LTS Termination Proof

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 = ___const_17HAT0 ∧ x4 = _a_128HAT0 ∧ x5 = _a_243HAT0 ∧ x6 = _c_15HAT0 ∧ x7 = _elem_16HAT0 ∧ x8 = _head_9HAT0 ∧ x9 = _i_8HAT0 ∧ x10 = _k_296HAT0 ∧ x11 = _len_246HAT0 ∧ x12 = _len_48HAT0 ∧ x13 = _length_7HAT0 ∧ x14 = _lt_18HAT0 ∧ x15 = _lt_19HAT0 ∧ x16 = _lt_20HAT0 ∧ x17 = _lt_21HAT0 ∧ x18 = _prev_17HAT0 ∧ x19 = _x_13HAT0 ∧ x20 = _x_23HAT0 ∧ x21 = _y_110HAT0 ∧ x22 = _y_14HAT0 ∧ x23 = _y_158HAT0 ∧ x24 = _y_259HAT0 ∧ x25 = _y_309HAT0 ∧ x26 = _y_80HAT0 ∧ x1 = _Result_6HATpost ∧ x2 = __HATpost ∧ x3 = ___const_17HATpost ∧ x4 = _a_128HATpost ∧ x5 = _a_243HATpost ∧ x6 = _c_15HATpost ∧ x7 = _elem_16HATpost ∧ x8 = _head_9HATpost ∧ x9 = _i_8HATpost ∧ x10 = _k_296HATpost ∧ x11 = _len_246HATpost ∧ x12 = _len_48HATpost ∧ x13 = _length_7HATpost ∧ x14 = _lt_18HATpost ∧ x15 = _lt_19HATpost ∧ x16 = _lt_20HATpost ∧ x17 = _lt_21HATpost ∧ x18 = _prev_17HATpost ∧ x19 = _x_13HATpost ∧ x20 = _x_23HATpost ∧ x21 = _y_110HATpost ∧ x22 = _y_14HATpost ∧ x23 = _y_158HATpost ∧ x24 = _y_259HATpost ∧ x25 = _y_309HATpost ∧ x26 = _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 ∧ ___const_17HAT0 = ___const_17HATpost ∧ _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 ∧ x26 = _x25 ∧ x1 = _x26 ∧ x2 = _x27 ∧ x3 = _x28 ∧ x4 = _x29 ∧ x5 = _x30 ∧ x6 = _x31 ∧ x7 = _x32 ∧ x8 = _x33 ∧ x9 = _x34 ∧ x10 = _x35 ∧ x11 = _x36 ∧ x12 = _x37 ∧ x13 = _x38 ∧ x14 = _x39 ∧ x15 = _x40 ∧ x16 = _x41 ∧ x17 = _x42 ∧ x18 = _x43 ∧ x19 = _x44 ∧ x20 = _x45 ∧ x21 = _x46 ∧ x22 = _x47 ∧ x23 = _x48 ∧ x24 = _x49 ∧ x25 = _x50 ∧ x26 = _x51 ∧ _x25 = _x51 ∧ _x24 = _x50 ∧ _x23 = _x49 ∧ _x22 = _x48 ∧ _x21 = _x47 ∧ _x20 = _x46 ∧ _x19 = _x45 ∧ _x18 = _x44 ∧ _x17 = _x43 ∧ _x16 = _x42 ∧ _x15 = _x41 ∧ _x14 = _x40 ∧ _x13 = _x39 ∧ _x12 = _x38 ∧ _x10 = _x36 ∧ _x9 = _x35 ∧ _x6 = _x32 ∧ _x5 = _x31 ∧ _x4 = _x30 ∧ _x3 = _x29 ∧ _x2 = _x28 ∧ _x1 = _x27 ∧ _x = _x26 ∧ _x34 = 1 + _x8 ∧ _x33 = _x33 ∧ 0 ≤ −1 − _x8 + _x12 ∧ _x37 = 1 + _x11 ∧ 0 ≤ _x11
l2	3	l0:	x1 = _x52 ∧ x2 = _x53 ∧ x3 = _x54 ∧ x4 = _x55 ∧ x5 = _x56 ∧ x6 = _x57 ∧ x7 = _x58 ∧ x8 = _x59 ∧ x9 = _x60 ∧ x10 = _x61 ∧ x11 = _x62 ∧ x12 = _x63 ∧ x13 = _x64 ∧ x14 = _x65 ∧ x15 = _x66 ∧ x16 = _x67 ∧ x17 = _x68 ∧ x18 = _x69 ∧ x19 = _x70 ∧ x20 = _x71 ∧ x21 = _x72 ∧ x22 = _x73 ∧ x23 = _x74 ∧ x24 = _x75 ∧ x25 = _x76 ∧ x26 = _x77 ∧ x1 = _x78 ∧ x2 = _x79 ∧ x3 = _x80 ∧ x4 = _x81 ∧ x5 = _x82 ∧ x6 = _x83 ∧ x7 = _x84 ∧ x8 = _x85 ∧ x9 = _x86 ∧ x10 = _x87 ∧ x11 = _x88 ∧ x12 = _x89 ∧ x13 = _x90 ∧ x14 = _x91 ∧ x15 = _x92 ∧ x16 = _x93 ∧ x17 = _x94 ∧ x18 = _x95 ∧ x19 = _x96 ∧ x20 = _x97 ∧ x21 = _x98 ∧ x22 = _x99 ∧ x23 = _x100 ∧ x24 = _x101 ∧ x25 = _x102 ∧ x26 = _x103 ∧ _x77 = _x103 ∧ _x76 = _x102 ∧ _x75 = _x101 ∧ _x74 = _x100 ∧ _x73 = _x99 ∧ _x72 = _x98 ∧ _x71 = _x97 ∧ _x70 = _x96 ∧ _x69 = _x95 ∧ _x68 = _x94 ∧ _x67 = _x93 ∧ _x66 = _x92 ∧ _x65 = _x91 ∧ _x64 = _x90 ∧ _x63 = _x89 ∧ _x62 = _x88 ∧ _x61 = _x87 ∧ _x60 = _x86 ∧ _x59 = _x85 ∧ _x58 = _x84 ∧ _x57 = _x83 ∧ _x56 = _x82 ∧ _x55 = _x81 ∧ _x54 = _x80 ∧ _x53 = _x79 ∧ _x52 = _x78
l3	4	l0:	x1 = _x104 ∧ x2 = _x105 ∧ x3 = _x106 ∧ x4 = _x107 ∧ x5 = _x108 ∧ x6 = _x109 ∧ x7 = _x110 ∧ x8 = _x111 ∧ x9 = _x112 ∧ x10 = _x113 ∧ x11 = _x114 ∧ x12 = _x115 ∧ x13 = _x116 ∧ x14 = _x117 ∧ x15 = _x118 ∧ x16 = _x119 ∧ x17 = _x120 ∧ x18 = _x121 ∧ x19 = _x122 ∧ x20 = _x123 ∧ x21 = _x124 ∧ x22 = _x125 ∧ x23 = _x126 ∧ x24 = _x127 ∧ x25 = _x128 ∧ x26 = _x129 ∧ x1 = _x130 ∧ x2 = _x131 ∧ x3 = _x132 ∧ x4 = _x133 ∧ x5 = _x134 ∧ x6 = _x135 ∧ x7 = _x136 ∧ x8 = _x137 ∧ x9 = _x138 ∧ x10 = _x139 ∧ x11 = _x140 ∧ x12 = _x141 ∧ x13 = _x142 ∧ x14 = _x143 ∧ x15 = _x144 ∧ x16 = _x145 ∧ x17 = _x146 ∧ x18 = _x147 ∧ x19 = _x148 ∧ x20 = _x149 ∧ x21 = _x150 ∧ x22 = _x151 ∧ x23 = _x152 ∧ x24 = _x153 ∧ x25 = _x154 ∧ x26 = _x155 ∧ _x156 = 0 ∧ _x142 = _x106 ∧ _x148 = _x123 ∧ _x157 = 0 ∧ _x158 = 0 ∧ _x141 = _x158 ∧ 0 ≤ −1 − _x158 + _x142 ∧ _x137 = _x137 ∧ _x138 = 1 + _x158 ∧ _x104 = _x130 ∧ _x105 = _x131 ∧ _x106 = _x132 ∧ _x107 = _x133 ∧ _x108 = _x134 ∧ _x109 = _x135 ∧ _x110 = _x136 ∧ _x113 = _x139 ∧ _x114 = _x140 ∧ _x117 = _x143 ∧ _x118 = _x144 ∧ _x119 = _x145 ∧ _x120 = _x146 ∧ _x121 = _x147 ∧ _x123 = _x149 ∧ _x124 = _x150 ∧ _x125 = _x151 ∧ _x126 = _x152 ∧ _x127 = _x153 ∧ _x128 = _x154 ∧ _x129 = _x155
l1	5	l4:	x1 = _x159 ∧ x2 = _x160 ∧ x3 = _x161 ∧ x4 = _x162 ∧ x5 = _x163 ∧ x6 = _x164 ∧ x7 = _x165 ∧ x8 = _x166 ∧ x9 = _x167 ∧ x10 = _x168 ∧ x11 = _x169 ∧ x12 = _x170 ∧ x13 = _x171 ∧ x14 = _x172 ∧ x15 = _x173 ∧ x16 = _x174 ∧ x17 = _x175 ∧ x18 = _x176 ∧ x19 = _x177 ∧ x20 = _x178 ∧ x21 = _x179 ∧ x22 = _x180 ∧ x23 = _x181 ∧ x24 = _x182 ∧ x25 = _x183 ∧ x26 = _x184 ∧ x1 = _x185 ∧ x2 = _x186 ∧ x3 = _x187 ∧ x4 = _x188 ∧ x5 = _x189 ∧ x6 = _x190 ∧ x7 = _x191 ∧ x8 = _x192 ∧ x9 = _x193 ∧ x10 = _x194 ∧ x11 = _x195 ∧ x12 = _x196 ∧ x13 = _x197 ∧ x14 = _x198 ∧ x15 = _x199 ∧ x16 = _x200 ∧ x17 = _x201 ∧ x18 = _x202 ∧ x19 = _x203 ∧ x20 = _x204 ∧ x21 = _x205 ∧ x22 = _x206 ∧ x23 = _x207 ∧ x24 = _x208 ∧ x25 = _x209 ∧ x26 = _x210 ∧ 0 ≤ _x163 ∧ 0 ≤ _x169 ∧ _x194 = _x169 ∧ _x211 = _x211 ∧ _x212 = _x212 ∧ 0 ≤ _x211 − _x212 ∧ _x199 = _x199 ∧ _x200 = _x200 ∧ _x176 ≤ 0 ∧ 0 ≤ _x176 ∧ _x203 = _x180 ∧ _x159 = _x185 ∧ _x160 = _x186 ∧ _x161 = _x187 ∧ _x162 = _x188 ∧ _x163 = _x189 ∧ _x164 = _x190 ∧ _x165 = _x191 ∧ _x166 = _x192 ∧ _x167 = _x193 ∧ _x169 = _x195 ∧ _x170 = _x196 ∧ _x171 = _x197 ∧ _x172 = _x198 ∧ _x175 = _x201 ∧ _x176 = _x202 ∧ _x178 = _x204 ∧ _x179 = _x205 ∧ _x180 = _x206 ∧ _x181 = _x207 ∧ _x182 = _x208 ∧ _x183 = _x209 ∧ _x184 = _x210
l1	6	l5:	x1 = _x213 ∧ x2 = _x214 ∧ x3 = _x215 ∧ x4 = _x216 ∧ x5 = _x217 ∧ x6 = _x218 ∧ x7 = _x219 ∧ x8 = _x220 ∧ x9 = _x221 ∧ x10 = _x222 ∧ x11 = _x223 ∧ x12 = _x224 ∧ x13 = _x225 ∧ x14 = _x226 ∧ x15 = _x227 ∧ x16 = _x228 ∧ x17 = _x229 ∧ x18 = _x230 ∧ x19 = _x231 ∧ x20 = _x232 ∧ x21 = _x233 ∧ x22 = _x234 ∧ x23 = _x235 ∧ x24 = _x236 ∧ x25 = _x237 ∧ x26 = _x238 ∧ x1 = _x239 ∧ x2 = _x240 ∧ x3 = _x241 ∧ x4 = _x242 ∧ x5 = _x243 ∧ x6 = _x244 ∧ x7 = _x245 ∧ x8 = _x246 ∧ x9 = _x247 ∧ x10 = _x248 ∧ x11 = _x249 ∧ x12 = _x250 ∧ x13 = _x251 ∧ x14 = _x252 ∧ x15 = _x253 ∧ x16 = _x254 ∧ x17 = _x255 ∧ x18 = _x256 ∧ x19 = _x257 ∧ x20 = _x258 ∧ x21 = _x259 ∧ x22 = _x260 ∧ x23 = _x261 ∧ x24 = _x262 ∧ x25 = _x263 ∧ x26 = _x264 ∧ 0 ≤ _x217 ∧ 0 ≤ _x223 ∧ _x265 = _x265 ∧ _x266 = _x266 ∧ 1 + _x265 − _x266 ≤ 0 ∧ _x253 = _x253 ∧ _x254 = _x254 ∧ _x256 = _x219 ∧ _x267 = _x236 ∧ _x245 = _x267 ∧ _x252 = _x252 ∧ 0 ≤ _x217 ∧ 0 ≤ −1 + _x223 ∧ _x213 = _x239 ∧ _x214 = _x240 ∧ _x215 = _x241 ∧ _x216 = _x242 ∧ _x217 = _x243 ∧ _x218 = _x244 ∧ _x220 = _x246 ∧ _x221 = _x247 ∧ _x222 = _x248 ∧ _x223 = _x249 ∧ _x224 = _x250 ∧ _x225 = _x251 ∧ _x229 = _x255 ∧ _x231 = _x257 ∧ _x232 = _x258 ∧ _x233 = _x259 ∧ _x234 = _x260 ∧ _x235 = _x261 ∧ _x236 = _x262 ∧ _x237 = _x263 ∧ _x238 = _x264
l4	7	l6:	x1 = _x268 ∧ x2 = _x269 ∧ x3 = _x270 ∧ x4 = _x271 ∧ x5 = _x272 ∧ x6 = _x273 ∧ x7 = _x274 ∧ x8 = _x275 ∧ x9 = _x276 ∧ x10 = _x277 ∧ x11 = _x278 ∧ x12 = _x279 ∧ x13 = _x280 ∧ x14 = _x281 ∧ x15 = _x282 ∧ x16 = _x283 ∧ x17 = _x284 ∧ x18 = _x285 ∧ x19 = _x286 ∧ x20 = _x287 ∧ x21 = _x288 ∧ x22 = _x289 ∧ x23 = _x290 ∧ x24 = _x291 ∧ x25 = _x292 ∧ x26 = _x293 ∧ x1 = _x294 ∧ x2 = _x295 ∧ x3 = _x296 ∧ x4 = _x297 ∧ x5 = _x298 ∧ x6 = _x299 ∧ x7 = _x300 ∧ x8 = _x301 ∧ x9 = _x302 ∧ x10 = _x303 ∧ x11 = _x304 ∧ x12 = _x305 ∧ x13 = _x306 ∧ x14 = _x307 ∧ x15 = _x308 ∧ x16 = _x309 ∧ x17 = _x310 ∧ x18 = _x311 ∧ x19 = _x312 ∧ x20 = _x313 ∧ x21 = _x314 ∧ x22 = _x315 ∧ x23 = _x316 ∧ x24 = _x317 ∧ x25 = _x318 ∧ x26 = _x319 ∧ _x293 = _x319 ∧ _x292 = _x318 ∧ _x291 = _x317 ∧ _x290 = _x316 ∧ _x289 = _x315 ∧ _x288 = _x314 ∧ _x287 = _x313 ∧ _x286 = _x312 ∧ _x285 = _x311 ∧ _x284 = _x310 ∧ _x283 = _x309 ∧ _x282 = _x308 ∧ _x281 = _x307 ∧ _x280 = _x306 ∧ _x279 = _x305 ∧ _x278 = _x304 ∧ _x277 = _x303 ∧ _x276 = _x302 ∧ _x275 = _x301 ∧ _x274 = _x300 ∧ _x273 = _x299 ∧ _x272 = _x298 ∧ _x271 = _x297 ∧ _x270 = _x296 ∧ _x269 = _x295 ∧ _x294 = _x294 ∧ 0 ≤ _x273 ∧ _x273 ≤ 0 ∧ 0 ≤ _x277 ∧ 0 ≤ _x272
l4	8	l1:	x1 = _x320 ∧ x2 = _x321 ∧ x3 = _x322 ∧ x4 = _x323 ∧ x5 = _x324 ∧ x6 = _x325 ∧ x7 = _x326 ∧ x8 = _x327 ∧ x9 = _x328 ∧ x10 = _x329 ∧ x11 = _x330 ∧ x12 = _x331 ∧ x13 = _x332 ∧ x14 = _x333 ∧ x15 = _x334 ∧ x16 = _x335 ∧ x17 = _x336 ∧ x18 = _x337 ∧ x19 = _x338 ∧ x20 = _x339 ∧ x21 = _x340 ∧ x22 = _x341 ∧ x23 = _x342 ∧ x24 = _x343 ∧ x25 = _x344 ∧ x26 = _x345 ∧ x1 = _x346 ∧ x2 = _x347 ∧ x3 = _x348 ∧ x4 = _x349 ∧ x5 = _x350 ∧ x6 = _x351 ∧ x7 = _x352 ∧ x8 = _x353 ∧ x9 = _x354 ∧ x10 = _x355 ∧ x11 = _x356 ∧ x12 = _x357 ∧ x13 = _x358 ∧ x14 = _x359 ∧ x15 = _x360 ∧ x16 = _x361 ∧ x17 = _x362 ∧ x18 = _x363 ∧ x19 = _x364 ∧ x20 = _x365 ∧ x21 = _x366 ∧ x22 = _x367 ∧ x23 = _x368 ∧ x24 = _x369 ∧ x25 = _x370 ∧ x26 = _x371 ∧ 0 ≤ _x324 ∧ 0 ≤ _x329 ∧ _x356 = 1 + _x329 ∧ _x350 = −1 + _x324 ∧ _x367 = _x325 ∧ _x372 = _x344 ∧ _x351 = _x372 ∧ _x362 = _x362 ∧ _x352 = _x338 ∧ _x363 = 0 ∧ _x320 = _x346 ∧ _x321 = _x347 ∧ _x322 = _x348 ∧ _x323 = _x349 ∧ _x327 = _x353 ∧ _x328 = _x354 ∧ _x329 = _x355 ∧ _x331 = _x357 ∧ _x332 = _x358 ∧ _x333 = _x359 ∧ _x334 = _x360 ∧ _x335 = _x361 ∧ _x338 = _x364 ∧ _x339 = _x365 ∧ _x340 = _x366 ∧ _x342 = _x368 ∧ _x343 = _x369 ∧ _x344 = _x370 ∧ _x345 = _x371
l7	9	l3:	x1 = _x373 ∧ x2 = _x374 ∧ x3 = _x375 ∧ x4 = _x376 ∧ x5 = _x377 ∧ x6 = _x378 ∧ x7 = _x379 ∧ x8 = _x380 ∧ x9 = _x381 ∧ x10 = _x382 ∧ x11 = _x383 ∧ x12 = _x384 ∧ x13 = _x385 ∧ x14 = _x386 ∧ x15 = _x387 ∧ x16 = _x388 ∧ x17 = _x389 ∧ x18 = _x390 ∧ x19 = _x391 ∧ x20 = _x392 ∧ x21 = _x393 ∧ x22 = _x394 ∧ x23 = _x395 ∧ x24 = _x396 ∧ x25 = _x397 ∧ x26 = _x398 ∧ x1 = _x399 ∧ x2 = _x400 ∧ x3 = _x401 ∧ x4 = _x402 ∧ x5 = _x403 ∧ x6 = _x404 ∧ x7 = _x405 ∧ x8 = _x406 ∧ x9 = _x407 ∧ x10 = _x408 ∧ x11 = _x409 ∧ x12 = _x410 ∧ x13 = _x411 ∧ x14 = _x412 ∧ x15 = _x413 ∧ x16 = _x414 ∧ x17 = _x415 ∧ x18 = _x416 ∧ x19 = _x417 ∧ x20 = _x418 ∧ x21 = _x419 ∧ x22 = _x420 ∧ x23 = _x421 ∧ x24 = _x422 ∧ x25 = _x423 ∧ x26 = _x424 ∧ _x398 = _x424 ∧ _x397 = _x423 ∧ _x396 = _x422 ∧ _x395 = _x421 ∧ _x394 = _x420 ∧ _x393 = _x419 ∧ _x392 = _x418 ∧ _x391 = _x417 ∧ _x390 = _x416 ∧ _x389 = _x415 ∧ _x388 = _x414 ∧ _x387 = _x413 ∧ _x386 = _x412 ∧ _x385 = _x411 ∧ _x384 = _x410 ∧ _x383 = _x409 ∧ _x382 = _x408 ∧ _x381 = _x407 ∧ _x380 = _x406 ∧ _x379 = _x405 ∧ _x378 = _x404 ∧ _x377 = _x403 ∧ _x376 = _x402 ∧ _x375 = _x401 ∧ _x374 = _x400 ∧ _x373 = _x399

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 ∧ x26 = x26
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 ∧ x26 = x26
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 ∧ x26 = x26
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 ∧ x26 = x26
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 ∧ x26 = x26
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 ∧ x26 = x26

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:	−2⋅x9 + 2⋅x13
l2:	−2⋅x9 + 2⋅x13 + 1

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:	1 + 2⋅x5 + 0⋅x18
l4:	2⋅x5

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)