# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l4, l7, l1, l3, l0, l2
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _Result_6HAT0 ∧ x2 = __HAT0 ∧ x3 = _a_128HAT0 ∧ x4 = _a_243HAT0 ∧ x5 = _c_15HAT0 ∧ x6 = _elem_16HAT0 ∧ x7 = _head_9HAT0 ∧ x8 = _i_8HAT0 ∧ x9 = _k_296HAT0 ∧ x10 = _len_246HAT0 ∧ x11 = _len_48HAT0 ∧ x12 = _length_7HAT0 ∧ x13 = _lt_18HAT0 ∧ x14 = _lt_19HAT0 ∧ x15 = _lt_20HAT0 ∧ x16 = _lt_21HAT0 ∧ x17 = _prev_17HAT0 ∧ x18 = _x_13HAT0 ∧ x19 = _x_23HAT0 ∧ x20 = _y_110HAT0 ∧ x21 = _y_14HAT0 ∧ x22 = _y_158HAT0 ∧ x23 = _y_259HAT0 ∧ x24 = _y_309HAT0 ∧ x25 = _y_80HAT0 ∧ x1 = _Result_6HATpost ∧ x2 = __HATpost ∧ x3 = _a_128HATpost ∧ x4 = _a_243HATpost ∧ x5 = _c_15HATpost ∧ x6 = _elem_16HATpost ∧ x7 = _head_9HATpost ∧ x8 = _i_8HATpost ∧ x9 = _k_296HATpost ∧ x10 = _len_246HATpost ∧ x11 = _len_48HATpost ∧ x12 = _length_7HATpost ∧ x13 = _lt_18HATpost ∧ x14 = _lt_19HATpost ∧ x15 = _lt_20HATpost ∧ x16 = _lt_21HATpost ∧ x17 = _prev_17HATpost ∧ x18 = _x_13HATpost ∧ x19 = _x_23HATpost ∧ x20 = _y_110HATpost ∧ x21 = _y_14HATpost ∧ x22 = _y_158HATpost ∧ x23 = _y_259HATpost ∧ x24 = _y_309HATpost ∧ x25 = _y_80HATpost ∧ 0 ≤ _len_48HAT0 ∧ − _i_8HAT0 + _length_7HAT0 ≤ 0 ∧ _Result_6HATpost = _head_9HAT0 ∧ 0 ≤ _len_48HAT0 ∧ 0 ≤ _len_48HAT0 ∧ _x_13HAT1 = _Result_6HATpost ∧ _c_15HAT1 = _x_13HAT1 ∧ _x_13HAT2 = 0 ∧ 0 ≤ _len_48HAT0 ∧ _y_14HAT1 = _c_15HAT1 ∧ _lt_21HAT1 = _y_80HAT0 ∧ _c_15HAT2 = _lt_21HAT1 ∧ _lt_21HAT2 = _lt_21HAT2 ∧ _elem_16HAT1 = _x_13HAT2 ∧ _prev_17HAT1 = 0 ∧ 0 ≤ −1 + _len_48HAT0 ∧ _elem_16HAT1 ≤ 0 ∧ 0 ≤ _elem_16HAT1 ∧ _prev_17HAT1 ≤ 0 ∧ 0 ≤ _prev_17HAT1 ∧ _x_13HAT3 = _y_14HAT1 ∧ 0 ≤ −1 + _len_48HAT0 ∧ _a_128HATpost = −2 + _len_48HAT0 ∧ _y_14HAT2 = _c_15HAT2 ∧ _lt_21HAT3 = _y_110HAT0 ∧ _c_15HAT3 = _lt_21HAT3 ∧ _lt_21HAT4 = _lt_21HAT4 ∧ _elem_16HAT2 = _x_13HAT3 ∧ _prev_17HAT2 = 0 ∧ 0 ≤ _a_128HATpost ∧ _lt_19HAT1 = _lt_19HAT1 ∧ _lt_20HAT1 = _lt_20HAT1 ∧ 0 ≤ _lt_19HAT1 − _lt_20HAT1 ∧ _lt_19HATpost = _lt_19HATpost ∧ _lt_20HATpost = _lt_20HATpost ∧ _prev_17HAT2 ≤ 0 ∧ 0 ≤ _prev_17HAT2 ∧ _x_13HATpost = _y_14HAT2 ∧ 0 ≤ _a_128HATpost ∧ _len_246HATpost = 1 ∧ _a_243HATpost = −1 + __HAT0 + _a_128HATpost ∧ _y_14HATpost = _c_15HAT3 ∧ _lt_21HAT5 = _y_158HAT0 ∧ _c_15HATpost = _lt_21HAT5 ∧ _lt_21HATpost = _lt_21HATpost ∧ _elem_16HATpost = _x_13HATpost ∧ _prev_17HATpost = 0 ∧ __HAT0 = __HATpost ∧ _head_9HAT0 = _head_9HATpost ∧ _i_8HAT0 = _i_8HATpost ∧ _k_296HAT0 = _k_296HATpost ∧ _len_48HAT0 = _len_48HATpost ∧ _length_7HAT0 = _length_7HATpost ∧ _lt_18HAT0 = _lt_18HATpost ∧ _x_23HAT0 = _x_23HATpost ∧ _y_110HAT0 = _y_110HATpost ∧ _y_158HAT0 = _y_158HATpost ∧ _y_259HAT0 = _y_259HATpost ∧ _y_309HAT0 = _y_309HATpost ∧ _y_80HAT0 = _y_80HATpost l0 2 l2: 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 ∧ x14 = _x13 ∧ x15 = _x14 ∧ x16 = _x15 ∧ x17 = _x16 ∧ x18 = _x17 ∧ x19 = _x18 ∧ x20 = _x19 ∧ x21 = _x20 ∧ x22 = _x21 ∧ x23 = _x22 ∧ x24 = _x23 ∧ x25 = _x24 ∧ x1 = _x25 ∧ x2 = _x26 ∧ x3 = _x27 ∧ x4 = _x28 ∧ x5 = _x29 ∧ x6 = _x30 ∧ x7 = _x31 ∧ x8 = _x32 ∧ x9 = _x33 ∧ x10 = _x34 ∧ x11 = _x35 ∧ x12 = _x36 ∧ x13 = _x37 ∧ x14 = _x38 ∧ x15 = _x39 ∧ x16 = _x40 ∧ x17 = _x41 ∧ x18 = _x42 ∧ x19 = _x43 ∧ x20 = _x44 ∧ x21 = _x45 ∧ x22 = _x46 ∧ x23 = _x47 ∧ x24 = _x48 ∧ x25 = _x49 ∧ _x24 = _x49 ∧ _x23 = _x48 ∧ _x22 = _x47 ∧ _x21 = _x46 ∧ _x20 = _x45 ∧ _x19 = _x44 ∧ _x18 = _x43 ∧ _x17 = _x42 ∧ _x16 = _x41 ∧ _x15 = _x40 ∧ _x14 = _x39 ∧ _x13 = _x38 ∧ _x12 = _x37 ∧ _x11 = _x36 ∧ _x9 = _x34 ∧ _x8 = _x33 ∧ _x5 = _x30 ∧ _x4 = _x29 ∧ _x3 = _x28 ∧ _x2 = _x27 ∧ _x1 = _x26 ∧ _x = _x25 ∧ _x32 = 1 + _x7 ∧ _x31 = _x31 ∧ 0 ≤ −1 − _x7 + _x11 ∧ _x35 = 1 + _x10 ∧ 0 ≤ _x10 l2 3 l0: x1 = _x50 ∧ x2 = _x51 ∧ x3 = _x52 ∧ x4 = _x53 ∧ x5 = _x54 ∧ x6 = _x55 ∧ x7 = _x56 ∧ x8 = _x57 ∧ x9 = _x58 ∧ x10 = _x59 ∧ x11 = _x60 ∧ x12 = _x61 ∧ x13 = _x62 ∧ x14 = _x63 ∧ x15 = _x64 ∧ x16 = _x65 ∧ x17 = _x66 ∧ x18 = _x67 ∧ x19 = _x68 ∧ x20 = _x69 ∧ x21 = _x70 ∧ x22 = _x71 ∧ x23 = _x72 ∧ x24 = _x73 ∧ x25 = _x74 ∧ x1 = _x75 ∧ x2 = _x76 ∧ x3 = _x77 ∧ x4 = _x78 ∧ x5 = _x79 ∧ x6 = _x80 ∧ x7 = _x81 ∧ x8 = _x82 ∧ x9 = _x83 ∧ x10 = _x84 ∧ x11 = _x85 ∧ x12 = _x86 ∧ x13 = _x87 ∧ x14 = _x88 ∧ x15 = _x89 ∧ x16 = _x90 ∧ x17 = _x91 ∧ x18 = _x92 ∧ x19 = _x93 ∧ x20 = _x94 ∧ x21 = _x95 ∧ x22 = _x96 ∧ x23 = _x97 ∧ x24 = _x98 ∧ x25 = _x99 ∧ _x74 = _x99 ∧ _x73 = _x98 ∧ _x72 = _x97 ∧ _x71 = _x96 ∧ _x70 = _x95 ∧ _x69 = _x94 ∧ _x68 = _x93 ∧ _x67 = _x92 ∧ _x66 = _x91 ∧ _x65 = _x90 ∧ _x64 = _x89 ∧ _x63 = _x88 ∧ _x62 = _x87 ∧ _x61 = _x86 ∧ _x60 = _x85 ∧ _x59 = _x84 ∧ _x58 = _x83 ∧ _x57 = _x82 ∧ _x56 = _x81 ∧ _x55 = _x80 ∧ _x54 = _x79 ∧ _x53 = _x78 ∧ _x52 = _x77 ∧ _x51 = _x76 ∧ _x50 = _x75 l3 4 l0: 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 ∧ x14 = _x113 ∧ x15 = _x114 ∧ x16 = _x115 ∧ x17 = _x116 ∧ x18 = _x117 ∧ x19 = _x118 ∧ x20 = _x119 ∧ x21 = _x120 ∧ x22 = _x121 ∧ x23 = _x122 ∧ x24 = _x123 ∧ x25 = _x124 ∧ x1 = _x125 ∧ x2 = _x126 ∧ x3 = _x127 ∧ x4 = _x128 ∧ x5 = _x129 ∧ x6 = _x130 ∧ x7 = _x131 ∧ x8 = _x132 ∧ x9 = _x133 ∧ x10 = _x134 ∧ x11 = _x135 ∧ x12 = _x136 ∧ x13 = _x137 ∧ x14 = _x138 ∧ x15 = _x139 ∧ x16 = _x140 ∧ x17 = _x141 ∧ x18 = _x142 ∧ x19 = _x143 ∧ x20 = _x144 ∧ x21 = _x145 ∧ x22 = _x146 ∧ x23 = _x147 ∧ x24 = _x148 ∧ x25 = _x149 ∧ _x150 = 0 ∧ _x136 = 17 ∧ _x142 = _x118 ∧ _x151 = 0 ∧ _x152 = 0 ∧ _x135 = _x152 ∧ 0 ≤ −1 − _x152 + _x136 ∧ _x131 = _x131 ∧ _x132 = 1 + _x152 ∧ _x100 = _x125 ∧ _x101 = _x126 ∧ _x102 = _x127 ∧ _x103 = _x128 ∧ _x104 = _x129 ∧ _x105 = _x130 ∧ _x108 = _x133 ∧ _x109 = _x134 ∧ _x112 = _x137 ∧ _x113 = _x138 ∧ _x114 = _x139 ∧ _x115 = _x140 ∧ _x116 = _x141 ∧ _x118 = _x143 ∧ _x119 = _x144 ∧ _x120 = _x145 ∧ _x121 = _x146 ∧ _x122 = _x147 ∧ _x123 = _x148 ∧ _x124 = _x149 l1 5 l4: 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 ∧ x14 = _x166 ∧ x15 = _x167 ∧ x16 = _x168 ∧ x17 = _x169 ∧ x18 = _x170 ∧ x19 = _x171 ∧ x20 = _x172 ∧ x21 = _x173 ∧ x22 = _x174 ∧ x23 = _x175 ∧ x24 = _x176 ∧ x25 = _x177 ∧ x1 = _x178 ∧ x2 = _x179 ∧ x3 = _x180 ∧ x4 = _x181 ∧ x5 = _x182 ∧ x6 = _x183 ∧ x7 = _x184 ∧ x8 = _x185 ∧ x9 = _x186 ∧ x10 = _x187 ∧ x11 = _x188 ∧ x12 = _x189 ∧ x13 = _x190 ∧ x14 = _x191 ∧ x15 = _x192 ∧ x16 = _x193 ∧ x17 = _x194 ∧ x18 = _x195 ∧ x19 = _x196 ∧ x20 = _x197 ∧ x21 = _x198 ∧ x22 = _x199 ∧ x23 = _x200 ∧ x24 = _x201 ∧ x25 = _x202 ∧ 0 ≤ _x156 ∧ 0 ≤ _x162 ∧ _x186 = _x162 ∧ _x203 = _x203 ∧ _x204 = _x204 ∧ 0 ≤ _x203 − _x204 ∧ _x191 = _x191 ∧ _x192 = _x192 ∧ _x169 ≤ 0 ∧ 0 ≤ _x169 ∧ _x195 = _x173 ∧ _x153 = _x178 ∧ _x154 = _x179 ∧ _x155 = _x180 ∧ _x156 = _x181 ∧ _x157 = _x182 ∧ _x158 = _x183 ∧ _x159 = _x184 ∧ _x160 = _x185 ∧ _x162 = _x187 ∧ _x163 = _x188 ∧ _x164 = _x189 ∧ _x165 = _x190 ∧ _x168 = _x193 ∧ _x169 = _x194 ∧ _x171 = _x196 ∧ _x172 = _x197 ∧ _x173 = _x198 ∧ _x174 = _x199 ∧ _x175 = _x200 ∧ _x176 = _x201 ∧ _x177 = _x202 l1 6 l5: x1 = _x205 ∧ x2 = _x206 ∧ x3 = _x207 ∧ x4 = _x208 ∧ x5 = _x209 ∧ x6 = _x210 ∧ x7 = _x211 ∧ x8 = _x212 ∧ x9 = _x213 ∧ x10 = _x214 ∧ x11 = _x215 ∧ x12 = _x216 ∧ x13 = _x217 ∧ x14 = _x218 ∧ x15 = _x219 ∧ x16 = _x220 ∧ x17 = _x221 ∧ x18 = _x222 ∧ x19 = _x223 ∧ x20 = _x224 ∧ x21 = _x225 ∧ x22 = _x226 ∧ x23 = _x227 ∧ x24 = _x228 ∧ x25 = _x229 ∧ x1 = _x230 ∧ x2 = _x231 ∧ x3 = _x232 ∧ x4 = _x233 ∧ x5 = _x234 ∧ x6 = _x235 ∧ x7 = _x236 ∧ x8 = _x237 ∧ x9 = _x238 ∧ x10 = _x239 ∧ x11 = _x240 ∧ x12 = _x241 ∧ x13 = _x242 ∧ x14 = _x243 ∧ x15 = _x244 ∧ x16 = _x245 ∧ x17 = _x246 ∧ x18 = _x247 ∧ x19 = _x248 ∧ x20 = _x249 ∧ x21 = _x250 ∧ x22 = _x251 ∧ x23 = _x252 ∧ x24 = _x253 ∧ x25 = _x254 ∧ 0 ≤ _x208 ∧ 0 ≤ _x214 ∧ _x255 = _x255 ∧ _x256 = _x256 ∧ 1 + _x255 − _x256 ≤ 0 ∧ _x243 = _x243 ∧ _x244 = _x244 ∧ _x246 = _x210 ∧ _x257 = _x227 ∧ _x235 = _x257 ∧ _x242 = _x242 ∧ 0 ≤ _x208 ∧ 0 ≤ −1 + _x214 ∧ _x205 = _x230 ∧ _x206 = _x231 ∧ _x207 = _x232 ∧ _x208 = _x233 ∧ _x209 = _x234 ∧ _x211 = _x236 ∧ _x212 = _x237 ∧ _x213 = _x238 ∧ _x214 = _x239 ∧ _x215 = _x240 ∧ _x216 = _x241 ∧ _x220 = _x245 ∧ _x222 = _x247 ∧ _x223 = _x248 ∧ _x224 = _x249 ∧ _x225 = _x250 ∧ _x226 = _x251 ∧ _x227 = _x252 ∧ _x228 = _x253 ∧ _x229 = _x254 l4 7 l6: x1 = _x258 ∧ x2 = _x259 ∧ x3 = _x260 ∧ x4 = _x261 ∧ x5 = _x262 ∧ x6 = _x263 ∧ x7 = _x264 ∧ x8 = _x265 ∧ x9 = _x266 ∧ x10 = _x267 ∧ x11 = _x268 ∧ x12 = _x269 ∧ x13 = _x270 ∧ x14 = _x271 ∧ x15 = _x272 ∧ x16 = _x273 ∧ x17 = _x274 ∧ x18 = _x275 ∧ x19 = _x276 ∧ x20 = _x277 ∧ x21 = _x278 ∧ x22 = _x279 ∧ x23 = _x280 ∧ x24 = _x281 ∧ x25 = _x282 ∧ x1 = _x283 ∧ x2 = _x284 ∧ x3 = _x285 ∧ x4 = _x286 ∧ x5 = _x287 ∧ x6 = _x288 ∧ x7 = _x289 ∧ x8 = _x290 ∧ x9 = _x291 ∧ x10 = _x292 ∧ x11 = _x293 ∧ x12 = _x294 ∧ x13 = _x295 ∧ x14 = _x296 ∧ x15 = _x297 ∧ x16 = _x298 ∧ x17 = _x299 ∧ x18 = _x300 ∧ x19 = _x301 ∧ x20 = _x302 ∧ x21 = _x303 ∧ x22 = _x304 ∧ x23 = _x305 ∧ x24 = _x306 ∧ x25 = _x307 ∧ _x282 = _x307 ∧ _x281 = _x306 ∧ _x280 = _x305 ∧ _x279 = _x304 ∧ _x278 = _x303 ∧ _x277 = _x302 ∧ _x276 = _x301 ∧ _x275 = _x300 ∧ _x274 = _x299 ∧ _x273 = _x298 ∧ _x272 = _x297 ∧ _x271 = _x296 ∧ _x270 = _x295 ∧ _x269 = _x294 ∧ _x268 = _x293 ∧ _x267 = _x292 ∧ _x266 = _x291 ∧ _x265 = _x290 ∧ _x264 = _x289 ∧ _x263 = _x288 ∧ _x262 = _x287 ∧ _x261 = _x286 ∧ _x260 = _x285 ∧ _x259 = _x284 ∧ _x283 = _x283 ∧ 0 ≤ _x262 ∧ _x262 ≤ 0 ∧ 0 ≤ _x266 ∧ 0 ≤ _x261 l4 8 l1: x1 = _x308 ∧ x2 = _x309 ∧ x3 = _x310 ∧ x4 = _x311 ∧ x5 = _x312 ∧ x6 = _x313 ∧ x7 = _x314 ∧ x8 = _x315 ∧ x9 = _x316 ∧ x10 = _x317 ∧ x11 = _x318 ∧ x12 = _x319 ∧ x13 = _x320 ∧ x14 = _x321 ∧ x15 = _x322 ∧ x16 = _x323 ∧ x17 = _x324 ∧ x18 = _x325 ∧ x19 = _x326 ∧ x20 = _x327 ∧ x21 = _x328 ∧ x22 = _x329 ∧ x23 = _x330 ∧ x24 = _x331 ∧ x25 = _x332 ∧ x1 = _x333 ∧ x2 = _x334 ∧ x3 = _x335 ∧ x4 = _x336 ∧ x5 = _x337 ∧ x6 = _x338 ∧ x7 = _x339 ∧ x8 = _x340 ∧ x9 = _x341 ∧ x10 = _x342 ∧ x11 = _x343 ∧ x12 = _x344 ∧ x13 = _x345 ∧ x14 = _x346 ∧ x15 = _x347 ∧ x16 = _x348 ∧ x17 = _x349 ∧ x18 = _x350 ∧ x19 = _x351 ∧ x20 = _x352 ∧ x21 = _x353 ∧ x22 = _x354 ∧ x23 = _x355 ∧ x24 = _x356 ∧ x25 = _x357 ∧ 0 ≤ _x311 ∧ 0 ≤ _x316 ∧ _x342 = 1 + _x316 ∧ _x336 = −1 + _x311 ∧ _x353 = _x312 ∧ _x358 = _x331 ∧ _x337 = _x358 ∧ _x348 = _x348 ∧ _x338 = _x325 ∧ _x349 = 0 ∧ _x308 = _x333 ∧ _x309 = _x334 ∧ _x310 = _x335 ∧ _x314 = _x339 ∧ _x315 = _x340 ∧ _x316 = _x341 ∧ _x318 = _x343 ∧ _x319 = _x344 ∧ _x320 = _x345 ∧ _x321 = _x346 ∧ _x322 = _x347 ∧ _x325 = _x350 ∧ _x326 = _x351 ∧ _x327 = _x352 ∧ _x329 = _x354 ∧ _x330 = _x355 ∧ _x331 = _x356 ∧ _x332 = _x357 l7 9 l3: x1 = _x359 ∧ x2 = _x360 ∧ x3 = _x361 ∧ x4 = _x362 ∧ x5 = _x363 ∧ x6 = _x364 ∧ x7 = _x365 ∧ x8 = _x366 ∧ x9 = _x367 ∧ x10 = _x368 ∧ x11 = _x369 ∧ x12 = _x370 ∧ x13 = _x371 ∧ x14 = _x372 ∧ x15 = _x373 ∧ x16 = _x374 ∧ x17 = _x375 ∧ x18 = _x376 ∧ x19 = _x377 ∧ x20 = _x378 ∧ x21 = _x379 ∧ x22 = _x380 ∧ x23 = _x381 ∧ x24 = _x382 ∧ x25 = _x383 ∧ x1 = _x384 ∧ x2 = _x385 ∧ x3 = _x386 ∧ x4 = _x387 ∧ x5 = _x388 ∧ x6 = _x389 ∧ x7 = _x390 ∧ x8 = _x391 ∧ x9 = _x392 ∧ x10 = _x393 ∧ x11 = _x394 ∧ x12 = _x395 ∧ x13 = _x396 ∧ x14 = _x397 ∧ x15 = _x398 ∧ x16 = _x399 ∧ x17 = _x400 ∧ x18 = _x401 ∧ x19 = _x402 ∧ x20 = _x403 ∧ x21 = _x404 ∧ x22 = _x405 ∧ x23 = _x406 ∧ x24 = _x407 ∧ x25 = _x408 ∧ _x383 = _x408 ∧ _x382 = _x407 ∧ _x381 = _x406 ∧ _x380 = _x405 ∧ _x379 = _x404 ∧ _x378 = _x403 ∧ _x377 = _x402 ∧ _x376 = _x401 ∧ _x375 = _x400 ∧ _x374 = _x399 ∧ _x373 = _x398 ∧ _x372 = _x397 ∧ _x371 = _x396 ∧ _x370 = _x395 ∧ _x369 = _x394 ∧ _x368 = _x393 ∧ _x367 = _x392 ∧ _x366 = _x391 ∧ _x365 = _x390 ∧ _x364 = _x389 ∧ _x363 = _x388 ∧ _x362 = _x387 ∧ _x361 = _x386 ∧ _x360 = _x385 ∧ _x359 = _x384

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 l4 l4 l4: 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 ∧ x23 = x23 ∧ x24 = x24 ∧ x25 = x25 l7 l7 l7: 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 ∧ x23 = x23 ∧ x24 = x24 ∧ x25 = x25 l1 l1 l1: 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 ∧ x23 = x23 ∧ x24 = x24 ∧ x25 = x25 l3 l3 l3: 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 ∧ x23 = x23 ∧ x24 = x24 ∧ x25 = x25 l0 l0 l0: 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 ∧ x23 = x23 ∧ x24 = x24 ∧ x25 = x25 l2 l2 l2: 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 ∧ x14 = x14 ∧ x15 = x15 ∧ x16 = x16 ∧ x17 = x17 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20 ∧ x21 = x21 ∧ x22 = x22 ∧ x23 = x23 ∧ x24 = x24 ∧ x25 = x25
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 { l0, l2 }.

### 2.1.1 Transition Removal

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

 l0: −1 − 2⋅x8 + x11 + 2⋅x12 l2: −1 − 2⋅x8 + x11 + 2⋅x12

### 2.1.2 Transition Removal

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

 l2: 0 l0: −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 { l4, l1 }.

### 2.2.1 Transition Removal

We remove transitions 5, 8 using the following ranking functions, which are bounded by 0.

 l1: 2⋅x4 + 1 l4: 2⋅x4

### 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)