LTS Termination Proof

Input

Integer Transition System

Initial Location: l5, l4, l7, l6, l11, l8, l1, l3, l0, l12, l2, l9

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = _Inner10HAT0 ∧ x2 = _InnerIndex7HAT0 ∧ x3 = _Ncnt14HAT0 ∧ x4 = _NegcntHAT0 ∧ x5 = _NegtotalHAT0 ∧ x6 = _Ntotal12HAT0 ∧ x7 = _Outer9HAT0 ∧ x8 = _OuterIndex6HAT0 ∧ x9 = _Pcnt13HAT0 ∧ x10 = _PoscntHAT0 ∧ x11 = _PostotalHAT0 ∧ x12 = _Ptotal11HAT0 ∧ x13 = _SeedHAT0 ∧ x14 = _StartTime2HAT0 ∧ x15 = _StopTime3HAT0 ∧ x16 = _TotalTime4HAT0 ∧ x17 = _ret_RandomInteger15HAT0 ∧ x1 = _Inner10HATpost ∧ x2 = _InnerIndex7HATpost ∧ x3 = _Ncnt14HATpost ∧ x4 = _NegcntHATpost ∧ x5 = _NegtotalHATpost ∧ x6 = _Ntotal12HATpost ∧ x7 = _Outer9HATpost ∧ x8 = _OuterIndex6HATpost ∧ x9 = _Pcnt13HATpost ∧ x10 = _PoscntHATpost ∧ x11 = _PostotalHATpost ∧ x12 = _Ptotal11HATpost ∧ x13 = _SeedHATpost ∧ x14 = _StartTime2HATpost ∧ x15 = _StopTime3HATpost ∧ x16 = _TotalTime4HATpost ∧ x17 = _ret_RandomInteger15HATpost ∧ _ret_RandomInteger15HAT0 = _ret_RandomInteger15HATpost ∧ _TotalTime4HAT0 = _TotalTime4HATpost ∧ _StopTime3HAT0 = _StopTime3HATpost ∧ _StartTime2HAT0 = _StartTime2HATpost ∧ _SeedHAT0 = _SeedHATpost ∧ _Ptotal11HAT0 = _Ptotal11HATpost ∧ _PostotalHAT0 = _PostotalHATpost ∧ _PoscntHAT0 = _PoscntHATpost ∧ _Pcnt13HAT0 = _Pcnt13HATpost ∧ _OuterIndex6HAT0 = _OuterIndex6HATpost ∧ _Outer9HAT0 = _Outer9HATpost ∧ _Ntotal12HAT0 = _Ntotal12HATpost ∧ _NegtotalHAT0 = _NegtotalHATpost ∧ _NegcntHAT0 = _NegcntHATpost ∧ _Ncnt14HAT0 = _Ncnt14HATpost ∧ _InnerIndex7HAT0 = _InnerIndex7HATpost ∧ _Inner10HAT0 = _Inner10HATpost
l2	2	l3:	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 ∧ x1 = _x17 ∧ x2 = _x18 ∧ x3 = _x19 ∧ x4 = _x20 ∧ x5 = _x21 ∧ x6 = _x22 ∧ x7 = _x23 ∧ x8 = _x24 ∧ x9 = _x25 ∧ x10 = _x26 ∧ x11 = _x27 ∧ x12 = _x28 ∧ x13 = _x29 ∧ x14 = _x30 ∧ x15 = _x31 ∧ x16 = _x32 ∧ x17 = _x33 ∧ _x16 = _x33 ∧ _x15 = _x32 ∧ _x14 = _x31 ∧ _x13 = _x30 ∧ _x12 = _x29 ∧ _x11 = _x28 ∧ _x10 = _x27 ∧ _x9 = _x26 ∧ _x8 = _x25 ∧ _x7 = _x24 ∧ _x6 = _x23 ∧ _x5 = _x22 ∧ _x4 = _x21 ∧ _x3 = _x20 ∧ _x2 = _x19 ∧ _x1 = _x18 ∧ _x17 = 1 + _x
l4	3	l5:	x1 = _x34 ∧ x2 = _x35 ∧ x3 = _x36 ∧ x4 = _x37 ∧ x5 = _x38 ∧ x6 = _x39 ∧ x7 = _x40 ∧ x8 = _x41 ∧ x9 = _x42 ∧ x10 = _x43 ∧ x11 = _x44 ∧ x12 = _x45 ∧ x13 = _x46 ∧ x14 = _x47 ∧ x15 = _x48 ∧ x16 = _x49 ∧ x17 = _x50 ∧ x1 = _x51 ∧ x2 = _x52 ∧ x3 = _x53 ∧ x4 = _x54 ∧ x5 = _x55 ∧ x6 = _x56 ∧ x7 = _x57 ∧ x8 = _x58 ∧ x9 = _x59 ∧ x10 = _x60 ∧ x11 = _x61 ∧ x12 = _x62 ∧ x13 = _x63 ∧ x14 = _x64 ∧ x15 = _x65 ∧ x16 = _x66 ∧ x17 = _x67 ∧ _x50 = _x67 ∧ _x49 = _x66 ∧ _x48 = _x65 ∧ _x47 = _x64 ∧ _x46 = _x63 ∧ _x45 = _x62 ∧ _x44 = _x61 ∧ _x43 = _x60 ∧ _x42 = _x59 ∧ _x41 = _x58 ∧ _x40 = _x57 ∧ _x39 = _x56 ∧ _x38 = _x55 ∧ _x37 = _x54 ∧ _x36 = _x53 ∧ _x35 = _x52 ∧ _x34 = _x51
l6	4	l2:	x1 = _x68 ∧ x2 = _x69 ∧ x3 = _x70 ∧ x4 = _x71 ∧ x5 = _x72 ∧ x6 = _x73 ∧ x7 = _x74 ∧ x8 = _x75 ∧ x9 = _x76 ∧ x10 = _x77 ∧ x11 = _x78 ∧ x12 = _x79 ∧ x13 = _x80 ∧ x14 = _x81 ∧ x15 = _x82 ∧ x16 = _x83 ∧ x17 = _x84 ∧ x1 = _x85 ∧ x2 = _x86 ∧ x3 = _x87 ∧ x4 = _x88 ∧ x5 = _x89 ∧ x6 = _x90 ∧ x7 = _x91 ∧ x8 = _x92 ∧ x9 = _x93 ∧ x10 = _x94 ∧ x11 = _x95 ∧ x12 = _x96 ∧ x13 = _x97 ∧ x14 = _x98 ∧ x15 = _x99 ∧ x16 = _x100 ∧ x17 = _x101 ∧ _x84 = _x101 ∧ _x83 = _x100 ∧ _x82 = _x99 ∧ _x81 = _x98 ∧ _x80 = _x97 ∧ _x78 = _x95 ∧ _x77 = _x94 ∧ _x75 = _x92 ∧ _x74 = _x91 ∧ _x73 = _x90 ∧ _x72 = _x89 ∧ _x71 = _x88 ∧ _x70 = _x87 ∧ _x69 = _x86 ∧ _x68 = _x85 ∧ _x93 = 1 + _x76 ∧ _x96 = _x96
l6	5	l2:	x1 = _x102 ∧ x2 = _x103 ∧ x3 = _x104 ∧ x4 = _x105 ∧ x5 = _x106 ∧ x6 = _x107 ∧ x7 = _x108 ∧ x8 = _x109 ∧ x9 = _x110 ∧ x10 = _x111 ∧ x11 = _x112 ∧ x12 = _x113 ∧ x13 = _x114 ∧ x14 = _x115 ∧ x15 = _x116 ∧ x16 = _x117 ∧ x17 = _x118 ∧ x1 = _x119 ∧ x2 = _x120 ∧ x3 = _x121 ∧ x4 = _x122 ∧ x5 = _x123 ∧ x6 = _x124 ∧ x7 = _x125 ∧ x8 = _x126 ∧ x9 = _x127 ∧ x10 = _x128 ∧ x11 = _x129 ∧ x12 = _x130 ∧ x13 = _x131 ∧ x14 = _x132 ∧ x15 = _x133 ∧ x16 = _x134 ∧ x17 = _x135 ∧ _x118 = _x135 ∧ _x117 = _x134 ∧ _x116 = _x133 ∧ _x115 = _x132 ∧ _x114 = _x131 ∧ _x113 = _x130 ∧ _x112 = _x129 ∧ _x111 = _x128 ∧ _x110 = _x127 ∧ _x109 = _x126 ∧ _x108 = _x125 ∧ _x106 = _x123 ∧ _x105 = _x122 ∧ _x103 = _x120 ∧ _x102 = _x119 ∧ _x121 = 1 + _x104 ∧ _x124 = _x124
l7	6	l8:	x1 = _x136 ∧ x2 = _x137 ∧ x3 = _x138 ∧ x4 = _x139 ∧ x5 = _x140 ∧ x6 = _x141 ∧ x7 = _x142 ∧ x8 = _x143 ∧ x9 = _x144 ∧ x10 = _x145 ∧ x11 = _x146 ∧ x12 = _x147 ∧ x13 = _x148 ∧ x14 = _x149 ∧ x15 = _x150 ∧ x16 = _x151 ∧ x17 = _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 ∧ x14 = _x166 ∧ x15 = _x167 ∧ x16 = _x168 ∧ x17 = _x169 ∧ _x152 = _x169 ∧ _x151 = _x168 ∧ _x150 = _x167 ∧ _x149 = _x166 ∧ _x148 = _x165 ∧ _x147 = _x164 ∧ _x146 = _x163 ∧ _x145 = _x162 ∧ _x144 = _x161 ∧ _x143 = _x160 ∧ _x141 = _x158 ∧ _x140 = _x157 ∧ _x139 = _x156 ∧ _x138 = _x155 ∧ _x137 = _x154 ∧ _x136 = _x153 ∧ _x159 = 1 + _x142 ∧ 10 ≤ _x136
l7	7	l6:	x1 = _x170 ∧ x2 = _x171 ∧ x3 = _x172 ∧ x4 = _x173 ∧ x5 = _x174 ∧ x6 = _x175 ∧ x7 = _x176 ∧ x8 = _x177 ∧ x9 = _x178 ∧ x10 = _x179 ∧ x11 = _x180 ∧ x12 = _x181 ∧ x13 = _x182 ∧ x14 = _x183 ∧ x15 = _x184 ∧ x16 = _x185 ∧ x17 = _x186 ∧ x1 = _x187 ∧ x2 = _x188 ∧ x3 = _x189 ∧ x4 = _x190 ∧ x5 = _x191 ∧ x6 = _x192 ∧ x7 = _x193 ∧ x8 = _x194 ∧ x9 = _x195 ∧ x10 = _x196 ∧ x11 = _x197 ∧ x12 = _x198 ∧ x13 = _x199 ∧ x14 = _x200 ∧ x15 = _x201 ∧ x16 = _x202 ∧ x17 = _x203 ∧ _x186 = _x203 ∧ _x185 = _x202 ∧ _x184 = _x201 ∧ _x183 = _x200 ∧ _x182 = _x199 ∧ _x181 = _x198 ∧ _x180 = _x197 ∧ _x179 = _x196 ∧ _x178 = _x195 ∧ _x177 = _x194 ∧ _x176 = _x193 ∧ _x175 = _x192 ∧ _x174 = _x191 ∧ _x173 = _x190 ∧ _x172 = _x189 ∧ _x171 = _x188 ∧ _x170 = _x187 ∧ 1 + _x170 ≤ 10
l9	8	l10:	x1 = _x204 ∧ x2 = _x205 ∧ x3 = _x206 ∧ x4 = _x207 ∧ x5 = _x208 ∧ x6 = _x209 ∧ x7 = _x210 ∧ x8 = _x211 ∧ x9 = _x212 ∧ x10 = _x213 ∧ x11 = _x214 ∧ x12 = _x215 ∧ x13 = _x216 ∧ x14 = _x217 ∧ x15 = _x218 ∧ x16 = _x219 ∧ x17 = _x220 ∧ x1 = _x221 ∧ x2 = _x222 ∧ x3 = _x223 ∧ x4 = _x224 ∧ x5 = _x225 ∧ x6 = _x226 ∧ x7 = _x227 ∧ x8 = _x228 ∧ x9 = _x229 ∧ x10 = _x230 ∧ x11 = _x231 ∧ x12 = _x232 ∧ x13 = _x233 ∧ x14 = _x234 ∧ x15 = _x235 ∧ x16 = _x236 ∧ x17 = _x237 ∧ _x220 = _x237 ∧ _x217 = _x234 ∧ _x216 = _x233 ∧ _x215 = _x232 ∧ _x212 = _x229 ∧ _x211 = _x228 ∧ _x210 = _x227 ∧ _x209 = _x226 ∧ _x206 = _x223 ∧ _x205 = _x222 ∧ _x204 = _x221 ∧ _x236 = _x236 ∧ _x235 = 1500 ∧ _x224 = _x206 ∧ _x225 = _x209 ∧ _x230 = _x212 ∧ _x231 = _x215 ∧ 10 ≤ _x210
l9	9	l3:	x1 = _x238 ∧ x2 = _x239 ∧ x3 = _x240 ∧ x4 = _x241 ∧ x5 = _x242 ∧ x6 = _x243 ∧ x7 = _x244 ∧ x8 = _x245 ∧ x9 = _x246 ∧ x10 = _x247 ∧ x11 = _x248 ∧ x12 = _x249 ∧ x13 = _x250 ∧ x14 = _x251 ∧ x15 = _x252 ∧ x16 = _x253 ∧ x17 = _x254 ∧ x1 = _x255 ∧ x2 = _x256 ∧ x3 = _x257 ∧ x4 = _x258 ∧ x5 = _x259 ∧ x6 = _x260 ∧ x7 = _x261 ∧ x8 = _x262 ∧ x9 = _x263 ∧ x10 = _x264 ∧ x11 = _x265 ∧ x12 = _x266 ∧ x13 = _x267 ∧ x14 = _x268 ∧ x15 = _x269 ∧ x16 = _x270 ∧ x17 = _x271 ∧ _x254 = _x271 ∧ _x253 = _x270 ∧ _x252 = _x269 ∧ _x251 = _x268 ∧ _x250 = _x267 ∧ _x249 = _x266 ∧ _x248 = _x265 ∧ _x247 = _x264 ∧ _x246 = _x263 ∧ _x245 = _x262 ∧ _x244 = _x261 ∧ _x243 = _x260 ∧ _x242 = _x259 ∧ _x241 = _x258 ∧ _x240 = _x257 ∧ _x239 = _x256 ∧ _x255 = 0 ∧ 1 + _x244 ≤ 10
l8	10	l9:	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 ∧ x14 = _x285 ∧ x15 = _x286 ∧ x16 = _x287 ∧ x17 = _x288 ∧ x1 = _x289 ∧ x2 = _x290 ∧ x3 = _x291 ∧ x4 = _x292 ∧ x5 = _x293 ∧ x6 = _x294 ∧ x7 = _x295 ∧ x8 = _x296 ∧ x9 = _x297 ∧ x10 = _x298 ∧ x11 = _x299 ∧ x12 = _x300 ∧ x13 = _x301 ∧ x14 = _x302 ∧ x15 = _x303 ∧ x16 = _x304 ∧ x17 = _x305 ∧ _x288 = _x305 ∧ _x287 = _x304 ∧ _x286 = _x303 ∧ _x285 = _x302 ∧ _x284 = _x301 ∧ _x283 = _x300 ∧ _x282 = _x299 ∧ _x281 = _x298 ∧ _x280 = _x297 ∧ _x279 = _x296 ∧ _x278 = _x295 ∧ _x277 = _x294 ∧ _x276 = _x293 ∧ _x275 = _x292 ∧ _x274 = _x291 ∧ _x273 = _x290 ∧ _x272 = _x289
l3	11	l7:	x1 = _x306 ∧ x2 = _x307 ∧ x3 = _x308 ∧ x4 = _x309 ∧ x5 = _x310 ∧ x6 = _x311 ∧ x7 = _x312 ∧ x8 = _x313 ∧ x9 = _x314 ∧ x10 = _x315 ∧ x11 = _x316 ∧ x12 = _x317 ∧ x13 = _x318 ∧ x14 = _x319 ∧ x15 = _x320 ∧ x16 = _x321 ∧ x17 = _x322 ∧ x1 = _x323 ∧ x2 = _x324 ∧ x3 = _x325 ∧ x4 = _x326 ∧ x5 = _x327 ∧ x6 = _x328 ∧ x7 = _x329 ∧ x8 = _x330 ∧ x9 = _x331 ∧ x10 = _x332 ∧ x11 = _x333 ∧ x12 = _x334 ∧ x13 = _x335 ∧ x14 = _x336 ∧ x15 = _x337 ∧ x16 = _x338 ∧ x17 = _x339 ∧ _x322 = _x339 ∧ _x321 = _x338 ∧ _x320 = _x337 ∧ _x319 = _x336 ∧ _x318 = _x335 ∧ _x317 = _x334 ∧ _x316 = _x333 ∧ _x315 = _x332 ∧ _x314 = _x331 ∧ _x313 = _x330 ∧ _x312 = _x329 ∧ _x311 = _x328 ∧ _x310 = _x327 ∧ _x309 = _x326 ∧ _x308 = _x325 ∧ _x307 = _x324 ∧ _x306 = _x323
l5	12	l0:	x1 = _x340 ∧ x2 = _x341 ∧ x3 = _x342 ∧ x4 = _x343 ∧ x5 = _x344 ∧ x6 = _x345 ∧ x7 = _x346 ∧ x8 = _x347 ∧ x9 = _x348 ∧ x10 = _x349 ∧ x11 = _x350 ∧ x12 = _x351 ∧ x13 = _x352 ∧ x14 = _x353 ∧ x15 = _x354 ∧ x16 = _x355 ∧ x17 = _x356 ∧ x1 = _x357 ∧ x2 = _x358 ∧ x3 = _x359 ∧ x4 = _x360 ∧ x5 = _x361 ∧ x6 = _x362 ∧ x7 = _x363 ∧ x8 = _x364 ∧ x9 = _x365 ∧ x10 = _x366 ∧ x11 = _x367 ∧ x12 = _x368 ∧ x13 = _x369 ∧ x14 = _x370 ∧ x15 = _x371 ∧ x16 = _x372 ∧ x17 = _x373 ∧ _x356 = _x373 ∧ _x355 = _x372 ∧ _x354 = _x371 ∧ _x353 = _x370 ∧ _x352 = _x369 ∧ _x351 = _x368 ∧ _x350 = _x367 ∧ _x349 = _x366 ∧ _x348 = _x365 ∧ _x346 = _x363 ∧ _x345 = _x362 ∧ _x344 = _x361 ∧ _x343 = _x360 ∧ _x342 = _x359 ∧ _x341 = _x358 ∧ _x340 = _x357 ∧ _x364 = 1 + _x347 ∧ 10 ≤ _x341
l5	13	l4:	x1 = _x374 ∧ x2 = _x375 ∧ x3 = _x376 ∧ x4 = _x377 ∧ x5 = _x378 ∧ x6 = _x379 ∧ x7 = _x380 ∧ x8 = _x381 ∧ x9 = _x382 ∧ x10 = _x383 ∧ x11 = _x384 ∧ x12 = _x385 ∧ x13 = _x386 ∧ x14 = _x387 ∧ x15 = _x388 ∧ x16 = _x389 ∧ x17 = _x390 ∧ x1 = _x391 ∧ x2 = _x392 ∧ x3 = _x393 ∧ x4 = _x394 ∧ x5 = _x395 ∧ x6 = _x396 ∧ x7 = _x397 ∧ x8 = _x398 ∧ x9 = _x399 ∧ x10 = _x400 ∧ x11 = _x401 ∧ x12 = _x402 ∧ x13 = _x403 ∧ x14 = _x404 ∧ x15 = _x405 ∧ x16 = _x406 ∧ x17 = _x407 ∧ _x389 = _x406 ∧ _x388 = _x405 ∧ _x387 = _x404 ∧ _x385 = _x402 ∧ _x384 = _x401 ∧ _x383 = _x400 ∧ _x382 = _x399 ∧ _x381 = _x398 ∧ _x380 = _x397 ∧ _x379 = _x396 ∧ _x378 = _x395 ∧ _x377 = _x394 ∧ _x376 = _x393 ∧ _x374 = _x391 ∧ _x392 = 1 + _x375 ∧ _x407 = _x403 ∧ _x403 = _x403 ∧ 1 + _x375 ≤ 10
l1	14	l8:	x1 = _x408 ∧ x2 = _x409 ∧ x3 = _x410 ∧ x4 = _x411 ∧ x5 = _x412 ∧ x6 = _x413 ∧ x7 = _x414 ∧ x8 = _x415 ∧ x9 = _x416 ∧ x10 = _x417 ∧ x11 = _x418 ∧ x12 = _x419 ∧ x13 = _x420 ∧ x14 = _x421 ∧ x15 = _x422 ∧ x16 = _x423 ∧ x17 = _x424 ∧ x1 = _x425 ∧ x2 = _x426 ∧ x3 = _x427 ∧ x4 = _x428 ∧ x5 = _x429 ∧ x6 = _x430 ∧ x7 = _x431 ∧ x8 = _x432 ∧ x9 = _x433 ∧ x10 = _x434 ∧ x11 = _x435 ∧ x12 = _x436 ∧ x13 = _x437 ∧ x14 = _x438 ∧ x15 = _x439 ∧ x16 = _x440 ∧ x17 = _x441 ∧ _x424 = _x441 ∧ _x423 = _x440 ∧ _x422 = _x439 ∧ _x420 = _x437 ∧ _x418 = _x435 ∧ _x417 = _x434 ∧ _x415 = _x432 ∧ _x412 = _x429 ∧ _x411 = _x428 ∧ _x409 = _x426 ∧ _x408 = _x425 ∧ _x431 = 0 ∧ _x427 = 0 ∧ _x433 = 0 ∧ _x430 = 0 ∧ _x436 = 0 ∧ _x438 = 1000 ∧ 10 ≤ _x415
l1	15	l4:	x1 = _x442 ∧ x2 = _x443 ∧ x3 = _x444 ∧ x4 = _x445 ∧ x5 = _x446 ∧ x6 = _x447 ∧ x7 = _x448 ∧ x8 = _x449 ∧ x9 = _x450 ∧ x10 = _x451 ∧ x11 = _x452 ∧ x12 = _x453 ∧ x13 = _x454 ∧ x14 = _x455 ∧ x15 = _x456 ∧ x16 = _x457 ∧ x17 = _x458 ∧ x1 = _x459 ∧ x2 = _x460 ∧ x3 = _x461 ∧ x4 = _x462 ∧ x5 = _x463 ∧ x6 = _x464 ∧ x7 = _x465 ∧ x8 = _x466 ∧ x9 = _x467 ∧ x10 = _x468 ∧ x11 = _x469 ∧ x12 = _x470 ∧ x13 = _x471 ∧ x14 = _x472 ∧ x15 = _x473 ∧ x16 = _x474 ∧ x17 = _x475 ∧ _x458 = _x475 ∧ _x457 = _x474 ∧ _x456 = _x473 ∧ _x455 = _x472 ∧ _x454 = _x471 ∧ _x453 = _x470 ∧ _x452 = _x469 ∧ _x451 = _x468 ∧ _x450 = _x467 ∧ _x449 = _x466 ∧ _x448 = _x465 ∧ _x447 = _x464 ∧ _x446 = _x463 ∧ _x445 = _x462 ∧ _x444 = _x461 ∧ _x442 = _x459 ∧ _x460 = 0 ∧ 1 + _x449 ≤ 10
l11	16	l0:	x1 = _x476 ∧ x2 = _x477 ∧ x3 = _x478 ∧ x4 = _x479 ∧ x5 = _x480 ∧ x6 = _x481 ∧ x7 = _x482 ∧ x8 = _x483 ∧ x9 = _x484 ∧ x10 = _x485 ∧ x11 = _x486 ∧ x12 = _x487 ∧ x13 = _x488 ∧ x14 = _x489 ∧ x15 = _x490 ∧ x16 = _x491 ∧ x17 = _x492 ∧ x1 = _x493 ∧ x2 = _x494 ∧ x3 = _x495 ∧ x4 = _x496 ∧ x5 = _x497 ∧ x6 = _x498 ∧ x7 = _x499 ∧ x8 = _x500 ∧ x9 = _x501 ∧ x10 = _x502 ∧ x11 = _x503 ∧ x12 = _x504 ∧ x13 = _x505 ∧ x14 = _x506 ∧ x15 = _x507 ∧ x16 = _x508 ∧ x17 = _x509 ∧ _x492 = _x509 ∧ _x491 = _x508 ∧ _x490 = _x507 ∧ _x489 = _x506 ∧ _x487 = _x504 ∧ _x486 = _x503 ∧ _x485 = _x502 ∧ _x484 = _x501 ∧ _x482 = _x499 ∧ _x481 = _x498 ∧ _x480 = _x497 ∧ _x479 = _x496 ∧ _x478 = _x495 ∧ _x477 = _x494 ∧ _x476 = _x493 ∧ _x500 = 0 ∧ _x505 = 0
l12	17	l11:	x1 = _x510 ∧ x2 = _x511 ∧ x3 = _x512 ∧ x4 = _x513 ∧ x5 = _x514 ∧ x6 = _x515 ∧ x7 = _x516 ∧ x8 = _x517 ∧ x9 = _x518 ∧ x10 = _x519 ∧ x11 = _x520 ∧ x12 = _x521 ∧ x13 = _x522 ∧ x14 = _x523 ∧ x15 = _x524 ∧ x16 = _x525 ∧ x17 = _x526 ∧ x1 = _x527 ∧ x2 = _x528 ∧ x3 = _x529 ∧ x4 = _x530 ∧ x5 = _x531 ∧ x6 = _x532 ∧ x7 = _x533 ∧ x8 = _x534 ∧ x9 = _x535 ∧ x10 = _x536 ∧ x11 = _x537 ∧ x12 = _x538 ∧ x13 = _x539 ∧ x14 = _x540 ∧ x15 = _x541 ∧ x16 = _x542 ∧ x17 = _x543 ∧ _x526 = _x543 ∧ _x525 = _x542 ∧ _x524 = _x541 ∧ _x523 = _x540 ∧ _x522 = _x539 ∧ _x521 = _x538 ∧ _x520 = _x537 ∧ _x519 = _x536 ∧ _x518 = _x535 ∧ _x517 = _x534 ∧ _x516 = _x533 ∧ _x515 = _x532 ∧ _x514 = _x531 ∧ _x513 = _x530 ∧ _x512 = _x529 ∧ _x511 = _x528 ∧ _x510 = _x527

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

l5	l5	l5:	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
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
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
l6	l6	l6:	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
l11	l11	l11:	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
l8	l8	l8:	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
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
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
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
l12	l12	l12:	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
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
l9	l9	l9:	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

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 { l5, l4, l1, l0 }.

2.1.1 Transition Removal

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

l0:	9 − x8
l1:	9 − x8
l5:	8 − x8
l4:	8 − x8

2.1.2 Transition Removal

We remove transitions 1, 12 using the following ranking functions, which are bounded by 0.

l0:	0
l1:	−1
l5:	1
l4:	1

2.1.3 Transition Removal

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

l4:	9 − x2
l5:	9 − x2

2.1.4 Transition Removal

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

l4:	0
l5:	−1

2.1.5 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 { l7, l6, l8, l3, l2, l9 }.

2.2.1 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 0.

l8:	9 − x7
l9:	9 − x7
l7:	8 − x7
l3:	8 − x7
l2:	8 − x7
l6:	8 − x7

2.2.2 Transition Removal

We remove transitions 10, 6 using the following ranking functions, which are bounded by 0.

l8:	0
l9:	−1
l7:	1
l3:	1
l2:	1
l6:	1

2.2.3 Transition Removal

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

l3:	9 − x1
l7:	9 − x1
l2:	8 − x1
l6:	8 − x1

2.2.4 Transition Removal

We remove transitions 11, 2, 5, 4 using the following ranking functions, which are bounded by 0.

l3:	0
l7:	−1
l2:	1
l6:	2

2.2.5 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 % (14 real / 0 unknown / 0 assumptions / 14 total proof steps)