ _x31 = _x45 ∧ _x32 = _x44 ∧ _x30 = _x43 ∧ 0 = _x42 ∧ 0 = _x29 ∧ _x32 + 3 ≤ _x28 ∧ _x30 + 3 ≤ _x28 ∧ _x32 + 5 ≤ _x27 ∧ _x30 + 5 ≤ _x27 ∧ 0 ≤ _x41 − 1 ∧ 5 ≤ _x40 − 1 ∧ 3 ≤ _x28 − 1 ∧ 5 ≤ _x27 − 1 ∧ _x41 + 3 ≤ _x28 ∧ _x41 + 5 ≤ _x27 ∧ _x40 − 2 ≤ _x28 ∧ _x40 ≤ _x27 ∧ −1 ≤ _x31 − 1 ∧ 0 ≤ _x30 − 1 f4935_0__init__GE 4 f4935_0__init__GE: x1 = _x53 ∧ x2 = _x54 ∧ x3 = _x55 ∧ x4 = _x56 ∧ x5 = _x57 ∧ x6 = _x58 ∧ x7 = _x59 ∧ x8 = _x60 ∧ x9 = _x61 ∧ x10 = _x62 ∧ x11 = _x63 ∧ x12 = _x64 ∧ x13 = _x65 ∧ x1 = _x66 ∧ x2 = _x67 ∧ x3 = _x68 ∧ x4 = _x69 ∧ x5 = _x70 ∧ x6 = _x71 ∧ x7 = _x72 ∧ x8 = _x73 ∧ x9 = _x74 ∧ x10 = _x75 ∧ x11 = _x76 ∧ x12 = _x77 ∧ x13 = _x78 ∧ _x58 = _x71 ∧ _x57 = _x70 ∧ _x56 = _x69 ∧ _x55 + 1 = _x68 ∧ _x57 + 5 ≤ _x53 ∧ _x56 + 5 ≤ _x53 ∧ _x55 + 2 ≤ _x53 ∧ 0 ≤ _x67 − 1 ∧ 5 ≤ _x66 − 1 ∧ 0 ≤ _x54 − 1 ∧ 5 ≤ _x53 − 1 ∧ _x67 ≤ _x54 ∧ _x67 + 5 ≤ _x53 ∧ _x66 − 1 ≤ _x53 ∧ −1 ≤ _x58 − 1 ∧ −1 ≤ _x55 − 1 ∧ _x55 ≤ _x58 − 1 f4935_0__init__GE 5 f5790_0_hasNext_NULL: x1 = _x79 ∧ x2 = _x80 ∧ x3 = _x81 ∧ x4 = _x82 ∧ x5 = _x83 ∧ x6 = _x84 ∧ x7 = _x85 ∧ x8 = _x86 ∧ x9 = _x87 ∧ x10 = _x88 ∧ x11 = _x89 ∧ x12 = _x90 ∧ x13 = _x91 ∧ x1 = _x92 ∧ x2 = _x93 ∧ x3 = _x94 ∧ x4 = _x95 ∧ x5 = _x96 ∧ x6 = _x97 ∧ x7 = _x100 ∧ x8 = _x101 ∧ x9 = _x102 ∧ x10 = _x103 ∧ x11 = _x104 ∧ x12 = _x105 ∧ x13 = _x106 ∧ _x83 = _x97 ∧ _x84 = _x96 ∧ _x82 = _x95 ∧ _x81 = _x94 ∧ _x83 + 5 ≤ _x79 ∧ _x82 + 5 ≤ _x79 ∧ _x81 + 2 ≤ _x79 ∧ −1 ≤ _x93 − 1 ∧ 5 ≤ _x92 − 1 ∧ 0 ≤ _x80 − 1 ∧ 5 ≤ _x79 − 1 ∧ _x93 + 1 ≤ _x80 ∧ _x93 + 6 ≤ _x79 ∧ _x84 ≤ _x81 ∧ _x92 ≤ _x79 f4935_0__init__GE 6 f5790_0_hasNext_NULL: x1 = _x107 ∧ x2 = _x108 ∧ x3 = _x109 ∧ x4 = _x110 ∧ x5 = _x113 ∧ x6 = _x114 ∧ x7 = _x115 ∧ x8 = _x116 ∧ x9 = _x117 ∧ x10 = _x118 ∧ x11 = _x119 ∧ x12 = _x120 ∧ x13 = _x121 ∧ x1 = _x122 ∧ x2 = _x123 ∧ x3 = _x124 ∧ x4 = _x125 ∧ x5 = _x126 ∧ x6 = _x127 ∧ x7 = _x128 ∧ x8 = _x129 ∧ x9 = _x130 ∧ x10 = _x131 ∧ x11 = _x132 ∧ x12 = _x133 ∧ x13 = _x134 ∧ _x113 = _x127 ∧ _x114 = _x126 ∧ _x110 = _x125 ∧ _x109 + 1 = _x124 ∧ _x113 + 5 ≤ _x107 ∧ _x110 + 5 ≤ _x107 ∧ _x109 + 2 ≤ _x107 ∧ 0 ≤ _x123 − 1 ∧ 5 ≤ _x122 − 1 ∧ 0 ≤ _x108 − 1 ∧ 5 ≤ _x107 − 1 ∧ −1 ≤ _x109 − 1 ∧ _x109 ≤ _x114 − 1 f5790_0_hasNext_NULL 7 f5950_0_nextEntry_GE: x1 = _x135 ∧ x2 = _x136 ∧ x3 = _x137 ∧ x4 = _x138 ∧ x5 = _x139 ∧ x6 = _x140 ∧ x7 = _x141 ∧ x8 = _x142 ∧ x9 = _x143 ∧ x10 = _x144 ∧ x11 = _x145 ∧ x12 = _x146 ∧ x13 = _x147 ∧ x1 = _x148 ∧ x2 = _x149 ∧ x3 = _x151 ∧ x4 = _x152 ∧ x5 = _x153 ∧ x6 = _x154 ∧ x7 = _x155 ∧ x8 = _x156 ∧ x9 = _x157 ∧ x10 = _x158 ∧ x11 = _x159 ∧ x12 = _x160 ∧ x13 = _x161 ∧ _x139 = _x154 ∧ _x140 = _x153 ∧ _x138 = _x152 ∧ _x137 = _x151 ∧ _x140 + 5 ≤ _x135 ∧ _x138 + 5 ≤ _x135 ∧ _x137 + 2 ≤ _x135 ∧ 0 ≤ _x149 − 1 ∧ 5 ≤ _x148 − 1 ∧ 1 ≤ _x136 − 1 ∧ 5 ≤ _x135 − 1 ∧ _x149 + 1 ≤ _x136 ∧ _x149 + 5 ≤ _x135 ∧ −1 ≤ _x139 − 1 ∧ _x148 ≤ _x135 f5790_0_hasNext_NULL 8 f5790_0_hasNext_NULL: x1 = _x162 ∧ x2 = _x163 ∧ x3 = _x164 ∧ x4 = _x165 ∧ x5 = _x166 ∧ x6 = _x167 ∧ x7 = _x168 ∧ x8 = _x169 ∧ x9 = _x170 ∧ x10 = _x171 ∧ x11 = _x172 ∧ x12 = _x173 ∧ x13 = _x174 ∧ x1 = _x175 ∧ x2 = _x176 ∧ x3 = _x177 ∧ x4 = _x178 ∧ x5 = _x179 ∧ x6 = _x180 ∧ x7 = _x181 ∧ x8 = _x182 ∧ x9 = _x183 ∧ x10 = _x184 ∧ x11 = _x185 ∧ x12 = _x186 ∧ x13 = _x187 ∧ _x167 = _x180 ∧ _x166 = _x179 ∧ _x165 = _x178 ∧ _x164 = _x177 ∧ _x167 + 5 ≤ _x162 ∧ _x165 + 5 ≤ _x162 ∧ _x164 + 2 ≤ _x162 ∧ 0 ≤ _x176 − 1 ∧ 5 ≤ _x175 − 1 ∧ 2 ≤ _x163 − 1 ∧ 5 ≤ _x162 − 1 ∧ _x176 + 2 ≤ _x163 ∧ _x176 + 4 ≤ _x162 ∧ _x175 ≤ _x162 f5950_0_nextEntry_GE 9 f5790_0_hasNext_NULL: x1 = _x188 ∧ x2 = _x189 ∧ x3 = _x190 ∧ x4 = _x191 ∧ x5 = _x192 ∧ x6 = _x193 ∧ x7 = _x194 ∧ x8 = _x195 ∧ x9 = _x196 ∧ x10 = _x197 ∧ x11 = _x198 ∧ x12 = _x199 ∧ x13 = _x200 ∧ x1 = _x201 ∧ x2 = _x202 ∧ x3 = _x203 ∧ x4 = _x204 ∧ x5 = _x205 ∧ x6 = _x206 ∧ x7 = _x207 ∧ x8 = _x208 ∧ x9 = _x209 ∧ x10 = _x210 ∧ x11 = _x211 ∧ x12 = _x212 ∧ x13 = _x213 ∧ _x192 = _x206 ∧ _x193 = _x205 ∧ _x191 = _x204 ∧ _x190 = _x203 ∧ _x192 + 5 ≤ _x188 ∧ _x191 + 5 ≤ _x188 ∧ _x190 + 2 ≤ _x188 ∧ −1 ≤ _x202 − 1 ∧ 5 ≤ _x201 − 1 ∧ 0 ≤ _x189 − 1 ∧ 5 ≤ _x188 − 1 ∧ _x202 + 1 ≤ _x189 ∧ _x202 + 6 ≤ _x188 ∧ _x193 ≤ _x190 ∧ _x201 ≤ _x188 f5950_0_nextEntry_GE 10 f5950_0_nextEntry_GE: x1 = _x214 ∧ x2 = _x215 ∧ x3 = _x216 ∧ x4 = _x217 ∧ x5 = _x218 ∧ x6 = _x219 ∧ x7 = _x220 ∧ x8 = _x221 ∧ x9 = _x222 ∧ x10 = _x223 ∧ x11 = _x224 ∧ x12 = _x225 ∧ x13 = _x226 ∧ x1 = _x227 ∧ x2 = _x228 ∧ x3 = _x229 ∧ x4 = _x230 ∧ x5 = _x231 ∧ x6 = _x232 ∧ x7 = _x233 ∧ x8 = _x234 ∧ x9 = _x235 ∧ x10 = _x236 ∧ x11 = _x237 ∧ x12 = _x238 ∧ x13 = _x239 ∧ _x219 = _x232 ∧ _x218 = _x231 ∧ _x217 = _x230 ∧ _x216 + 1 = _x229 ∧ _x218 + 5 ≤ _x214 ∧ _x217 + 5 ≤ _x214 ∧ _x216 + 2 ≤ _x214 ∧ 0 ≤ _x228 − 1 ∧ 5 ≤ _x227 − 1 ∧ 0 ≤ _x215 − 1 ∧ 5 ≤ _x214 − 1 ∧ _x228 ≤ _x215 ∧ _x228 + 5 ≤ _x214 ∧ _x227 − 1 ≤ _x214 ∧ _x216 ≤ _x219 − 1 ∧ −1 ≤ _x219 − 1 f5950_0_nextEntry_GE 11 f5790_0_hasNext_NULL: 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 ∧ x1 = _x253 ∧ x2 = _x254 ∧ x3 = _x255 ∧ x4 = _x256 ∧ x5 = _x257 ∧ x6 = _x258 ∧ x7 = _x259 ∧ x8 = _x260 ∧ x9 = _x261 ∧ x10 = _x262 ∧ x11 = _x263 ∧ x12 = _x264 ∧ x13 = _x265 ∧ _x244 = _x258 ∧ _x245 = _x257 ∧ _x243 = _x256 ∧ _x242 + 1 = _x255 ∧ _x244 + 5 ≤ _x240 ∧ _x243 + 5 ≤ _x240 ∧ _x242 + 2 ≤ _x240 ∧ 0 ≤ _x254 − 1 ∧ 5 ≤ _x253 − 1 ∧ 0 ≤ _x241 − 1 ∧ _x242 ≤ _x245 − 1 ∧ 5 ≤ _x240 − 1 f1_0_main_Load 12 f4279_0_createMap_LE: 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 ∧ x1 = _x279 ∧ x2 = _x280 ∧ x3 = _x281 ∧ x4 = _x282 ∧ x5 = _x283 ∧ x6 = _x284 ∧ x7 = _x286 ∧ x8 = _x287 ∧ x9 = _x288 ∧ x10 = _x289 ∧ x11 = _x290 ∧ x12 = _x291 ∧ x13 = _x292 ∧ 12 = _x286 ∧ 16 = _x284 ∧ 0 = _x283 ∧ 1 = _x282 ∧ _x267 = _x281 ∧ 14 ≤ _x279 − 1 ∧ 0 ≤ _x266 − 1 ∧ _x279 − 14 ≤ _x266 ∧ 0 ≤ _x267 − 1 ∧ −1 ≤ _x280 − 1 f4279_0_createMap_LE 13 f4279_0_createMap_LE: x1 = _x293 ∧ x2 = _x294 ∧ x3 = _x295 ∧ x4 = _x296 ∧ x5 = _x297 ∧ x6 = _x298 ∧ x7 = _x299 ∧ x8 = _x300 ∧ x9 = _x301 ∧ x10 = _x302 ∧ x11 = _x303 ∧ x12 = _x304 ∧ x13 = _x305 ∧ x1 = _x306 ∧ x2 = _x307 ∧ x3 = _x308 ∧ x4 = _x309 ∧ x5 = _x310 ∧ x6 = _x311 ∧ x7 = _x312 ∧ x8 = _x313 ∧ x9 = _x314 ∧ x10 = _x315 ∧ x11 = _x316 ∧ x12 = _x317 ∧ x13 = _x318 ∧ 0 ≤ _x294 − 1 ∧ _x296 + 1 ≤ _x295 − 1 ∧ −1 ≤ _x295 − 1 ∧ −1 ≤ _x296 − 1 ∧ −1 ≤ _x319 − 1 ∧ −1 ≤ _x320 − 1 ∧ 1 ≤ _x298 − 1 ∧ 3 ≤ _x293 − 1 ∧ 3 ≤ _x306 − 1 ∧ _x297 + 3 ≤ _x293 ∧ _x299 + 3 ≤ _x293 ∧ _x294 − 1 = _x307 ∧ _x295 = _x308 ∧ _x296 + 2 = _x309 f4279_0_createMap_LE 14 f4900_0_put_NULL: x1 = _x321 ∧ x2 = _x322 ∧ x3 = _x323 ∧ x4 = _x324 ∧ x5 = _x325 ∧ x6 = _x326 ∧ x7 = _x327 ∧ x8 = _x328 ∧ x9 = _x329 ∧ x10 = _x330 ∧ x11 = _x331 ∧ x12 = _x332 ∧ x13 = _x333 ∧ x1 = _x334 ∧ x2 = _x335 ∧ x3 = _x336 ∧ x4 = _x337 ∧ x5 = _x338 ∧ x6 = _x339 ∧ x7 = _x340 ∧ x8 = _x341 ∧ x9 = _x342 ∧ x10 = _x343 ∧ x11 = _x344 ∧ x12 = _x345 ∧ x13 = _x346 ∧ _x324 + 1 ≤ _x323 − 1 ∧ 1 ≤ _x326 − 1 ∧ 0 ≤ _x322 − 1 ∧ −1 ≤ _x323 − 1 ∧ −1 ≤ _x324 − 1 ∧ −1 ≤ _x347 − 1 ∧ −1 ≤ _x348 − 1 ∧ _x336 ≤ _x326 − 1 ∧ _x334 ≤ _x321 ∧ 3 ≤ _x321 − 1 ∧ 3 ≤ _x334 − 1 ∧ −1 ≤ _x337 − 1 ∧ _x325 + 3 ≤ _x321 ∧ _x327 + 3 ≤ _x321 ∧ _x323 = _x338 ∧ _x324 + 2 = _x339 ∧ _x325 = _x340 ∧ _x326 = _x341 ∧ _x327 = _x342 f4900_0_put_NULL 15 f5022_0_put_EQ: x1 = _x349 ∧ x2 = _x350 ∧ x3 = _x351 ∧ x4 = _x352 ∧ x5 = _x353 ∧ x6 = _x354 ∧ x7 = _x355 ∧ x8 = _x356 ∧ x9 = _x357 ∧ x10 = _x358 ∧ x11 = _x359 ∧ x12 = _x360 ∧ x13 = _x361 ∧ x1 = _x362 ∧ x2 = _x363 ∧ x3 = _x364 ∧ x4 = _x365 ∧ x5 = _x366 ∧ x6 = _x367 ∧ x7 = _x368 ∧ x8 = _x369 ∧ x9 = _x370 ∧ x10 = _x371 ∧ x11 = _x372 ∧ x12 = _x373 ∧ x13 = _x374 ∧ _x350 = _x371 ∧ _x357 = _x368 ∧ _x356 = _x367 ∧ _x355 = _x366 ∧ 0 = _x365 ∧ _x351 = _x363 ∧ _x370 + 4 ≤ _x352 ∧ _x350 + 2 ≤ _x352 ∧ _x357 + 3 ≤ _x349 ∧ _x355 + 3 ≤ _x349 ∧ −1 ≤ _x369 − 1 ∧ 2 ≤ _x364 − 1 ∧ 3 ≤ _x362 − 1 ∧ 2 ≤ _x352 − 1 ∧ 3 ≤ _x349 − 1 ∧ _x369 + 2 ≤ _x352 ∧ _x364 ≤ _x352 ∧ 1 ≤ _x356 − 1 ∧ _x362 ≤ _x349 f4900_0_put_NULL 16 f5022_0_put_EQ: x1 = _x375 ∧ x2 = _x376 ∧ x3 = _x377 ∧ x4 = _x378 ∧ x5 = _x379 ∧ x6 = _x380 ∧ x7 = _x381 ∧ x8 = _x382 ∧ x9 = _x383 ∧ x10 = _x384 ∧ x11 = _x385 ∧ x12 = _x386 ∧ x13 = _x387 ∧ x1 = _x388 ∧ x2 = _x389 ∧ x3 = _x390 ∧ x4 = _x391 ∧ x5 = _x392 ∧ x6 = _x393 ∧ x7 = _x394 ∧ x8 = _x395 ∧ x9 = _x396 ∧ x10 = _x397 ∧ x11 = _x398 ∧ x12 = _x399 ∧ x13 = _x400 ∧ _x376 = _x397 ∧ _x383 = _x394 ∧ _x382 = _x393 ∧ _x381 = _x392 ∧ 1 = _x391 ∧ _x377 = _x389 ∧ _x396 + 4 ≤ _x378 ∧ _x376 + 2 ≤ _x378 ∧ _x383 + 3 ≤ _x375 ∧ _x381 + 3 ≤ _x375 ∧ −1 ≤ _x395 − 1 ∧ 2 ≤ _x390 − 1 ∧ 3 ≤ _x388 − 1 ∧ 2 ≤ _x378 − 1 ∧ 3 ≤ _x375 − 1 ∧ _x395 + 2 ≤ _x378 ∧ _x390 ≤ _x378 ∧ 1 ≤ _x382 − 1 ∧ _x388 ≤ _x375 f4900_0_put_NULL 17 f4900_0_put_NULL: x1 = _x401 ∧ x2 = _x402 ∧ x3 = _x403 ∧ x4 = _x404 ∧ x5 = _x405 ∧ x6 = _x406 ∧ x7 = _x407 ∧ x8 = _x408 ∧ x9 = _x409 ∧ x10 = _x410 ∧ x11 = _x411 ∧ x12 = _x412 ∧ x13 = _x413 ∧ x1 = _x414 ∧ x2 = _x415 ∧ x3 = _x416 ∧ x4 = _x417 ∧ x5 = _x418 ∧ x6 = _x419 ∧ x7 = _x420 ∧ x8 = _x421 ∧ x9 = _x422 ∧ x10 = _x423 ∧ x11 = _x424 ∧ x12 = _x425 ∧ x13 = _x426 ∧ _x414 ≤ _x401 ∧ _x427 ≤ _x402 − 1 ∧ _x417 + 1 ≤ _x404 ∧ 3 ≤ _x401 − 1 ∧ 0 ≤ _x404 − 1 ∧ 3 ≤ _x414 − 1 ∧ −1 ≤ _x417 − 1 ∧ _x407 + 3 ≤ _x401 ∧ _x409 + 3 ≤ _x401 ∧ _x402 = _x415 ∧ _x403 = _x416 ∧ _x405 = _x418 ∧ _x406 = _x419 ∧ _x407 = _x420 ∧ _x408 = _x421 ∧ _x409 = _x422 f4900_0_put_NULL 18 f4900_0_put_NULL: 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 ∧ x1 = _x441 ∧ x2 = _x442 ∧ x3 = _x443 ∧ x4 = _x444 ∧ x5 = _x445 ∧ x6 = _x446 ∧ x7 = _x447 ∧ x8 = _x448 ∧ x9 = _x449 ∧ x10 = _x450 ∧ x11 = _x451 ∧ x12 = _x452 ∧ x13 = _x453 ∧ _x441 ≤ _x428 ∧ _x429 ≤ _x454 − 1 ∧ _x444 + 1 ≤ _x431 ∧ 3 ≤ _x428 − 1 ∧ 0 ≤ _x431 − 1 ∧ 3 ≤ _x441 − 1 ∧ −1 ≤ _x444 − 1 ∧ _x434 + 3 ≤ _x428 ∧ _x436 + 3 ≤ _x428 ∧ _x429 = _x442 ∧ _x430 = _x443 ∧ _x432 = _x445 ∧ _x433 = _x446 ∧ _x434 = _x447 ∧ _x435 = _x448 ∧ _x436 = _x449 f4900_0_put_NULL 19 f4900_0_put_NULL: 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 ∧ _x463 = _x476 ∧ _x462 = _x475 ∧ _x461 = _x474 ∧ _x460 = _x473 ∧ _x459 = _x472 ∧ _x457 = _x470 ∧ _x456 = _x469 ∧ _x456 + 2 ≤ _x458 ∧ _x463 + 3 ≤ _x455 ∧ _x461 + 3 ≤ _x455 ∧ −1 ≤ _x471 − 1 ∧ 3 ≤ _x468 − 1 ∧ 1 ≤ _x458 − 1 ∧ 3 ≤ _x455 − 1 ∧ _x471 + 2 ≤ _x458 ∧ 1 ≤ _x462 − 1 ∧ _x468 ≤ _x455 f4900_0_put_NULL 20 f4900_0_put_NULL: 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 ∧ _x489 = _x502 ∧ _x488 = _x501 ∧ _x487 = _x500 ∧ _x486 = _x499 ∧ _x485 = _x498 ∧ _x483 = _x496 ∧ _x482 = _x495 ∧ _x482 + 2 ≤ _x484 ∧ _x489 + 3 ≤ _x481 ∧ _x487 + 3 ≤ _x481 ∧ −1 ≤ _x497 − 1 ∧ 3 ≤ _x494 − 1 ∧ 2 ≤ _x484 − 1 ∧ 3 ≤ _x481 − 1 ∧ _x497 + 2 ≤ _x484 ∧ 1 ≤ _x488 − 1 ∧ _x494 ≤ _x481 f5022_0_put_EQ 21 f4900_0_put_NULL: x1 = _x507 ∧ x2 = _x508 ∧ x3 = _x509 ∧ x4 = _x510 ∧ x5 = _x511 ∧ x6 = _x512 ∧ x7 = _x513 ∧ x8 = _x514 ∧ x9 = _x515 ∧ x10 = _x516 ∧ x11 = _x517 ∧ x12 = _x518 ∧ x13 = _x519 ∧ x1 = _x520 ∧ x2 = _x521 ∧ x3 = _x522 ∧ x4 = _x523 ∧ x5 = _x524 ∧ x6 = _x525 ∧ x7 = _x526 ∧ x8 = _x527 ∧ x9 = _x528 ∧ x10 = _x529 ∧ x11 = _x530 ∧ x12 = _x531 ∧ x13 = _x532 ∧ _x513 = _x528 ∧ _x512 = _x527 ∧ _x511 = _x526 ∧ _x508 = _x522 ∧ _x516 = _x521 ∧ 0 = _x510 ∧ _x516 + 2 ≤ _x509 ∧ _x515 + 4 ≤ _x509 ∧ _x513 + 3 ≤ _x507 ∧ _x511 + 3 ≤ _x507 ∧ −1 ≤ _x523 − 1 ∧ 3 ≤ _x520 − 1 ∧ −1 ≤ _x514 − 1 ∧ 2 ≤ _x509 − 1 ∧ 3 ≤ _x507 − 1 ∧ _x523 ≤ _x514 ∧ _x523 + 2 ≤ _x509 ∧ _x520 ≤ _x507 f4900_0_put_NULL 22 f5797_0_transfer_GE: x1 = _x533 ∧ x2 = _x534 ∧ x3 = _x535 ∧ x4 = _x536 ∧ x5 = _x537 ∧ x6 = _x538 ∧ x7 = _x539 ∧ x8 = _x540 ∧ x9 = _x541 ∧ x10 = _x542 ∧ x11 = _x543 ∧ x12 = _x544 ∧ x13 = _x545 ∧ x1 = _x546 ∧ x2 = _x547 ∧ x3 = _x548 ∧ x4 = _x549 ∧ x5 = _x550 ∧ x6 = _x551 ∧ x7 = _x552 ∧ x8 = _x553 ∧ x9 = _x554 ∧ x10 = _x555 ∧ x11 = _x556 ∧ x12 = _x557 ∧ x13 = _x558 ∧ _x540 = _x553 ∧ 2⋅_x540 = _x552 ∧ _x541 = _x551 ∧ _x539 + 1 = _x550 ∧ 0 = _x549 ∧ _x541 + 3 ≤ _x533 ∧ _x539 + 3 ≤ _x533 ∧ 0 ≤ _x548 − 1 ∧ 0 ≤ _x547 − 1 ∧ 3 ≤ _x546 − 1 ∧ −1 ≤ _x536 − 1 ∧ 3 ≤ _x533 − 1 ∧ _x548 − 1 ≤ _x536 ∧ _x548 + 3 ≤ _x533 ∧ _x547 − 1 ≤ _x536 ∧ _x547 + 3 ≤ _x533 ∧ _x546 − 1 ≤ _x533 ∧ _x540 ≤ 1073741823 ∧ 0 ≤ 2⋅_x540 ∧ _x541 ≤ _x539 ∧ 1 ≤ _x540 − 1 ∧ _x535 ≤ _x540 − 1 f4900_0_put_NULL 23 f5797_0_transfer_GE: x1 = _x559 ∧ x2 = _x560 ∧ x3 = _x561 ∧ x4 = _x562 ∧ x5 = _x563 ∧ x6 = _x564 ∧ x7 = _x565 ∧ x8 = _x566 ∧ x9 = _x567 ∧ x10 = _x568 ∧ x11 = _x569 ∧ x12 = _x570 ∧ x13 = _x571 ∧ x1 = _x572 ∧ x2 = _x573 ∧ x3 = _x574 ∧ x4 = _x575 ∧ x5 = _x576 ∧ x6 = _x577 ∧ x7 = _x578 ∧ x8 = _x579 ∧ x9 = _x580 ∧ x10 = _x581 ∧ x11 = _x582 ∧ x12 = _x583 ∧ x13 = _x584 ∧ _x566 = _x579 ∧ 2⋅_x566 = _x578 ∧ _x567 = _x577 ∧ _x565 + 1 = _x576 ∧ 0 = _x575 ∧ _x567 + 3 ≤ _x559 ∧ _x565 + 3 ≤ _x559 ∧ 0 ≤ _x574 − 1 ∧ 0 ≤ _x573 − 1 ∧ 3 ≤ _x572 − 1 ∧ −1 ≤ _x562 − 1 ∧ 3 ≤ _x559 − 1 ∧ _x574 − 1 ≤ _x562 ∧ _x574 + 3 ≤ _x559 ∧ _x573 − 1 ≤ _x562 ∧ _x573 + 3 ≤ _x559 ∧ _x572 − 1 ≤ _x559 ∧ _x567 ≤ _x565 ∧ 0 ≤ 2⋅_x566 ∧ 1073741824 ≤ _x566 − 1 ∧ _x561 ≤ _x566 − 1 f5797_0_transfer_GE 24 f5935_0_transfer_ArrayAccess: x1 = _x585 ∧ x2 = _x586 ∧ x3 = _x587 ∧ x4 = _x588 ∧ x5 = _x589 ∧ x6 = _x590 ∧ x7 = _x591 ∧ x8 = _x592 ∧ x9 = _x593 ∧ x10 = _x594 ∧ x11 = _x595 ∧ x12 = _x596 ∧ x13 = _x597 ∧ x1 = _x598 ∧ x2 = _x599 ∧ x3 = _x600 ∧ x4 = _x601 ∧ x5 = _x602 ∧ x6 = _x603 ∧ x7 = _x604 ∧ x8 = _x605 ∧ x9 = _x606 ∧ x10 = _x607 ∧ x11 = _x608 ∧ x12 = _x609 ∧ x13 = _x610 ∧ _x591 = _x610 ∧ _x592 = _x607 ∧ _x590 = _x606 ∧ _x589 = _x605 ∧ _x588 = _x600 ∧ _x590 + 3 ≤ _x585 ∧ _x589 + 3 ≤ _x585 ∧ 0 ≤ _x603 − 1 ∧ 0 ≤ _x602 − 1 ∧ −1 ≤ _x601 − 1 ∧ 0 ≤ _x599 − 1 ∧ 3 ≤ _x598 − 1 ∧ 0 ≤ _x587 − 1 ∧ 0 ≤ _x586 − 1 ∧ 3 ≤ _x585 − 1 ∧ _x603 ≤ _x587 ∧ _x603 ≤ _x586 ∧ _x603 + 3 ≤ _x585 ∧ _x599 ≤ _x587 ∧ _x599 ≤ _x586 ∧ _x599 + 3 ≤ _x585 ∧ _x598 ≤ _x585 ∧ _x588 ≤ _x592 − 1 ∧ 0 ≤ _x591 − 1 f5935_0_transfer_ArrayAccess 25 f5935_0_transfer_ArrayAccess: x1 = _x611 ∧ x2 = _x612 ∧ x3 = _x613 ∧ x4 = _x614 ∧ x5 = _x615 ∧ x6 = _x616 ∧ x7 = _x617 ∧ x8 = _x618 ∧ x9 = _x619 ∧ x10 = _x620 ∧ x11 = _x621 ∧ x12 = _x622 ∧ x13 = _x623 ∧ x1 = _x624 ∧ x2 = _x625 ∧ x3 = _x626 ∧ x4 = _x627 ∧ x5 = _x628 ∧ x6 = _x629 ∧ x7 = _x630 ∧ x8 = _x631 ∧ x9 = _x632 ∧ x10 = _x633 ∧ x11 = _x634 ∧ x12 = _x635 ∧ x13 = _x636 ∧ _x623 = _x636 ∧ _x620 = _x633 ∧ _x619 = _x632 ∧ _x618 = _x631 ∧ _x613 = _x626 ∧ _x622 + 2 ≤ _x615 ∧ _x621 + 2 ≤ _x615 ∧ _x635 + 4 ≤ _x615 ∧ _x634 + 4 ≤ _x615 ∧ _x635 + 2 ≤ _x614 ∧ _x634 + 2 ≤ _x614 ∧ _x619 + 3 ≤ _x611 ∧ _x618 + 3 ≤ _x611 ∧ 0 ≤ _x629 − 1 ∧ 0 ≤ _x628 − 1 ∧ −1 ≤ _x627 − 1 ∧ 0 ≤ _x625 − 1 ∧ 3 ≤ _x624 − 1 ∧ 0 ≤ _x616 − 1 ∧ 2 ≤ _x615 − 1 ∧ 0 ≤ _x614 − 1 ∧ 0 ≤ _x612 − 1 ∧ 3 ≤ _x611 − 1 ∧ _x629 ≤ _x616 ∧ _x629 + 2 ≤ _x615 ∧ _x629 ≤ _x614 ∧ _x629 ≤ _x612 ∧ _x629 + 3 ≤ _x611 ∧ _x628 + 2 ≤ _x615 ∧ _x628 ≤ _x614 ∧ _x627 + 3 ≤ _x615 ∧ _x627 + 1 ≤ _x614 ∧ _x625 ≤ _x616 ∧ _x625 + 2 ≤ _x615 ∧ _x625 ≤ _x614 ∧ _x625 ≤ _x612 ∧ _x625 + 3 ≤ _x611 ∧ _x624 ≤ _x611 ∧ 0 ≤ _x623 − 1 ∧ _x617 ≤ _x623 − 1 f5797_0_transfer_GE 26 f5797_0_transfer_GE: x1 = _x637 ∧ x2 = _x638 ∧ x3 = _x639 ∧ x4 = _x640 ∧ x5 = _x641 ∧ x6 = _x642 ∧ x7 = _x643 ∧ x8 = _x644 ∧ x9 = _x645 ∧ x10 = _x646 ∧ x11 = _x647 ∧ x12 = _x648 ∧ x13 = _x649 ∧ x1 = _x650 ∧ x2 = _x651 ∧ x3 = _x652 ∧ x4 = _x653 ∧ x5 = _x654 ∧ x6 = _x655 ∧ x7 = _x656 ∧ x8 = _x657 ∧ x9 = _x658 ∧ x10 = _x659 ∧ x11 = _x660 ∧ x12 = _x661 ∧ x13 = _x662 ∧ _x644 = _x657 ∧ _x643 = _x656 ∧ _x642 = _x655 ∧ _x641 = _x654 ∧ _x640 + 1 = _x653 ∧ _x642 + 3 ≤ _x637 ∧ _x641 + 3 ≤ _x637 ∧ 0 ≤ _x652 − 1 ∧ 0 ≤ _x651 − 1 ∧ 3 ≤ _x650 − 1 ∧ 0 ≤ _x639 − 1 ∧ 0 ≤ _x638 − 1 ∧ 3 ≤ _x637 − 1 ∧ _x652 ≤ _x639 ∧ _x652 ≤ _x638 ∧ _x652 + 3 ≤ _x637 ∧ _x651 ≤ _x639 ∧ _x651 ≤ _x638 ∧ _x651 + 3 ≤ _x637 ∧ _x650 ≤ _x637 ∧ _x640 ≤ _x644 − 1 ∧ −1 ≤ _x644 − 1 f5935_0_transfer_ArrayAccess 27 f5797_0_transfer_GE: x1 = _x663 ∧ x2 = _x664 ∧ x3 = _x665 ∧ x4 = _x666 ∧ x5 = _x667 ∧ x6 = _x668 ∧ x7 = _x669 ∧ x8 = _x670 ∧ x9 = _x671 ∧ x10 = _x672 ∧ x11 = _x673 ∧ x12 = _x674 ∧ x13 = _x675 ∧ x1 = _x676 ∧ x2 = _x677 ∧ x3 = _x678 ∧ x4 = _x679 ∧ x5 = _x680 ∧ x6 = _x681 ∧ x7 = _x682 ∧ x8 = _x683 ∧ x9 = _x684 ∧ x10 = _x685 ∧ x11 = _x686 ∧ x12 = _x687 ∧ x13 = _x688 ∧ _x672 = _x683 ∧ _x675 = _x682 ∧ _x671 = _x681 ∧ _x670 = _x680 ∧ _x665 + 1 = _x679 ∧ _x674 + 2 ≤ _x667 ∧ _x673 + 2 ≤ _x667 ∧ _x671 + 3 ≤ _x663 ∧ _x670 + 3 ≤ _x663 ∧ 0 ≤ _x678 − 1 ∧ 0 ≤ _x677 − 1 ∧ 3 ≤ _x676 − 1 ∧ 0 ≤ _x668 − 1 ∧ 1 ≤ _x667 − 1 ∧ −1 ≤ _x666 − 1 ∧ 0 ≤ _x664 − 1 ∧ 3 ≤ _x663 − 1 ∧ _x678 ≤ _x668 ∧ _x678 + 1 ≤ _x667 ∧ _x678 − 1 ≤ _x666 ∧ _x678 ≤ _x664 ∧ _x678 + 3 ≤ _x663 ∧ _x677 ≤ _x668 ∧ _x677 + 1 ≤ _x667 ∧ _x677 − 1 ≤ _x666 ∧ _x677 ≤ _x664 ∧ _x677 + 3 ≤ _x663 ∧ _x676 ≤ _x663 ∧ _x669 ≤ _x675 − 1 ∧ −1 ≤ _x672 − 1 __init 28 f1_0_main_Load: x1 = _x689 ∧ x2 = _x690 ∧ x3 = _x691 ∧ x4 = _x692 ∧ x5 = _x693 ∧ x6 = _x694 ∧ x7 = _x695 ∧ x8 = _x696 ∧ x9 = _x697 ∧ x10 = _x698 ∧ x11 = _x699 ∧ x12 = _x700 ∧ x13 = _x701 ∧ x1 = _x702 ∧ x2 = _x703 ∧ x3 = _x704 ∧ x4 = _x705 ∧ x5 = _x706 ∧ x6 = _x707 ∧ x7 = _x708 ∧ x8 = _x709 ∧ x9 = _x710 ∧ x10 = _x711 ∧ x11 = _x712 ∧ x12 = _x713 ∧ x13 = _x714 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f532_0_createMap_Return f532_0_createMap_Return f532_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 f5950_0_nextEntry_GE f5950_0_nextEntry_GE f5950_0_nextEntry_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 f5790_0_hasNext_NULL f5790_0_hasNext_NULL f5790_0_hasNext_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 f4279_0_createMap_LE f4279_0_createMap_LE f4279_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 f5935_0_transfer_ArrayAccess f5935_0_transfer_ArrayAccess f5935_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 f4729_0__init__LE f4729_0__init__LE f4729_0__init__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 f5797_0_transfer_GE f5797_0_transfer_GE f5797_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 f4900_0_put_NULL f4900_0_put_NULL f4900_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 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 f4935_0__init__GE f4935_0__init__GE f4935_0__init__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 f5022_0_put_EQ f5022_0_put_EQ f5022_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
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

We consider subproblems for each of the 5 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/5

Here we consider the SCC { f4279_0_createMap_LE }.

### 2.1.1 Transition Removal

We remove transition 13 using the following ranking functions, which are bounded by 0.

 f4279_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 2/5

Here we consider the SCC { f4900_0_put_NULL, f5022_0_put_EQ }.

### 2.2.1 Transition Removal

We remove transitions 15, 17, 18, 19, 20, 21, 16 using the following ranking functions, which are bounded by 0.

 f4900_0_put_NULL: 1 + x4 f5022_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 3/5

Here we consider the SCC { f5935_0_transfer_ArrayAccess, f5797_0_transfer_GE }.

### 2.3.1 Transition Removal

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

 f5797_0_transfer_GE: −2⋅x4 + 2⋅x8 + 1 f5935_0_transfer_ArrayAccess: −2⋅x3 + 2⋅x10

### 2.3.2 Transition Removal

We remove transition 24 using the following ranking functions, which are bounded by 0.

 f5797_0_transfer_GE: −2⋅x4 + 2⋅x8 + 2 f5935_0_transfer_ArrayAccess: −2⋅x3 + 2⋅x10 + 1

### 2.3.3 Transition Removal

We remove transitions 27, 25 using the following ranking functions, which are bounded by 0.

 f5935_0_transfer_ArrayAccess: x4 f5797_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 4/5

Here we consider the SCC { f4935_0__init__GE }.

### 2.4.1 Transition Removal

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

 f4935_0__init__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.

### 2.5 SCC Subproblem 5/5

Here we consider the SCC { f5950_0_nextEntry_GE, f5790_0_hasNext_NULL }.

### 2.5.1 Transition Removal

We remove transitions 11, 10 using the following ranking functions, which are bounded by 0.

 f5790_0_hasNext_NULL: − x3 + x5 f5950_0_nextEntry_GE: − x3 + x6

### 2.5.2 Transition Removal

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

 f5790_0_hasNext_NULL: x2 f5950_0_nextEntry_GE: x2

### 2.5.3 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 % (20 real / 0 unknown / 0 assumptions / 20 total proof steps)