# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: f507_0_sort_GE, f229_0_main_GE, f507_0_sort_GE', f1503_0_sort_InvokeMethod, f757_0_merge_GT, f1440_0_merge_GT, f1_0_main_Load, f774_0_merge_GT, __init
• Transitions: (pre-variables and post-variables)  f1_0_main_Load 1 f229_0_main_GE: x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x4 = _arg4 ∧ x5 = _arg5 ∧ x6 = _arg6 ∧ x7 = _arg7 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ x4 = _arg4P ∧ x5 = _arg5P ∧ x6 = _arg6P ∧ x7 = _arg7P ∧ _arg2 = _arg3P ∧ 0 = _arg2P ∧ 0 ≤ _arg1P − 1 ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg2 − 1 ∧ _arg1P ≤ _arg1 f229_0_main_GE 2 f229_0_main_GE: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x1 = _x7 ∧ x2 = _x8 ∧ x3 = _x9 ∧ x4 = _x10 ∧ x5 = _x11 ∧ x6 = _x12 ∧ x7 = _x13 ∧ _x2 = _x9 ∧ _x1 + 1 = _x8 ∧ 0 ≤ _x7 − 1 ∧ 0 ≤ _x − 1 ∧ _x1 ≤ _x2 − 1 ∧ _x7 ≤ _x f229_0_main_GE 3 f507_0_sort_GE: x1 = _x14 ∧ x2 = _x15 ∧ x3 = _x16 ∧ x4 = _x17 ∧ x5 = _x18 ∧ x6 = _x19 ∧ x7 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ x4 = _x24 ∧ x5 = _x25 ∧ x6 = _x26 ∧ x7 = _x27 ∧ _x16 = _x25 ∧ _x16 − 1 = _x24 ∧ 0 = _x23 ∧ 0 ≤ _x22 − 1 ∧ 0 ≤ _x21 − 1 ∧ 0 ≤ _x14 − 1 ∧ _x22 ≤ _x14 ∧ _x21 ≤ _x14 ∧ _x16 ≤ _x15 ∧ −1 ≤ _x16 − 1 ∧ _x16 − 1 ≤ _x16 − 1 f507_0_sort_GE 4 f507_0_sort_GE': x1 = _x28 ∧ x2 = _x29 ∧ x3 = _x30 ∧ x4 = _x31 ∧ x5 = _x32 ∧ x6 = _x33 ∧ x7 = _x34 ∧ x1 = _x35 ∧ x2 = _x36 ∧ x3 = _x37 ∧ x4 = _x38 ∧ x5 = _x39 ∧ x6 = _x40 ∧ x7 = _x41 ∧ _x30 ≤ _x31 − 1 ∧ _x42 − _x30 ≤ _x31 − _x30 − 1 ∧ _x43 ≤ _x28 ∧ _x43 ≤ _x29 ∧ _x44 ≤ _x28 ∧ _x44 ≤ _x29 ∧ 0 ≤ _x28 − 1 ∧ 0 ≤ _x29 − 1 ∧ 0 ≤ _x43 − 1 ∧ 0 ≤ _x44 − 1 ∧ _x28 = _x35 ∧ _x29 = _x36 ∧ _x30 = _x37 ∧ _x31 = _x38 ∧ _x32 = _x39 f507_0_sort_GE' 5 f507_0_sort_GE: x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ x4 = _x48 ∧ x5 = _x49 ∧ x6 = _x50 ∧ x7 = _x51 ∧ x1 = _x52 ∧ x2 = _x53 ∧ x3 = _x54 ∧ x4 = _x55 ∧ x5 = _x57 ∧ x6 = _x58 ∧ x7 = _x59 ∧ _x49 = _x57 ∧ _x47 = _x54 ∧ 0 ≤ _x47 + _x48 − 2⋅_x55 ∧ _x47 + _x48 − 2⋅_x55 ≤ 1 ∧ 0 ≤ _x53 − 1 ∧ 0 ≤ _x52 − 1 ∧ 0 ≤ _x46 − 1 ∧ 0 ≤ _x45 − 1 ∧ _x53 ≤ _x46 ∧ _x53 ≤ _x45 ∧ _x52 ≤ _x46 ∧ _x52 ≤ _x45 ∧ _x55 − _x47 ≤ _x48 − _x47 − 1 ∧ _x47 ≤ _x48 − 1 f507_0_sort_GE 6 f507_0_sort_GE': x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x64 ∧ x5 = _x65 ∧ x6 = _x66 ∧ x7 = _x67 ∧ x1 = _x68 ∧ x2 = _x69 ∧ x3 = _x70 ∧ x4 = _x71 ∧ x5 = _x72 ∧ x6 = _x73 ∧ x7 = _x74 ∧ _x62 ≤ _x64 − 1 ∧ _x64 − _x62 ≤ _x75 − _x62 ∧ _x64 − _x75 + 1 ≤ _x64 − _x62 − 1 ∧ _x75 ≤ _x75 + 1 − 1 ∧ _x76 ≤ _x60 ∧ _x76 ≤ _x61 ∧ _x77 ≤ _x60 ∧ _x77 ≤ _x61 ∧ 0 ≤ _x60 − 1 ∧ 0 ≤ _x61 − 1 ∧ 0 ≤ _x76 − 1 ∧ 0 ≤ _x77 − 1 ∧ _x60 = _x68 ∧ _x61 = _x69 ∧ _x62 = _x70 ∧ _x64 = _x71 ∧ _x65 = _x72 f507_0_sort_GE' 7 f507_0_sort_GE: x1 = _x78 ∧ x2 = _x79 ∧ x3 = _x80 ∧ x4 = _x81 ∧ x5 = _x82 ∧ x6 = _x83 ∧ x7 = _x84 ∧ x1 = _x85 ∧ x2 = _x86 ∧ x3 = _x87 ∧ x4 = _x88 ∧ x5 = _x89 ∧ x6 = _x90 ∧ x7 = _x91 ∧ _x80 ≤ _x81 − 1 ∧ _x81 − _x80 ≤ _x92 − _x80 ∧ _x81 − _x92 + 1 ≤ _x81 − _x80 − 1 ∧ _x92 ≤ _x92 + 1 − 1 ∧ _x85 ≤ _x78 ∧ _x85 ≤ _x79 ∧ _x86 ≤ _x78 ∧ _x86 ≤ _x79 ∧ 0 ≤ _x78 − 1 ∧ 0 ≤ _x79 − 1 ∧ 0 ≤ _x85 − 1 ∧ 0 ≤ _x86 − 1 ∧ _x80 + _x81 − 2⋅_x92 ≤ 1 ∧ 0 ≤ _x80 + _x81 − 2⋅_x92 ∧ _x92 + 1 = _x87 ∧ _x81 = _x88 ∧ _x82 = _x89 f507_0_sort_GE 8 f507_0_sort_GE': x1 = _x93 ∧ x2 = _x94 ∧ x3 = _x95 ∧ x4 = _x96 ∧ x5 = _x97 ∧ x6 = _x98 ∧ x7 = _x99 ∧ x1 = _x100 ∧ x2 = _x101 ∧ x3 = _x102 ∧ x4 = _x103 ∧ x5 = _x104 ∧ x6 = _x107 ∧ x7 = _x108 ∧ _x95 ≤ _x96 − 1 ∧ _x109 − _x95 ≤ _x96 − _x95 − 1 ∧ _x109 ≤ _x109 + 1 − 1 ∧ _x96 − _x109 + 1 ≤ _x96 − _x95 − 1 ∧ _x110 ≤ _x93 ∧ _x110 ≤ _x94 ∧ _x111 ≤ _x93 ∧ _x111 ≤ _x94 ∧ 0 ≤ _x93 − 1 ∧ 0 ≤ _x94 − 1 ∧ 0 ≤ _x110 − 1 ∧ 0 ≤ _x111 − 1 ∧ _x93 = _x100 ∧ _x94 = _x101 ∧ _x95 = _x102 ∧ _x96 = _x103 ∧ _x97 = _x104 f507_0_sort_GE' 9 f507_0_sort_GE: x1 = _x112 ∧ x2 = _x113 ∧ x3 = _x117 ∧ x4 = _x118 ∧ x5 = _x119 ∧ x6 = _x120 ∧ x7 = _x121 ∧ x1 = _x122 ∧ x2 = _x123 ∧ x3 = _x124 ∧ x4 = _x125 ∧ x5 = _x126 ∧ x6 = _x127 ∧ x7 = _x128 ∧ _x117 ≤ _x118 − 1 ∧ _x129 − _x117 ≤ _x118 − _x117 − 1 ∧ _x129 ≤ _x129 + 1 − 1 ∧ _x118 − _x129 + 1 ≤ _x118 − _x117 − 1 ∧ _x122 ≤ _x112 ∧ _x122 ≤ _x113 ∧ _x123 ≤ _x112 ∧ _x123 ≤ _x113 ∧ 0 ≤ _x112 − 1 ∧ 0 ≤ _x113 − 1 ∧ 0 ≤ _x122 − 1 ∧ 0 ≤ _x123 − 1 ∧ _x117 + _x118 − 2⋅_x129 ≤ 1 ∧ 0 ≤ _x117 + _x118 − 2⋅_x129 ∧ _x129 + 1 = _x124 ∧ _x118 = _x125 ∧ _x119 = _x126 f507_0_sort_GE 10 f507_0_sort_GE': x1 = _x133 ∧ x2 = _x134 ∧ x3 = _x135 ∧ x4 = _x136 ∧ x5 = _x137 ∧ x6 = _x138 ∧ x7 = _x139 ∧ x1 = _x141 ∧ x2 = _x142 ∧ x3 = _x143 ∧ x4 = _x144 ∧ x5 = _x145 ∧ x6 = _x149 ∧ x7 = _x150 ∧ _x135 ≤ _x136 − 1 ∧ _x151 − _x135 ≤ _x136 − _x135 − 1 ∧ _x136 − _x135 ≤ _x136 − _x151 + 1 ∧ _x152 ≤ _x133 ∧ _x152 ≤ _x134 ∧ 0 ≤ _x133 − 1 ∧ 0 ≤ _x134 − 1 ∧ 0 ≤ _x152 − 1 ∧ _x133 = _x141 ∧ _x134 = _x142 ∧ _x135 = _x143 ∧ _x136 = _x144 ∧ _x137 = _x145 f507_0_sort_GE' 11 f1503_0_sort_InvokeMethod: x1 = _x153 ∧ x2 = _x154 ∧ x3 = _x155 ∧ x4 = _x157 ∧ x5 = _x158 ∧ x6 = _x159 ∧ x7 = _x160 ∧ x1 = _x161 ∧ x2 = _x164 ∧ x3 = _x165 ∧ x4 = _x166 ∧ x5 = _x167 ∧ x6 = _x168 ∧ x7 = _x169 ∧ _x158 = _x167 ∧ _x157 = _x164 ∧ _x155 = _x161 ∧ 0 ≤ _x155 + _x157 − 2⋅_x165 ∧ _x155 + _x157 − 2⋅_x165 ≤ 1 ∧ 0 ≤ _x166 − 1 ∧ 0 ≤ _x154 − 1 ∧ 0 ≤ _x153 − 1 ∧ _x166 ≤ _x154 ∧ _x166 ≤ _x153 ∧ _x157 − _x155 ≤ _x157 − _x165 + 1 ∧ _x165 − _x155 ≤ _x157 − _x155 − 1 ∧ _x155 ≤ _x157 − 1 f507_0_sort_GE 12 f507_0_sort_GE': x1 = _x170 ∧ x2 = _x171 ∧ x3 = _x172 ∧ x4 = _x173 ∧ x5 = _x174 ∧ x6 = _x175 ∧ x7 = _x178 ∧ x1 = _x179 ∧ x2 = _x180 ∧ x3 = _x181 ∧ x4 = _x182 ∧ x5 = _x183 ∧ x6 = _x184 ∧ x7 = _x185 ∧ _x172 ≤ _x173 − 1 ∧ _x186 − _x172 ≤ _x173 − _x172 − 1 ∧ _x186 ≤ _x186 + 1 − 1 ∧ _x173 − _x186 + 1 ≤ _x173 − _x172 − 1 ∧ _x187 ≤ _x170 ∧ _x187 ≤ _x171 ∧ 0 ≤ _x170 − 1 ∧ 0 ≤ _x171 − 1 ∧ 0 ≤ _x187 − 1 ∧ _x170 = _x179 ∧ _x171 = _x180 ∧ _x172 = _x181 ∧ _x173 = _x182 ∧ _x174 = _x183 f507_0_sort_GE' 13 f1503_0_sort_InvokeMethod: x1 = _x188 ∧ x2 = _x189 ∧ x3 = _x192 ∧ x4 = _x193 ∧ x5 = _x194 ∧ x6 = _x195 ∧ x7 = _x196 ∧ x1 = _x197 ∧ x2 = _x198 ∧ x3 = _x199 ∧ x4 = _x200 ∧ x5 = _x201 ∧ x6 = _x202 ∧ x7 = _x203 ∧ _x194 = _x201 ∧ _x193 = _x198 ∧ _x192 = _x197 ∧ 0 ≤ _x192 + _x193 − 2⋅_x199 ∧ _x192 + _x193 − 2⋅_x199 ≤ 1 ∧ 0 ≤ _x200 − 1 ∧ 0 ≤ _x189 − 1 ∧ 0 ≤ _x188 − 1 ∧ _x200 ≤ _x189 ∧ _x200 ≤ _x188 ∧ _x193 − _x199 + 1 ≤ _x193 − _x192 − 1 ∧ _x199 ≤ _x199 + 1 − 1 ∧ _x199 − _x192 ≤ _x193 − _x192 − 1 ∧ _x192 ≤ _x193 − 1 f507_0_sort_GE 14 f507_0_sort_GE': x1 = _x206 ∧ x2 = _x207 ∧ x3 = _x208 ∧ x4 = _x209 ∧ x5 = _x210 ∧ x6 = _x211 ∧ x7 = _x212 ∧ x1 = _x213 ∧ x2 = _x214 ∧ x3 = _x215 ∧ x4 = _x216 ∧ x5 = _x217 ∧ x6 = _x218 ∧ x7 = _x219 ∧ _x208 ≤ _x209 − 1 ∧ _x209 − _x208 ≤ _x220 − _x208 ∧ _x209 − _x208 ≤ _x209 − _x220 + 1 ∧ −1 ≤ _x210 − 1 ∧ _x221 ≤ _x206 ∧ _x221 ≤ _x207 ∧ 0 ≤ _x206 − 1 ∧ 0 ≤ _x207 − 1 ∧ 0 ≤ _x221 − 1 ∧ _x206 = _x213 ∧ _x207 = _x214 ∧ _x208 = _x215 ∧ _x209 = _x216 ∧ _x210 = _x217 f507_0_sort_GE' 15 f757_0_merge_GT: x1 = _x222 ∧ x2 = _x223 ∧ x3 = _x224 ∧ x4 = _x225 ∧ x5 = _x226 ∧ x6 = _x227 ∧ x7 = _x228 ∧ x1 = _x229 ∧ x2 = _x230 ∧ x3 = _x231 ∧ x4 = _x232 ∧ x5 = _x233 ∧ x6 = _x234 ∧ x7 = _x235 ∧ _x226 = _x235 ∧ _x224 = _x233 ∧ _x224 = _x232 ∧ _x225 = _x230 ∧ _x224 = _x229 ∧ 0 ≤ _x224 + _x225 − 2⋅_x234 ∧ _x224 + _x225 − 2⋅_x234 ≤ 1 ∧ 0 ≤ _x231 − 1 ∧ 0 ≤ _x223 − 1 ∧ 0 ≤ _x222 − 1 ∧ _x231 ≤ _x223 ∧ _x231 ≤ _x222 ∧ −1 ≤ _x226 − 1 ∧ _x225 − _x224 ≤ _x225 − _x234 + 1 ∧ _x225 − _x224 ≤ _x234 − _x224 ∧ _x224 ≤ _x225 − 1 f507_0_sort_GE 16 f507_0_sort_GE': x1 = _x236 ∧ x2 = _x237 ∧ x3 = _x238 ∧ x4 = _x239 ∧ x5 = _x240 ∧ x6 = _x241 ∧ x7 = _x242 ∧ x1 = _x243 ∧ x2 = _x244 ∧ x3 = _x245 ∧ x4 = _x246 ∧ x5 = _x247 ∧ x6 = _x248 ∧ x7 = _x249 ∧ _x238 ≤ _x239 − 1 ∧ _x239 − _x238 ≤ _x250 − _x238 ∧ _x239 − _x250 + 1 ≤ _x239 − _x238 − 1 ∧ _x250 ≤ _x250 + 1 − 1 ∧ −1 ≤ _x240 − 1 ∧ _x251 ≤ _x236 ∧ _x251 ≤ _x237 ∧ 0 ≤ _x236 − 1 ∧ 0 ≤ _x237 − 1 ∧ 0 ≤ _x251 − 1 ∧ _x236 = _x243 ∧ _x237 = _x244 ∧ _x238 = _x245 ∧ _x239 = _x246 ∧ _x240 = _x247 f507_0_sort_GE' 17 f757_0_merge_GT: x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ x1 = _x259 ∧ x2 = _x260 ∧ x3 = _x261 ∧ x4 = _x262 ∧ x5 = _x263 ∧ x6 = _x264 ∧ x7 = _x265 ∧ _x256 = _x265 ∧ _x254 = _x263 ∧ _x254 = _x262 ∧ _x255 = _x260 ∧ _x254 = _x259 ∧ 0 ≤ _x254 + _x255 − 2⋅_x264 ∧ _x254 + _x255 − 2⋅_x264 ≤ 1 ∧ 0 ≤ _x261 − 1 ∧ 0 ≤ _x253 − 1 ∧ 0 ≤ _x252 − 1 ∧ _x261 ≤ _x253 ∧ _x261 ≤ _x252 ∧ −1 ≤ _x256 − 1 ∧ _x264 ≤ _x264 + 1 − 1 ∧ _x255 − _x264 + 1 ≤ _x255 − _x254 − 1 ∧ _x255 − _x254 ≤ _x264 − _x254 ∧ _x254 ≤ _x255 − 1 f1503_0_sort_InvokeMethod 18 f757_0_merge_GT: x1 = _x266 ∧ x2 = _x267 ∧ x3 = _x268 ∧ x4 = _x269 ∧ x5 = _x270 ∧ x6 = _x271 ∧ x7 = _x272 ∧ x1 = _x273 ∧ x2 = _x274 ∧ x3 = _x275 ∧ x4 = _x276 ∧ x5 = _x277 ∧ x6 = _x278 ∧ x7 = _x279 ∧ _x270 = _x279 ∧ _x268 = _x278 ∧ _x266 = _x277 ∧ _x266 = _x276 ∧ _x267 = _x274 ∧ _x266 = _x273 ∧ 0 ≤ _x275 − 1 ∧ 0 ≤ _x269 − 1 ∧ −1 ≤ _x270 − 1 ∧ _x275 ≤ _x269 f757_0_merge_GT 19 f774_0_merge_GT: x1 = _x280 ∧ x2 = _x281 ∧ x3 = _x282 ∧ x4 = _x283 ∧ x5 = _x284 ∧ x6 = _x285 ∧ x7 = _x286 ∧ x1 = _x287 ∧ x2 = _x288 ∧ x3 = _x289 ∧ x4 = _x290 ∧ x5 = _x291 ∧ x6 = _x292 ∧ x7 = _x293 ∧ _x286 = _x292 ∧ _x281 = _x291 ∧ _x285 + 1 = _x290 ∧ _x285 = _x288 ∧ _x280 = _x287 ∧ _x283 = _x284 ∧ 0 ≤ _x289 − 1 ∧ 0 ≤ _x282 − 1 ∧ _x285 ≤ _x283 − 1 ∧ _x289 ≤ _x282 f757_0_merge_GT 20 f757_0_merge_GT: x1 = _x294 ∧ x2 = _x295 ∧ x3 = _x296 ∧ x4 = _x297 ∧ x5 = _x298 ∧ x6 = _x299 ∧ x7 = _x300 ∧ x1 = _x301 ∧ x2 = _x302 ∧ x3 = _x303 ∧ x4 = _x304 ∧ x5 = _x305 ∧ x6 = _x306 ∧ x7 = _x307 ∧ _x300 = _x307 ∧ _x299 = _x306 ∧ _x297 + 1 = _x305 ∧ _x297 + 1 = _x304 ∧ _x295 = _x302 ∧ _x294 = _x301 ∧ _x297 = _x298 ∧ 0 ≤ _x303 − 1 ∧ 0 ≤ _x296 − 1 ∧ _x303 ≤ _x296 ∧ _x297 ≤ _x300 − 1 ∧ _x297 ≤ _x299 f774_0_merge_GT 21 f774_0_merge_GT: x1 = _x308 ∧ x2 = _x309 ∧ x3 = _x310 ∧ x4 = _x311 ∧ x5 = _x312 ∧ x6 = _x313 ∧ x7 = _x314 ∧ x1 = _x315 ∧ x2 = _x316 ∧ x3 = _x317 ∧ x4 = _x318 ∧ x5 = _x319 ∧ x6 = _x320 ∧ x7 = _x321 ∧ _x313 = _x320 ∧ _x312 = _x319 ∧ _x311 + 1 = _x318 ∧ _x309 = _x316 ∧ _x308 = _x315 ∧ 0 ≤ _x317 − 1 ∧ 0 ≤ _x310 − 1 ∧ _x317 ≤ _x310 ∧ _x311 ≤ _x313 − 1 ∧ _x311 ≤ _x312 ∧ _x312 + _x309 + 1 − _x311 ≤ _x313 − 1 f774_0_merge_GT 22 f1440_0_merge_GT: x1 = _x322 ∧ x2 = _x323 ∧ x3 = _x324 ∧ x4 = _x325 ∧ x5 = _x326 ∧ x6 = _x327 ∧ x7 = _x328 ∧ x1 = _x329 ∧ x2 = _x330 ∧ x3 = _x331 ∧ x4 = _x332 ∧ x5 = _x333 ∧ x6 = _x334 ∧ x7 = _x335 ∧ _x327 = _x335 ∧ _x326 = _x334 ∧ _x322 = _x333 ∧ _x322 = _x332 ∧ _x326 = _x331 ∧ _x322 = _x330 ∧ 0 ≤ _x329 − 1 ∧ 0 ≤ _x324 − 1 ∧ _x326 ≤ _x325 − 1 ∧ _x329 ≤ _x324 f1440_0_merge_GT 23 f1440_0_merge_GT: x1 = _x336 ∧ x2 = _x337 ∧ x3 = _x338 ∧ x4 = _x339 ∧ x5 = _x340 ∧ x6 = _x341 ∧ x7 = _x342 ∧ x1 = _x343 ∧ x2 = _x344 ∧ x3 = _x345 ∧ x4 = _x346 ∧ x5 = _x347 ∧ x6 = _x348 ∧ x7 = _x349 ∧ _x339 ≤ _x341 ∧ _x337 ≤ _x342 − 1 ∧ _x338 ≤ _x342 − 1 ∧ _x350 ≤ _x351 ∧ _x339 ≤ _x342 − 1 ∧ _x343 ≤ _x336 ∧ 0 ≤ _x336 − 1 ∧ 0 ≤ _x343 − 1 ∧ _x339 = _x340 ∧ _x337 = _x344 ∧ _x338 − 1 = _x345 ∧ _x339 + 1 = _x346 ∧ _x339 + 1 = _x347 ∧ _x341 = _x348 ∧ _x342 = _x349 f1440_0_merge_GT 24 f1440_0_merge_GT: x1 = _x352 ∧ x2 = _x353 ∧ x3 = _x354 ∧ x4 = _x355 ∧ x5 = _x356 ∧ x6 = _x357 ∧ x7 = _x358 ∧ x1 = _x359 ∧ x2 = _x360 ∧ x3 = _x361 ∧ x4 = _x362 ∧ x5 = _x363 ∧ x6 = _x364 ∧ x7 = _x365 ∧ _x355 ≤ _x357 ∧ _x353 ≤ _x358 − 1 ∧ _x354 ≤ _x358 − 1 ∧ _x366 ≤ _x367 − 1 ∧ _x355 ≤ _x358 − 1 ∧ _x359 ≤ _x352 ∧ 0 ≤ _x352 − 1 ∧ 0 ≤ _x359 − 1 ∧ _x355 = _x356 ∧ _x353 + 1 = _x360 ∧ _x354 = _x361 ∧ _x355 + 1 = _x362 ∧ _x355 + 1 = _x363 ∧ _x357 = _x364 ∧ _x358 = _x365 __init 25 f1_0_main_Load: x1 = _x368 ∧ x2 = _x369 ∧ x3 = _x370 ∧ x4 = _x371 ∧ x5 = _x372 ∧ x6 = _x373 ∧ x7 = _x374 ∧ x1 = _x375 ∧ x2 = _x376 ∧ x3 = _x377 ∧ x4 = _x378 ∧ x5 = _x379 ∧ x6 = _x380 ∧ x7 = _x381 ∧ 0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 f507_0_sort_GE f507_0_sort_GE f507_0_sort_GE: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 f229_0_main_GE f229_0_main_GE f229_0_main_GE: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 f507_0_sort_GE' f507_0_sort_GE' f507_0_sort_GE': x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 f1503_0_sort_InvokeMethod f1503_0_sort_InvokeMethod f1503_0_sort_InvokeMethod: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 f757_0_merge_GT f757_0_merge_GT f757_0_merge_GT: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 f1440_0_merge_GT f1440_0_merge_GT f1440_0_merge_GT: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 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 f774_0_merge_GT f774_0_merge_GT f774_0_merge_GT: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 __init __init __init: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7
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 { f229_0_main_GE }.

### 2.1.1 Transition Removal

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

 f229_0_main_GE: − x2 + x3

### 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 { f507_0_sort_GE, f507_0_sort_GE' }.

### 2.2.1 Transition Removal

We remove transitions 4, 5, 6, 7, 8, 9, 16, 14, 12, 10 using the following ranking functions, which are bounded by 0.

 f507_0_sort_GE: −2⋅x3 + 2⋅x4 f507_0_sort_GE': −2⋅x3 + 2⋅x4 − 1

### 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 { f757_0_merge_GT }.

### 2.3.1 Transition Removal

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

 f757_0_merge_GT: − x5 + x6

### 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 4/5

Here we consider the SCC { f774_0_merge_GT }.

### 2.4.1 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by 0.

 f774_0_merge_GT: − x4 + x5

### 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 { f1440_0_merge_GT }.

### 2.5.1 Transition Removal

We remove transitions 23, 24 using the following ranking functions, which are bounded by 0.

 f1440_0_merge_GT: − x5 + x7

### 2.5.2 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)