# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: f2651_0_buildExpression_GT, f2554_0_buildExpression_GE, f1944_0_buildExpression_GT, f2578_0_toPostfix_NULL, f1999_0_toPostfix_NULL, f1_0_main_Load, __init
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f1944_0_buildExpression_GT: x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x7 = _arg7 ∧ x8 = _arg8 ∧ x9 = _arg9 ∧ x10 = _arg10 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ x7 = _arg7P ∧ x8 = _arg8P ∧ x9 = _arg9P ∧ x10 = _arg10P ∧ _arg2 = _arg4P ∧ 1 = _arg3P ∧ −1 ≤ _arg2P − 1 ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg2P + 1 ≤ _arg1 ∧ −1 ≤ _arg2 − 1 ∧ _arg1P ≤ _arg1 f1944_0_buildExpression_GT 2 f2554_0_buildExpression_GE: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x10 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ x3 = _x12 ∧ x4 = _x13 ∧ x5 = _x14 ∧ x6 = _x15 ∧ x7 = _x16 ∧ x8 = _x17 ∧ x9 = _x18 ∧ x10 = _x19 ∧ _x3 = _x13 ∧ 1 = _x12 ∧ −1 ≤ _x11 − 1 ∧ 0 ≤ _x10 − 1 ∧ −1 ≤ _x1 − 1 ∧ 0 ≤ _x − 1 ∧ _x11 ≤ _x1 ∧ _x10 − 1 ≤ _x1 ∧ _x3 ≤ _x2 − 1 ∧ _x10 ≤ _x f1944_0_buildExpression_GT 3 f2651_0_buildExpression_GT: x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x23 ∧ x5 = _x24 ∧ x6 = _x25 ∧ x7 = _x26 ∧ x8 = _x27 ∧ x9 = _x28 ∧ x10 = _x29 ∧ x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x4 = _x33 ∧ x5 = _x34 ∧ x6 = _x35 ∧ x7 = _x36 ∧ x8 = _x37 ∧ x9 = _x38 ∧ x10 = _x39 ∧ 41 = _x39 ∧ 98 = _x38 ∧ 43 = _x37 ∧ 97 = _x36 ∧ 40 = _x35 ∧ _x23 = _x34 ∧ _x23 − 1 = _x33 ∧ _x22 = _x32 ∧ 105 ≤ _x31 − 1 ∧ 0 ≤ _x30 − 1 ∧ −1 ≤ _x21 − 1 ∧ 0 ≤ _x20 − 1 ∧ _x31 − 106 ≤ _x21 ∧ _x30 − 1 ≤ _x21 ∧ _x30 ≤ _x20 ∧ _x23 − 1 ≤ _x22 − 1 ∧ 0 ≤ _x23 − 1 ∧ _x22 ≤ _x23 f2554_0_buildExpression_GE 4 f2554_0_buildExpression_GE: x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x7 = _x46 ∧ x8 = _x47 ∧ x9 = _x48 ∧ x10 = _x49 ∧ x1 = _x50 ∧ x2 = _x51 ∧ x3 = _x52 ∧ x4 = _x53 ∧ x5 = _x54 ∧ x6 = _x55 ∧ x7 = _x56 ∧ x8 = _x57 ∧ x9 = _x58 ∧ x10 = _x59 ∧ _x43 = _x53 ∧ _x42 + 1 = _x52 ∧ 41 ≤ _x51 − 1 ∧ 0 ≤ _x50 − 1 ∧ −1 ≤ _x41 − 1 ∧ 0 ≤ _x40 − 1 ∧ _x51 − 42 ≤ _x41 ∧ _x50 − 1 ≤ _x41 ∧ _x42 ≤ _x43 − 1 ∧ _x50 ≤ _x40 f2651_0_buildExpression_GT 5 f1944_0_buildExpression_GT: x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x63 ∧ x5 = _x64 ∧ x6 = _x65 ∧ x7 = _x66 ∧ x8 = _x67 ∧ x9 = _x68 ∧ x10 = _x69 ∧ x1 = _x70 ∧ x2 = _x71 ∧ x3 = _x72 ∧ x4 = _x73 ∧ x5 = _x74 ∧ x6 = _x75 ∧ x7 = _x76 ∧ x8 = _x77 ∧ x9 = _x78 ∧ x10 = _x79 ∧ _x64 = _x73 ∧ _x62 + 1 = _x72 ∧ 41 = _x69 ∧ 98 = _x68 ∧ 43 = _x67 ∧ 97 = _x66 ∧ 40 = _x65 ∧ 105 ≤ _x71 − 1 ∧ 0 ≤ _x70 − 1 ∧ 105 ≤ _x61 − 1 ∧ 0 ≤ _x60 − 1 ∧ _x71 ≤ _x61 ∧ _x70 + 105 ≤ _x61 ∧ _x63 ≤ _x62 − 1 ∧ _x70 ≤ _x60 f1944_0_buildExpression_GT 6 f2651_0_buildExpression_GT: x1 = _x80 ∧ x2 = _x81 ∧ x3 = _x82 ∧ x4 = _x83 ∧ x5 = _x84 ∧ x6 = _x85 ∧ x7 = _x86 ∧ x8 = _x87 ∧ x9 = _x88 ∧ x10 = _x89 ∧ x1 = _x90 ∧ x2 = _x91 ∧ x3 = _x92 ∧ x4 = _x93 ∧ x5 = _x94 ∧ x6 = _x95 ∧ x7 = _x96 ∧ x8 = _x97 ∧ x9 = _x98 ∧ x10 = _x99 ∧ 41 = _x99 ∧ 98 = _x98 ∧ 43 = _x97 ∧ 97 = _x96 ∧ 40 = _x95 ∧ _x83 = _x94 ∧ _x83 − 1 = _x93 ∧ _x82 = _x92 ∧ 105 ≤ _x91 − 1 ∧ 0 ≤ _x90 − 1 ∧ −1 ≤ _x81 − 1 ∧ 0 ≤ _x80 − 1 ∧ _x91 − 106 ≤ _x81 ∧ _x90 − 1 ≤ _x81 ∧ _x90 ≤ _x80 ∧ _x82 ≤ _x83 − 1 ∧ 0 ≤ _x83 − 1 ∧ _x82 ≤ _x83 f2651_0_buildExpression_GT 7 f1944_0_buildExpression_GT: x1 = _x100 ∧ x2 = _x101 ∧ x3 = _x102 ∧ x4 = _x104 ∧ x5 = _x105 ∧ x6 = _x106 ∧ x7 = _x107 ∧ x8 = _x108 ∧ x9 = _x109 ∧ x10 = _x110 ∧ x1 = _x111 ∧ x2 = _x113 ∧ x3 = _x114 ∧ x4 = _x115 ∧ x5 = _x116 ∧ x6 = _x117 ∧ x7 = _x118 ∧ x8 = _x119 ∧ x9 = _x120 ∧ x10 = _x121 ∧ _x105 = _x115 ∧ _x102 + 1 = _x114 ∧ 41 = _x110 ∧ 98 = _x109 ∧ 43 = _x108 ∧ 97 = _x107 ∧ 40 = _x106 ∧ 107 ≤ _x113 − 1 ∧ 0 ≤ _x111 − 1 ∧ 105 ≤ _x101 − 1 ∧ 0 ≤ _x100 − 1 ∧ _x113 − 2 ≤ _x101 ∧ _x111 + 105 ≤ _x101 ∧ _x102 ≤ _x104 ∧ _x111 ≤ _x100 f2554_0_buildExpression_GE 8 f1999_0_toPostfix_NULL: x1 = _x122 ∧ x2 = _x123 ∧ x3 = _x124 ∧ x4 = _x125 ∧ x5 = _x126 ∧ x6 = _x127 ∧ x7 = _x128 ∧ x8 = _x129 ∧ x9 = _x130 ∧ x10 = _x131 ∧ x1 = _x132 ∧ x2 = _x133 ∧ x3 = _x134 ∧ x4 = _x135 ∧ x5 = _x136 ∧ x6 = _x137 ∧ x7 = _x138 ∧ x8 = _x139 ∧ x9 = _x140 ∧ x10 = _x141 ∧ −1 ≤ _x135 − 1 ∧ −1 ≤ _x134 − 1 ∧ −1 ≤ _x133 − 1 ∧ −1 ≤ _x132 − 1 ∧ −1 ≤ _x123 − 1 ∧ 0 ≤ _x122 − 1 ∧ _x135 ≤ _x123 ∧ _x134 ≤ _x123 ∧ _x134 + 1 ≤ _x122 ∧ _x133 ≤ _x123 ∧ _x133 + 1 ≤ _x122 ∧ _x125 ≤ _x124 ∧ _x132 ≤ _x123 f1999_0_toPostfix_NULL 9 f1999_0_toPostfix_NULL: x1 = _x142 ∧ x2 = _x143 ∧ x3 = _x144 ∧ x4 = _x145 ∧ x5 = _x146 ∧ x6 = _x147 ∧ x7 = _x148 ∧ x8 = _x149 ∧ x9 = _x150 ∧ x10 = _x151 ∧ x1 = _x152 ∧ x2 = _x153 ∧ x3 = _x154 ∧ x4 = _x155 ∧ x5 = _x156 ∧ x6 = _x157 ∧ x7 = _x158 ∧ x8 = _x159 ∧ x9 = _x160 ∧ x10 = _x161 ∧ −1 ≤ _x155 − 1 ∧ −1 ≤ _x154 − 1 ∧ −1 ≤ _x153 − 1 ∧ −1 ≤ _x152 − 1 ∧ 41 ≤ _x145 − 1 ∧ −1 ≤ _x144 − 1 ∧ −1 ≤ _x143 − 1 ∧ 41 ≤ _x142 − 1 ∧ _x155 + 2 ≤ _x145 ∧ _x155 + 2 ≤ _x142 ∧ _x154 ≤ _x144 ∧ _x153 ≤ _x143 ∧ _x152 + 2 ≤ _x145 ∧ _x152 + 2 ≤ _x142 f1999_0_toPostfix_NULL 10 f2578_0_toPostfix_NULL: x1 = _x162 ∧ x2 = _x163 ∧ x3 = _x164 ∧ x4 = _x165 ∧ x5 = _x166 ∧ x6 = _x167 ∧ x7 = _x168 ∧ x8 = _x169 ∧ x9 = _x170 ∧ x10 = _x171 ∧ x1 = _x172 ∧ x2 = _x173 ∧ x3 = _x174 ∧ x4 = _x175 ∧ x5 = _x176 ∧ x6 = _x177 ∧ x7 = _x178 ∧ x8 = _x179 ∧ x9 = _x180 ∧ x10 = _x181 ∧ −1 ≤ _x172 − 1 ∧ −1 ≤ _x165 − 1 ∧ −1 ≤ _x164 − 1 ∧ −1 ≤ _x163 − 1 ∧ −1 ≤ _x162 − 1 ∧ _x172 ≤ _x164 f1999_0_toPostfix_NULL 11 f1999_0_toPostfix_NULL: x1 = _x182 ∧ x2 = _x183 ∧ x3 = _x184 ∧ x4 = _x185 ∧ x5 = _x186 ∧ x6 = _x187 ∧ x7 = _x188 ∧ x8 = _x189 ∧ x9 = _x190 ∧ x10 = _x191 ∧ x1 = _x192 ∧ x2 = _x193 ∧ x3 = _x194 ∧ x4 = _x195 ∧ x5 = _x196 ∧ x6 = _x197 ∧ x7 = _x198 ∧ x8 = _x199 ∧ x9 = _x200 ∧ x10 = _x201 ∧ −1 ≤ _x195 − 1 ∧ −1 ≤ _x194 − 1 ∧ 43 ≤ _x193 − 1 ∧ −1 ≤ _x192 − 1 ∧ 43 ≤ _x185 − 1 ∧ −1 ≤ _x184 − 1 ∧ −1 ≤ _x183 − 1 ∧ 43 ≤ _x182 − 1 ∧ _x195 + 2 ≤ _x185 ∧ _x195 + 2 ≤ _x182 ∧ _x194 ≤ _x184 ∧ _x193 − 44 ≤ _x183 ∧ _x192 + 2 ≤ _x185 ∧ _x192 + 2 ≤ _x182 f1999_0_toPostfix_NULL 12 f1999_0_toPostfix_NULL: x1 = _x202 ∧ x2 = _x203 ∧ x3 = _x204 ∧ x4 = _x205 ∧ x5 = _x206 ∧ x6 = _x207 ∧ x7 = _x208 ∧ x8 = _x209 ∧ x9 = _x210 ∧ x10 = _x211 ∧ x1 = _x212 ∧ x2 = _x213 ∧ x3 = _x214 ∧ x4 = _x215 ∧ x5 = _x216 ∧ x6 = _x217 ∧ x7 = _x218 ∧ x8 = _x219 ∧ x9 = _x220 ∧ x10 = _x221 ∧ −1 ≤ _x215 − 1 ∧ −1 ≤ _x214 − 1 ∧ 44 ≤ _x213 − 1 ∧ −1 ≤ _x212 − 1 ∧ 44 ≤ _x205 − 1 ∧ −1 ≤ _x204 − 1 ∧ −1 ≤ _x203 − 1 ∧ 44 ≤ _x202 − 1 ∧ _x215 + 2 ≤ _x205 ∧ _x215 + 2 ≤ _x202 ∧ _x214 ≤ _x204 ∧ _x213 − 45 ≤ _x203 ∧ _x212 + 2 ≤ _x205 ∧ _x212 + 2 ≤ _x202 f1999_0_toPostfix_NULL 13 f1999_0_toPostfix_NULL: x1 = _x222 ∧ x2 = _x223 ∧ x3 = _x224 ∧ x4 = _x225 ∧ x5 = _x226 ∧ x6 = _x227 ∧ x7 = _x228 ∧ x8 = _x229 ∧ x9 = _x230 ∧ x10 = _x231 ∧ x1 = _x232 ∧ x2 = _x233 ∧ x3 = _x234 ∧ x4 = _x235 ∧ x5 = _x236 ∧ x6 = _x237 ∧ x7 = _x238 ∧ x8 = _x239 ∧ x9 = _x240 ∧ x10 = _x241 ∧ −1 ≤ _x235 − 1 ∧ −1 ≤ _x234 − 1 ∧ 46 ≤ _x233 − 1 ∧ −1 ≤ _x232 − 1 ∧ 46 ≤ _x225 − 1 ∧ −1 ≤ _x224 − 1 ∧ −1 ≤ _x223 − 1 ∧ 46 ≤ _x222 − 1 ∧ _x235 + 2 ≤ _x225 ∧ _x235 + 2 ≤ _x222 ∧ _x234 ≤ _x224 ∧ _x233 − 47 ≤ _x223 ∧ _x232 + 2 ≤ _x225 ∧ _x232 + 2 ≤ _x222 f1999_0_toPostfix_NULL 14 f1999_0_toPostfix_NULL: x1 = _x242 ∧ x2 = _x243 ∧ x3 = _x244 ∧ x4 = _x245 ∧ x5 = _x246 ∧ x6 = _x247 ∧ x7 = _x248 ∧ x8 = _x249 ∧ x9 = _x250 ∧ x10 = _x251 ∧ x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ x8 = _x259 ∧ x9 = _x260 ∧ x10 = _x261 ∧ −1 ≤ _x255 − 1 ∧ −1 ≤ _x254 − 1 ∧ 48 ≤ _x253 − 1 ∧ −1 ≤ _x252 − 1 ∧ 48 ≤ _x245 − 1 ∧ −1 ≤ _x244 − 1 ∧ −1 ≤ _x243 − 1 ∧ 48 ≤ _x242 − 1 ∧ _x255 + 2 ≤ _x245 ∧ _x255 + 2 ≤ _x242 ∧ _x254 ≤ _x244 ∧ _x253 − 49 ≤ _x243 ∧ _x252 + 2 ≤ _x245 ∧ _x252 + 2 ≤ _x242 f1999_0_toPostfix_NULL 15 f1999_0_toPostfix_NULL: x1 = _x262 ∧ x2 = _x263 ∧ x3 = _x264 ∧ x4 = _x265 ∧ x5 = _x266 ∧ x6 = _x267 ∧ x7 = _x268 ∧ x8 = _x269 ∧ x9 = _x270 ∧ x10 = _x271 ∧ x1 = _x272 ∧ x2 = _x273 ∧ x3 = _x274 ∧ x4 = _x275 ∧ x5 = _x276 ∧ x6 = _x277 ∧ x7 = _x278 ∧ x8 = _x279 ∧ x9 = _x280 ∧ x10 = _x281 ∧ _x272 + 1 ≤ _x262 ∧ 47 ≤ _x282 − 1 ∧ _x272 + 1 ≤ _x265 ∧ _x273 ≤ _x263 ∧ _x275 + 1 ≤ _x262 ∧ _x275 + 1 ≤ _x265 ∧ 0 ≤ _x262 − 1 ∧ −1 ≤ _x263 − 1 ∧ −1 ≤ _x264 − 1 ∧ 0 ≤ _x265 − 1 ∧ −1 ≤ _x272 − 1 ∧ −1 ≤ _x273 − 1 ∧ 0 ≤ _x274 − 1 ∧ −1 ≤ _x275 − 1 f1999_0_toPostfix_NULL 16 f1999_0_toPostfix_NULL: x1 = _x283 ∧ x2 = _x284 ∧ x3 = _x285 ∧ x4 = _x286 ∧ x5 = _x287 ∧ x6 = _x288 ∧ x7 = _x289 ∧ x8 = _x290 ∧ x9 = _x291 ∧ x10 = _x292 ∧ x1 = _x293 ∧ x2 = _x294 ∧ x3 = _x295 ∧ x4 = _x296 ∧ x5 = _x297 ∧ x6 = _x298 ∧ x7 = _x299 ∧ x8 = _x300 ∧ x9 = _x301 ∧ x10 = _x302 ∧ _x293 + 1 ≤ _x283 ∧ _x303 ≤ 39 ∧ _x293 + 1 ≤ _x286 ∧ _x294 ≤ _x284 ∧ _x296 + 1 ≤ _x283 ∧ _x296 + 1 ≤ _x286 ∧ 0 ≤ _x283 − 1 ∧ −1 ≤ _x284 − 1 ∧ −1 ≤ _x285 − 1 ∧ 0 ≤ _x286 − 1 ∧ −1 ≤ _x293 − 1 ∧ −1 ≤ _x294 − 1 ∧ 0 ≤ _x295 − 1 ∧ −1 ≤ _x296 − 1 f1999_0_toPostfix_NULL 17 f1999_0_toPostfix_NULL: x1 = _x304 ∧ x2 = _x305 ∧ x3 = _x306 ∧ x4 = _x307 ∧ x5 = _x308 ∧ x6 = _x309 ∧ x7 = _x310 ∧ x8 = _x311 ∧ x9 = _x312 ∧ x10 = _x313 ∧ x1 = _x314 ∧ x2 = _x315 ∧ x3 = _x316 ∧ x4 = _x317 ∧ x5 = _x318 ∧ x6 = _x319 ∧ x7 = _x320 ∧ x8 = _x321 ∧ x9 = _x322 ∧ x10 = _x323 ∧ −1 ≤ _x317 − 1 ∧ 45 ≤ _x316 − 1 ∧ −1 ≤ _x315 − 1 ∧ −1 ≤ _x314 − 1 ∧ 45 ≤ _x307 − 1 ∧ −1 ≤ _x306 − 1 ∧ −1 ≤ _x305 − 1 ∧ 45 ≤ _x304 − 1 ∧ _x317 + 2 ≤ _x307 ∧ _x317 + 2 ≤ _x304 ∧ _x316 − 46 ≤ _x306 ∧ _x315 ≤ _x305 ∧ _x314 + 2 ≤ _x307 ∧ _x314 + 2 ≤ _x304 f1999_0_toPostfix_NULL 18 f1999_0_toPostfix_NULL: x1 = _x324 ∧ x2 = _x325 ∧ x3 = _x326 ∧ x4 = _x327 ∧ x5 = _x328 ∧ x6 = _x329 ∧ x7 = _x330 ∧ x8 = _x331 ∧ x9 = _x332 ∧ x10 = _x333 ∧ x1 = _x334 ∧ x2 = _x335 ∧ x3 = _x336 ∧ x4 = _x337 ∧ x5 = _x338 ∧ x6 = _x339 ∧ x7 = _x340 ∧ x8 = _x341 ∧ x9 = _x342 ∧ x10 = _x343 ∧ −1 ≤ _x337 − 1 ∧ 47 ≤ _x336 − 1 ∧ −1 ≤ _x335 − 1 ∧ −1 ≤ _x334 − 1 ∧ 47 ≤ _x327 − 1 ∧ −1 ≤ _x326 − 1 ∧ −1 ≤ _x325 − 1 ∧ 47 ≤ _x324 − 1 ∧ _x337 + 2 ≤ _x327 ∧ _x337 + 2 ≤ _x324 ∧ _x336 − 48 ≤ _x326 ∧ _x335 ≤ _x325 ∧ _x334 + 2 ≤ _x327 ∧ _x334 + 2 ≤ _x324 f1999_0_toPostfix_NULL 19 f1999_0_toPostfix_NULL: x1 = _x344 ∧ x2 = _x345 ∧ x3 = _x346 ∧ x4 = _x347 ∧ x5 = _x348 ∧ x6 = _x349 ∧ x7 = _x350 ∧ x8 = _x351 ∧ x9 = _x352 ∧ x10 = _x353 ∧ x1 = _x354 ∧ x2 = _x355 ∧ x3 = _x356 ∧ x4 = _x357 ∧ x5 = _x358 ∧ x6 = _x359 ∧ x7 = _x360 ∧ x8 = _x361 ∧ x9 = _x362 ∧ x10 = _x363 ∧ −1 ≤ _x357 − 1 ∧ 0 ≤ _x356 − 1 ∧ −1 ≤ _x355 − 1 ∧ −1 ≤ _x354 − 1 ∧ 42 ≤ _x347 − 1 ∧ −1 ≤ _x346 − 1 ∧ 0 ≤ _x345 − 1 ∧ 42 ≤ _x344 − 1 ∧ _x357 + 2 ≤ _x347 ∧ _x357 + 2 ≤ _x344 ∧ _x355 + 1 ≤ _x345 ∧ _x354 + 2 ≤ _x347 ∧ _x354 + 2 ≤ _x344 f2578_0_toPostfix_NULL 20 f2578_0_toPostfix_NULL: x1 = _x364 ∧ x2 = _x365 ∧ x3 = _x366 ∧ x4 = _x367 ∧ x5 = _x368 ∧ x6 = _x369 ∧ x7 = _x370 ∧ x8 = _x371 ∧ x9 = _x372 ∧ x10 = _x373 ∧ x1 = _x374 ∧ x2 = _x375 ∧ x3 = _x376 ∧ x4 = _x377 ∧ x5 = _x378 ∧ x6 = _x379 ∧ x7 = _x380 ∧ x8 = _x381 ∧ x9 = _x382 ∧ x10 = _x383 ∧ −1 ≤ _x374 − 1 ∧ 0 ≤ _x364 − 1 ∧ _x374 + 1 ≤ _x364 __init 21 f1_0_main_Load: x1 = _x384 ∧ x2 = _x385 ∧ x3 = _x386 ∧ x4 = _x387 ∧ x5 = _x388 ∧ x6 = _x389 ∧ x7 = _x390 ∧ x8 = _x391 ∧ x9 = _x392 ∧ x10 = _x393 ∧ x1 = _x394 ∧ x2 = _x395 ∧ x3 = _x396 ∧ x4 = _x397 ∧ x5 = _x398 ∧ x6 = _x399 ∧ x7 = _x400 ∧ x8 = _x401 ∧ x9 = _x402 ∧ x10 = _x403 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f2651_0_buildExpression_GT f2651_0_buildExpression_GT f2651_0_buildExpression_GT: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 f2554_0_buildExpression_GE f2554_0_buildExpression_GE f2554_0_buildExpression_GE: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 f1944_0_buildExpression_GT f1944_0_buildExpression_GT f1944_0_buildExpression_GT: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 f2578_0_toPostfix_NULL f2578_0_toPostfix_NULL f2578_0_toPostfix_NULL: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 f1999_0_toPostfix_NULL f1999_0_toPostfix_NULL f1999_0_toPostfix_NULL: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10 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 __init __init __init: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9 ∧ x10 = x10
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 { f2651_0_buildExpression_GT, f1944_0_buildExpression_GT }.

### 2.1.1 Transition Removal

We remove transitions 3, 6 using the following ranking functions, which are bounded by 0.

 f1944_0_buildExpression_GT: 2⋅x4 − 2⋅x3 f2651_0_buildExpression_GT: −2⋅x3 + 2⋅x5 − 1

### 2.1.2 Transition Removal

We remove transitions 5, 7 using the following ranking functions, which are bounded by 0.

 f2651_0_buildExpression_GT: 0 f1944_0_buildExpression_GT: −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 2/4

Here we consider the SCC { f2554_0_buildExpression_GE }.

### 2.2.1 Transition Removal

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

 f2554_0_buildExpression_GE: − x3 + x4

### 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 { f1999_0_toPostfix_NULL }.

### 2.3.1 Transition Removal

We remove transitions 9, 11, 12, 13, 14, 15, 16, 17, 18, 19 using the following ranking functions, which are bounded by 0.

 f1999_0_toPostfix_NULL: x4

### 2.3.2 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 { f2578_0_toPostfix_NULL }.

### 2.4.1 Transition Removal

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

 f2578_0_toPostfix_NULL: x1

### 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 % (15 real / 0 unknown / 0 assumptions / 15 total proof steps)