# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: f2907_0_createMap_LE, f3374_0_put_NULL, f3898_0_transfer_GE, f3452_0_put_EQ, f1_0_main_Load, f3993_0_transfer_ArrayAccess, __init
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f2907_0_createMap_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 ∧ 12 = _arg7P ∧ 0 = _arg6P ∧ 16 = _arg5P ∧ 1 = _arg4P ∧ _arg2 = _arg3P ∧ 14 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg1P − 14 ≤ _arg1 ∧ 0 ≤ _arg2 − 1 ∧ −1 ≤ _arg2P − 1 f2907_0_createMap_LE 2 f2907_0_createMap_LE: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x10 = _x9 ∧ x11 = _x10 ∧ x12 = _x11 ∧ x13 = _x12 ∧ x1 = _x13 ∧ x2 = _x14 ∧ x3 = _x17 ∧ x4 = _x18 ∧ x5 = _x19 ∧ x6 = _x20 ∧ x7 = _x21 ∧ x8 = _x22 ∧ x9 = _x23 ∧ x10 = _x24 ∧ x11 = _x25 ∧ x12 = _x26 ∧ x13 = _x27 ∧ 0 ≤ _x1 − 1 ∧ _x3 + 1 ≤ _x2 − 1 ∧ −1 ≤ _x2 − 1 ∧ −1 ≤ _x3 − 1 ∧ −1 ≤ _x30 − 1 ∧ −1 ≤ _x31 − 1 ∧ 1 ≤ _x4 − 1 ∧ 3 ≤ _x − 1 ∧ 3 ≤ _x13 − 1 ∧ _x6 + 3 ≤ _x ∧ _x5 + 3 ≤ _x ∧ _x1 − 1 = _x14 ∧ _x2 = _x17 ∧ _x3 + 2 = _x18 f2907_0_createMap_LE 3 f3374_0_put_NULL: x1 = _x32 ∧ x2 = _x33 ∧ x3 = _x34 ∧ x4 = _x35 ∧ x5 = _x36 ∧ x6 = _x37 ∧ x7 = _x38 ∧ x8 = _x39 ∧ x9 = _x40 ∧ 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 ∧ _x35 + 1 ≤ _x34 − 1 ∧ 1 ≤ _x36 − 1 ∧ 0 ≤ _x33 − 1 ∧ −1 ≤ _x34 − 1 ∧ −1 ≤ _x35 − 1 ∧ −1 ≤ _x58 − 1 ∧ −1 ≤ _x59 − 1 ∧ _x47 ≤ _x36 − 1 ∧ _x45 ≤ _x32 ∧ 3 ≤ _x32 − 1 ∧ 3 ≤ _x45 − 1 ∧ −1 ≤ _x48 − 1 ∧ _x38 + 3 ≤ _x32 ∧ _x37 + 3 ≤ _x32 ∧ _x34 = _x49 ∧ _x35 + 2 = _x50 ∧ _x36 = _x51 ∧ _x37 = _x52 ∧ _x38 = _x53 f3374_0_put_NULL 4 f3452_0_put_EQ: x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x63 ∧ x5 = _x64 ∧ x6 = _x65 ∧ x7 = _x66 ∧ x8 = _x68 ∧ x9 = _x69 ∧ x10 = _x70 ∧ x11 = _x71 ∧ x12 = _x72 ∧ x13 = _x73 ∧ x1 = _x74 ∧ x2 = _x75 ∧ x3 = _x76 ∧ x4 = _x77 ∧ x5 = _x78 ∧ x6 = _x79 ∧ x7 = _x80 ∧ x8 = _x81 ∧ x9 = _x82 ∧ x10 = _x83 ∧ x11 = _x84 ∧ x12 = _x85 ∧ x13 = _x86 ∧ _x61 = _x81 ∧ _x69 = _x80 ∧ _x68 = _x79 ∧ _x66 = _x78 ∧ 0 = _x77 ∧ _x62 = _x75 ∧ _x83 + 4 ≤ _x63 ∧ _x61 + 2 ≤ _x63 ∧ _x69 + 3 ≤ _x60 ∧ _x68 + 3 ≤ _x60 ∧ −1 ≤ _x82 − 1 ∧ 2 ≤ _x76 − 1 ∧ 3 ≤ _x74 − 1 ∧ 2 ≤ _x63 − 1 ∧ 3 ≤ _x60 − 1 ∧ _x82 + 2 ≤ _x63 ∧ _x76 ≤ _x63 ∧ 1 ≤ _x66 − 1 ∧ _x74 ≤ _x60 f3374_0_put_NULL 5 f3452_0_put_EQ: x1 = _x87 ∧ x2 = _x88 ∧ x3 = _x89 ∧ x4 = _x90 ∧ x5 = _x91 ∧ x6 = _x92 ∧ x7 = _x93 ∧ x8 = _x94 ∧ x9 = _x95 ∧ x10 = _x96 ∧ x11 = _x97 ∧ x12 = _x98 ∧ x13 = _x99 ∧ x1 = _x100 ∧ x2 = _x101 ∧ x3 = _x102 ∧ x4 = _x103 ∧ x5 = _x104 ∧ x6 = _x105 ∧ x7 = _x106 ∧ x8 = _x107 ∧ x9 = _x108 ∧ x10 = _x109 ∧ x11 = _x110 ∧ x12 = _x111 ∧ x13 = _x112 ∧ _x88 = _x107 ∧ _x95 = _x106 ∧ _x94 = _x105 ∧ _x93 = _x104 ∧ 1 = _x103 ∧ _x89 = _x101 ∧ _x109 + 4 ≤ _x90 ∧ _x88 + 2 ≤ _x90 ∧ _x95 + 3 ≤ _x87 ∧ _x94 + 3 ≤ _x87 ∧ −1 ≤ _x108 − 1 ∧ 2 ≤ _x102 − 1 ∧ 3 ≤ _x100 − 1 ∧ 2 ≤ _x90 − 1 ∧ 3 ≤ _x87 − 1 ∧ _x108 + 2 ≤ _x90 ∧ _x102 ≤ _x90 ∧ 1 ≤ _x93 − 1 ∧ _x100 ≤ _x87 f3374_0_put_NULL 6 f3374_0_put_NULL: x1 = _x113 ∧ x2 = _x114 ∧ x3 = _x115 ∧ x4 = _x116 ∧ x5 = _x117 ∧ x6 = _x118 ∧ x7 = _x119 ∧ x8 = _x120 ∧ x9 = _x121 ∧ x10 = _x122 ∧ x11 = _x123 ∧ x12 = _x124 ∧ x13 = _x125 ∧ x1 = _x126 ∧ x2 = _x127 ∧ x3 = _x128 ∧ x4 = _x129 ∧ x5 = _x130 ∧ x6 = _x131 ∧ x7 = _x132 ∧ x8 = _x133 ∧ x9 = _x134 ∧ x10 = _x135 ∧ x11 = _x136 ∧ x12 = _x137 ∧ x13 = _x138 ∧ _x126 ≤ _x113 ∧ _x139 ≤ _x114 − 1 ∧ _x129 + 1 ≤ _x116 ∧ 3 ≤ _x113 − 1 ∧ 0 ≤ _x116 − 1 ∧ 3 ≤ _x126 − 1 ∧ −1 ≤ _x129 − 1 ∧ _x120 + 3 ≤ _x113 ∧ _x121 + 3 ≤ _x113 ∧ _x114 = _x127 ∧ _x115 = _x128 ∧ _x117 = _x130 ∧ _x118 = _x131 ∧ _x119 = _x132 ∧ _x120 = _x133 ∧ _x121 = _x134 f3374_0_put_NULL 7 f3374_0_put_NULL: 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 ∧ _x153 ≤ _x140 ∧ _x141 ≤ _x166 − 1 ∧ _x156 + 1 ≤ _x143 ∧ 3 ≤ _x140 − 1 ∧ 0 ≤ _x143 − 1 ∧ 3 ≤ _x153 − 1 ∧ −1 ≤ _x156 − 1 ∧ _x147 + 3 ≤ _x140 ∧ _x148 + 3 ≤ _x140 ∧ _x141 = _x154 ∧ _x142 = _x155 ∧ _x144 = _x157 ∧ _x145 = _x158 ∧ _x146 = _x159 ∧ _x147 = _x160 ∧ _x148 = _x161 f3374_0_put_NULL 8 f3374_0_put_NULL: x1 = _x167 ∧ x2 = _x168 ∧ x3 = _x169 ∧ x4 = _x170 ∧ x5 = _x171 ∧ x6 = _x172 ∧ x7 = _x173 ∧ x8 = _x174 ∧ x9 = _x175 ∧ x10 = _x176 ∧ x11 = _x177 ∧ x12 = _x178 ∧ x13 = _x179 ∧ x1 = _x180 ∧ x2 = _x181 ∧ x3 = _x182 ∧ x4 = _x183 ∧ x5 = _x184 ∧ x6 = _x185 ∧ x7 = _x186 ∧ x8 = _x187 ∧ x9 = _x188 ∧ x10 = _x189 ∧ x11 = _x190 ∧ x12 = _x191 ∧ x13 = _x192 ∧ _x175 = _x188 ∧ _x174 = _x187 ∧ _x173 = _x186 ∧ _x172 = _x185 ∧ _x171 = _x184 ∧ _x169 = _x182 ∧ _x168 = _x181 ∧ _x168 + 2 ≤ _x170 ∧ _x175 + 3 ≤ _x167 ∧ _x174 + 3 ≤ _x167 ∧ −1 ≤ _x183 − 1 ∧ 3 ≤ _x180 − 1 ∧ 1 ≤ _x170 − 1 ∧ 3 ≤ _x167 − 1 ∧ _x183 + 2 ≤ _x170 ∧ 1 ≤ _x173 − 1 ∧ _x180 ≤ _x167 f3374_0_put_NULL 9 f3374_0_put_NULL: x1 = _x193 ∧ x2 = _x194 ∧ x3 = _x195 ∧ x4 = _x196 ∧ x5 = _x197 ∧ x6 = _x198 ∧ x7 = _x199 ∧ x8 = _x200 ∧ x9 = _x201 ∧ x10 = _x203 ∧ x11 = _x204 ∧ x12 = _x205 ∧ x13 = _x206 ∧ x1 = _x207 ∧ x2 = _x208 ∧ x3 = _x209 ∧ x4 = _x210 ∧ x5 = _x211 ∧ x6 = _x212 ∧ x7 = _x213 ∧ x8 = _x214 ∧ x9 = _x215 ∧ x10 = _x216 ∧ x11 = _x217 ∧ x12 = _x218 ∧ x13 = _x219 ∧ _x201 = _x215 ∧ _x200 = _x214 ∧ _x199 = _x213 ∧ _x198 = _x212 ∧ _x197 = _x211 ∧ _x195 = _x209 ∧ _x194 = _x208 ∧ _x194 + 2 ≤ _x196 ∧ _x201 + 3 ≤ _x193 ∧ _x200 + 3 ≤ _x193 ∧ −1 ≤ _x210 − 1 ∧ 3 ≤ _x207 − 1 ∧ 2 ≤ _x196 − 1 ∧ 3 ≤ _x193 − 1 ∧ _x210 + 2 ≤ _x196 ∧ 1 ≤ _x199 − 1 ∧ _x207 ≤ _x193 f3452_0_put_EQ 10 f3374_0_put_NULL: x1 = _x220 ∧ x2 = _x221 ∧ x3 = _x222 ∧ 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 ∧ _x226 = _x241 ∧ _x225 = _x240 ∧ _x224 = _x239 ∧ _x221 = _x235 ∧ _x227 = _x234 ∧ 0 = _x223 ∧ _x229 + 4 ≤ _x222 ∧ _x227 + 2 ≤ _x222 ∧ _x226 + 3 ≤ _x220 ∧ _x225 + 3 ≤ _x220 ∧ −1 ≤ _x236 − 1 ∧ 3 ≤ _x233 − 1 ∧ −1 ≤ _x228 − 1 ∧ 2 ≤ _x222 − 1 ∧ 3 ≤ _x220 − 1 ∧ _x236 ≤ _x228 ∧ _x236 + 2 ≤ _x222 ∧ _x233 ≤ _x220 f3374_0_put_NULL 11 f3898_0_transfer_GE: x1 = _x246 ∧ x2 = _x247 ∧ x3 = _x248 ∧ x4 = _x249 ∧ x5 = _x250 ∧ x6 = _x251 ∧ x7 = _x252 ∧ x8 = _x253 ∧ x9 = _x254 ∧ x10 = _x255 ∧ x11 = _x256 ∧ x12 = _x257 ∧ x13 = _x258 ∧ x1 = _x259 ∧ x2 = _x260 ∧ x3 = _x261 ∧ x4 = _x262 ∧ x5 = _x263 ∧ x6 = _x264 ∧ x7 = _x265 ∧ x8 = _x266 ∧ x9 = _x267 ∧ x10 = _x268 ∧ x11 = _x269 ∧ x12 = _x270 ∧ x13 = _x271 ∧ _x252 = _x266 ∧ 2⋅_x252 = _x265 ∧ _x254 = _x264 ∧ _x253 + 1 = _x263 ∧ 0 = _x262 ∧ _x254 + 3 ≤ _x246 ∧ _x253 + 3 ≤ _x246 ∧ 0 ≤ _x261 − 1 ∧ 0 ≤ _x260 − 1 ∧ 3 ≤ _x259 − 1 ∧ −1 ≤ _x249 − 1 ∧ 3 ≤ _x246 − 1 ∧ _x261 − 1 ≤ _x249 ∧ _x261 + 3 ≤ _x246 ∧ _x260 − 1 ≤ _x249 ∧ _x260 + 3 ≤ _x246 ∧ _x259 − 1 ≤ _x246 ∧ _x252 ≤ 1073741823 ∧ 0 ≤ 2⋅_x252 ∧ _x254 ≤ _x253 ∧ 1 ≤ _x252 − 1 ∧ _x248 ≤ _x252 − 1 f3374_0_put_NULL 12 f3898_0_transfer_GE: x1 = _x272 ∧ x2 = _x273 ∧ x3 = _x274 ∧ x4 = _x275 ∧ x5 = _x276 ∧ x6 = _x277 ∧ x7 = _x278 ∧ x8 = _x279 ∧ x9 = _x280 ∧ x10 = _x281 ∧ x11 = _x282 ∧ x12 = _x283 ∧ x13 = _x284 ∧ x1 = _x285 ∧ x2 = _x286 ∧ x3 = _x287 ∧ x4 = _x288 ∧ x5 = _x289 ∧ x6 = _x290 ∧ x7 = _x291 ∧ x8 = _x292 ∧ x9 = _x293 ∧ x10 = _x294 ∧ x11 = _x295 ∧ x12 = _x296 ∧ x13 = _x297 ∧ _x278 = _x292 ∧ 2⋅_x278 = _x291 ∧ _x280 = _x290 ∧ _x279 + 1 = _x289 ∧ 0 = _x288 ∧ _x280 + 3 ≤ _x272 ∧ _x279 + 3 ≤ _x272 ∧ 0 ≤ _x287 − 1 ∧ 0 ≤ _x286 − 1 ∧ 3 ≤ _x285 − 1 ∧ −1 ≤ _x275 − 1 ∧ 3 ≤ _x272 − 1 ∧ _x287 − 1 ≤ _x275 ∧ _x287 + 3 ≤ _x272 ∧ _x286 − 1 ≤ _x275 ∧ _x286 + 3 ≤ _x272 ∧ _x285 − 1 ≤ _x272 ∧ _x280 ≤ _x279 ∧ 0 ≤ 2⋅_x278 ∧ 1073741824 ≤ _x278 − 1 ∧ _x274 ≤ _x278 − 1 f3898_0_transfer_GE 13 f3993_0_transfer_ArrayAccess: x1 = _x298 ∧ x2 = _x299 ∧ x3 = _x300 ∧ x4 = _x301 ∧ x5 = _x302 ∧ x6 = _x303 ∧ x7 = _x304 ∧ x8 = _x305 ∧ x9 = _x306 ∧ x10 = _x307 ∧ x11 = _x308 ∧ x12 = _x309 ∧ x13 = _x310 ∧ x1 = _x311 ∧ x2 = _x312 ∧ x3 = _x313 ∧ x4 = _x314 ∧ x5 = _x315 ∧ x6 = _x316 ∧ x7 = _x317 ∧ x8 = _x318 ∧ x9 = _x319 ∧ x10 = _x320 ∧ x11 = _x321 ∧ x12 = _x322 ∧ x13 = _x323 ∧ _x304 = _x323 ∧ _x305 = _x320 ∧ _x303 = _x319 ∧ _x302 = _x318 ∧ _x301 = _x313 ∧ _x303 + 3 ≤ _x298 ∧ _x302 + 3 ≤ _x298 ∧ 0 ≤ _x316 − 1 ∧ 0 ≤ _x315 − 1 ∧ −1 ≤ _x314 − 1 ∧ 0 ≤ _x312 − 1 ∧ 3 ≤ _x311 − 1 ∧ 0 ≤ _x300 − 1 ∧ 0 ≤ _x299 − 1 ∧ 3 ≤ _x298 − 1 ∧ _x316 ≤ _x300 ∧ _x316 ≤ _x299 ∧ _x316 + 3 ≤ _x298 ∧ _x312 ≤ _x300 ∧ _x312 ≤ _x299 ∧ _x312 + 3 ≤ _x298 ∧ _x311 ≤ _x298 ∧ _x301 ≤ _x305 − 1 ∧ 0 ≤ _x304 − 1 f3993_0_transfer_ArrayAccess 14 f3993_0_transfer_ArrayAccess: x1 = _x324 ∧ x2 = _x325 ∧ x3 = _x326 ∧ x4 = _x327 ∧ x5 = _x328 ∧ x6 = _x329 ∧ x7 = _x330 ∧ x8 = _x331 ∧ x9 = _x332 ∧ x10 = _x333 ∧ x11 = _x334 ∧ x12 = _x335 ∧ x13 = _x336 ∧ x1 = _x337 ∧ x2 = _x338 ∧ x3 = _x339 ∧ x4 = _x340 ∧ x5 = _x341 ∧ x6 = _x342 ∧ x7 = _x343 ∧ x8 = _x344 ∧ x9 = _x345 ∧ x10 = _x346 ∧ x11 = _x347 ∧ x12 = _x348 ∧ x13 = _x349 ∧ _x336 = _x349 ∧ _x333 = _x346 ∧ _x332 = _x345 ∧ _x331 = _x344 ∧ _x326 = _x339 ∧ _x335 + 2 ≤ _x328 ∧ _x348 + 4 ≤ _x328 ∧ _x347 + 4 ≤ _x328 ∧ _x334 + 2 ≤ _x328 ∧ _x348 + 2 ≤ _x327 ∧ _x347 + 2 ≤ _x327 ∧ _x332 + 3 ≤ _x324 ∧ _x331 + 3 ≤ _x324 ∧ 0 ≤ _x342 − 1 ∧ 0 ≤ _x341 − 1 ∧ −1 ≤ _x340 − 1 ∧ 0 ≤ _x338 − 1 ∧ 3 ≤ _x337 − 1 ∧ 0 ≤ _x329 − 1 ∧ 2 ≤ _x328 − 1 ∧ 0 ≤ _x327 − 1 ∧ 0 ≤ _x325 − 1 ∧ 3 ≤ _x324 − 1 ∧ _x342 ≤ _x329 ∧ _x342 + 2 ≤ _x328 ∧ _x342 ≤ _x327 ∧ _x342 ≤ _x325 ∧ _x342 + 3 ≤ _x324 ∧ _x341 + 2 ≤ _x328 ∧ _x341 ≤ _x327 ∧ _x340 + 3 ≤ _x328 ∧ _x340 + 1 ≤ _x327 ∧ _x338 ≤ _x329 ∧ _x338 + 2 ≤ _x328 ∧ _x338 ≤ _x327 ∧ _x338 ≤ _x325 ∧ _x338 + 3 ≤ _x324 ∧ _x337 ≤ _x324 ∧ 0 ≤ _x336 − 1 ∧ _x330 ≤ _x336 − 1 f3898_0_transfer_GE 15 f3898_0_transfer_GE: x1 = _x350 ∧ x2 = _x351 ∧ x3 = _x352 ∧ x4 = _x353 ∧ x5 = _x354 ∧ x6 = _x355 ∧ x7 = _x356 ∧ x8 = _x357 ∧ x9 = _x358 ∧ x10 = _x359 ∧ x11 = _x360 ∧ x12 = _x361 ∧ x13 = _x362 ∧ x1 = _x363 ∧ x2 = _x364 ∧ x3 = _x365 ∧ x4 = _x366 ∧ x5 = _x367 ∧ x6 = _x368 ∧ x7 = _x369 ∧ x8 = _x370 ∧ x9 = _x371 ∧ x10 = _x372 ∧ x11 = _x373 ∧ x12 = _x374 ∧ x13 = _x375 ∧ _x357 = _x370 ∧ _x356 = _x369 ∧ _x355 = _x368 ∧ _x354 = _x367 ∧ _x353 + 1 = _x366 ∧ _x355 + 3 ≤ _x350 ∧ _x354 + 3 ≤ _x350 ∧ 0 ≤ _x365 − 1 ∧ 0 ≤ _x364 − 1 ∧ 3 ≤ _x363 − 1 ∧ 0 ≤ _x352 − 1 ∧ 0 ≤ _x351 − 1 ∧ 3 ≤ _x350 − 1 ∧ _x365 ≤ _x352 ∧ _x365 ≤ _x351 ∧ _x365 + 3 ≤ _x350 ∧ _x364 ≤ _x352 ∧ _x364 ≤ _x351 ∧ _x364 + 3 ≤ _x350 ∧ _x363 ≤ _x350 ∧ _x353 ≤ _x357 − 1 ∧ −1 ≤ _x357 − 1 f3993_0_transfer_ArrayAccess 16 f3898_0_transfer_GE: x1 = _x376 ∧ x2 = _x377 ∧ x3 = _x378 ∧ x4 = _x379 ∧ x5 = _x380 ∧ x6 = _x381 ∧ x7 = _x382 ∧ x8 = _x383 ∧ x9 = _x384 ∧ x10 = _x385 ∧ x11 = _x386 ∧ x12 = _x387 ∧ x13 = _x388 ∧ x1 = _x389 ∧ x2 = _x390 ∧ x3 = _x391 ∧ x4 = _x392 ∧ x5 = _x393 ∧ x6 = _x394 ∧ x7 = _x395 ∧ x8 = _x396 ∧ x9 = _x397 ∧ x10 = _x398 ∧ x11 = _x399 ∧ x12 = _x400 ∧ x13 = _x401 ∧ _x385 = _x396 ∧ _x388 = _x395 ∧ _x384 = _x394 ∧ _x383 = _x393 ∧ _x378 + 1 = _x392 ∧ _x387 + 2 ≤ _x380 ∧ _x386 + 2 ≤ _x380 ∧ _x384 + 3 ≤ _x376 ∧ _x383 + 3 ≤ _x376 ∧ 0 ≤ _x391 − 1 ∧ 0 ≤ _x390 − 1 ∧ 3 ≤ _x389 − 1 ∧ 0 ≤ _x381 − 1 ∧ 1 ≤ _x380 − 1 ∧ −1 ≤ _x379 − 1 ∧ 0 ≤ _x377 − 1 ∧ 3 ≤ _x376 − 1 ∧ _x391 ≤ _x381 ∧ _x391 + 1 ≤ _x380 ∧ _x391 − 1 ≤ _x379 ∧ _x391 ≤ _x377 ∧ _x391 + 3 ≤ _x376 ∧ _x390 ≤ _x381 ∧ _x390 + 1 ≤ _x380 ∧ _x390 − 1 ≤ _x379 ∧ _x390 ≤ _x377 ∧ _x390 + 3 ≤ _x376 ∧ _x389 ≤ _x376 ∧ _x382 ≤ _x388 − 1 ∧ −1 ≤ _x385 − 1 __init 17 f1_0_main_Load: x1 = _x402 ∧ x2 = _x403 ∧ x3 = _x404 ∧ x4 = _x405 ∧ x5 = _x406 ∧ x6 = _x407 ∧ x7 = _x408 ∧ x8 = _x409 ∧ x9 = _x410 ∧ x10 = _x411 ∧ x11 = _x412 ∧ x12 = _x413 ∧ x13 = _x414 ∧ x1 = _x415 ∧ x2 = _x416 ∧ x3 = _x417 ∧ x4 = _x418 ∧ x5 = _x419 ∧ x6 = _x420 ∧ x7 = _x421 ∧ x8 = _x422 ∧ x9 = _x423 ∧ x10 = _x424 ∧ x11 = _x425 ∧ x12 = _x426 ∧ x13 = _x427 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f2907_0_createMap_LE f2907_0_createMap_LE f2907_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 f3374_0_put_NULL f3374_0_put_NULL f3374_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 f3898_0_transfer_GE f3898_0_transfer_GE f3898_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 f3452_0_put_EQ f3452_0_put_EQ f3452_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 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 f3993_0_transfer_ArrayAccess f3993_0_transfer_ArrayAccess f3993_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 __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 3 SCC(s) of the program graph.

### 2.1 SCC Subproblem 1/3

Here we consider the SCC { f2907_0_createMap_LE }.

### 2.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 0.

 f2907_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 { f3374_0_put_NULL, f3452_0_put_EQ }.

### 2.2.1 Transition Removal

We remove transitions 4, 6, 7, 8, 9, 10, 5 using the following ranking functions, which are bounded by 0.

 f3374_0_put_NULL: 1 + x4 f3452_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 { f3898_0_transfer_GE, f3993_0_transfer_ArrayAccess }.

### 2.3.1 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by 0.

 f3898_0_transfer_GE: −1 − x4 + 2⋅x8 f3993_0_transfer_ArrayAccess: −1 − x3 + 2⋅x10

### 2.3.2 Transition Removal

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

 f3898_0_transfer_GE: −1 − x4 + x7 + x8 f3993_0_transfer_ArrayAccess: −2 − x3 + x10 + x13

### 2.3.3 Transition Removal

We remove transitions 16, 14 using the following ranking functions, which are bounded by 0.

 f3993_0_transfer_ArrayAccess: x4 f3898_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.

## 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)