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 = ___const_1000HAT0 ∧ x18 = ___const_10HAT0 ∧ x19 = ___const_1500HAT0 ∧ x20 = _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 = ___const_1000HATpost ∧ x18 = ___const_10HATpost ∧ x19 = ___const_1500HATpost ∧ x20 = _ret_RandomInteger15HATpost ∧ _ret_RandomInteger15HAT0 = _ret_RandomInteger15HATpost ∧ ___const_1500HAT0 = ___const_1500HATpost ∧ ___const_1000HAT0 = ___const_1000HATpost ∧ ___const_10HAT0 = ___const_10HATpost ∧ _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 ∧ x18 = _x17 ∧ x19 = _x18 ∧ x20 = _x19 ∧ x1 = _x20 ∧ x2 = _x21 ∧ x3 = _x22 ∧ x4 = _x23 ∧ x5 = _x24 ∧ x6 = _x25 ∧ x7 = _x26 ∧ x8 = _x27 ∧ x9 = _x28 ∧ x10 = _x29 ∧ x11 = _x30 ∧ x12 = _x31 ∧ x13 = _x32 ∧ x14 = _x33 ∧ x15 = _x34 ∧ x16 = _x35 ∧ x17 = _x36 ∧ x18 = _x37 ∧ x19 = _x38 ∧ x20 = _x39 ∧ _x19 = _x39 ∧ _x18 = _x38 ∧ _x16 = _x36 ∧ _x17 = _x37 ∧ _x15 = _x35 ∧ _x14 = _x34 ∧ _x13 = _x33 ∧ _x12 = _x32 ∧ _x11 = _x31 ∧ _x10 = _x30 ∧ _x9 = _x29 ∧ _x8 = _x28 ∧ _x7 = _x27 ∧ _x6 = _x26 ∧ _x5 = _x25 ∧ _x4 = _x24 ∧ _x3 = _x23 ∧ _x2 = _x22 ∧ _x1 = _x21 ∧ _x20 = 1 + _x
l4	3	l5:	x1 = _x40 ∧ x2 = _x41 ∧ x3 = _x42 ∧ x4 = _x43 ∧ x5 = _x44 ∧ x6 = _x45 ∧ x7 = _x46 ∧ x8 = _x47 ∧ x9 = _x48 ∧ x10 = _x49 ∧ x11 = _x50 ∧ x12 = _x51 ∧ x13 = _x52 ∧ x14 = _x53 ∧ x15 = _x54 ∧ x16 = _x55 ∧ x17 = _x56 ∧ x18 = _x57 ∧ x19 = _x58 ∧ x20 = _x59 ∧ x1 = _x60 ∧ x2 = _x61 ∧ x3 = _x62 ∧ x4 = _x63 ∧ x5 = _x64 ∧ x6 = _x65 ∧ x7 = _x66 ∧ x8 = _x67 ∧ x9 = _x68 ∧ x10 = _x69 ∧ x11 = _x70 ∧ x12 = _x71 ∧ x13 = _x72 ∧ x14 = _x73 ∧ x15 = _x74 ∧ x16 = _x75 ∧ x17 = _x76 ∧ x18 = _x77 ∧ x19 = _x78 ∧ x20 = _x79 ∧ _x59 = _x79 ∧ _x58 = _x78 ∧ _x56 = _x76 ∧ _x57 = _x77 ∧ _x55 = _x75 ∧ _x54 = _x74 ∧ _x53 = _x73 ∧ _x52 = _x72 ∧ _x51 = _x71 ∧ _x50 = _x70 ∧ _x49 = _x69 ∧ _x48 = _x68 ∧ _x47 = _x67 ∧ _x46 = _x66 ∧ _x45 = _x65 ∧ _x44 = _x64 ∧ _x43 = _x63 ∧ _x42 = _x62 ∧ _x41 = _x61 ∧ _x40 = _x60
l6	4	l2:	x1 = _x80 ∧ x2 = _x81 ∧ x3 = _x82 ∧ x4 = _x83 ∧ x5 = _x84 ∧ x6 = _x85 ∧ x7 = _x86 ∧ x8 = _x87 ∧ x9 = _x88 ∧ x10 = _x89 ∧ x11 = _x90 ∧ x12 = _x91 ∧ x13 = _x92 ∧ x14 = _x93 ∧ x15 = _x94 ∧ x16 = _x95 ∧ x17 = _x96 ∧ x18 = _x97 ∧ x19 = _x98 ∧ x20 = _x99 ∧ 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 ∧ _x99 = _x119 ∧ _x98 = _x118 ∧ _x96 = _x116 ∧ _x97 = _x117 ∧ _x95 = _x115 ∧ _x94 = _x114 ∧ _x93 = _x113 ∧ _x92 = _x112 ∧ _x90 = _x110 ∧ _x89 = _x109 ∧ _x87 = _x107 ∧ _x86 = _x106 ∧ _x85 = _x105 ∧ _x84 = _x104 ∧ _x83 = _x103 ∧ _x82 = _x102 ∧ _x81 = _x101 ∧ _x80 = _x100 ∧ _x108 = 1 + _x88 ∧ _x111 = _x111
l6	5	l2:	x1 = _x120 ∧ x2 = _x121 ∧ x3 = _x122 ∧ x4 = _x123 ∧ x5 = _x124 ∧ x6 = _x125 ∧ x7 = _x126 ∧ x8 = _x127 ∧ x9 = _x128 ∧ x10 = _x129 ∧ x11 = _x130 ∧ x12 = _x131 ∧ x13 = _x132 ∧ x14 = _x133 ∧ x15 = _x134 ∧ x16 = _x135 ∧ x17 = _x136 ∧ x18 = _x137 ∧ x19 = _x138 ∧ x20 = _x139 ∧ x1 = _x140 ∧ x2 = _x141 ∧ x3 = _x142 ∧ x4 = _x143 ∧ x5 = _x144 ∧ x6 = _x145 ∧ x7 = _x146 ∧ x8 = _x147 ∧ x9 = _x148 ∧ x10 = _x149 ∧ x11 = _x150 ∧ x12 = _x151 ∧ x13 = _x152 ∧ x14 = _x153 ∧ x15 = _x154 ∧ x16 = _x155 ∧ x17 = _x156 ∧ x18 = _x157 ∧ x19 = _x158 ∧ x20 = _x159 ∧ _x139 = _x159 ∧ _x138 = _x158 ∧ _x136 = _x156 ∧ _x137 = _x157 ∧ _x135 = _x155 ∧ _x134 = _x154 ∧ _x133 = _x153 ∧ _x132 = _x152 ∧ _x131 = _x151 ∧ _x130 = _x150 ∧ _x129 = _x149 ∧ _x128 = _x148 ∧ _x127 = _x147 ∧ _x126 = _x146 ∧ _x124 = _x144 ∧ _x123 = _x143 ∧ _x121 = _x141 ∧ _x120 = _x140 ∧ _x142 = 1 + _x122 ∧ _x145 = _x145
l7	6	l8:	x1 = _x160 ∧ x2 = _x161 ∧ x3 = _x162 ∧ x4 = _x163 ∧ x5 = _x164 ∧ x6 = _x165 ∧ x7 = _x166 ∧ x8 = _x167 ∧ x9 = _x168 ∧ x10 = _x169 ∧ x11 = _x170 ∧ x12 = _x171 ∧ x13 = _x172 ∧ x14 = _x173 ∧ x15 = _x174 ∧ x16 = _x175 ∧ x17 = _x176 ∧ x18 = _x177 ∧ x19 = _x178 ∧ x20 = _x179 ∧ x1 = _x180 ∧ x2 = _x181 ∧ x3 = _x182 ∧ x4 = _x183 ∧ x5 = _x184 ∧ x6 = _x185 ∧ x7 = _x186 ∧ x8 = _x187 ∧ x9 = _x188 ∧ x10 = _x189 ∧ x11 = _x190 ∧ x12 = _x191 ∧ x13 = _x192 ∧ x14 = _x193 ∧ x15 = _x194 ∧ x16 = _x195 ∧ x17 = _x196 ∧ x18 = _x197 ∧ x19 = _x198 ∧ x20 = _x199 ∧ _x179 = _x199 ∧ _x178 = _x198 ∧ _x176 = _x196 ∧ _x177 = _x197 ∧ _x175 = _x195 ∧ _x174 = _x194 ∧ _x173 = _x193 ∧ _x172 = _x192 ∧ _x171 = _x191 ∧ _x170 = _x190 ∧ _x169 = _x189 ∧ _x168 = _x188 ∧ _x167 = _x187 ∧ _x165 = _x185 ∧ _x164 = _x184 ∧ _x163 = _x183 ∧ _x162 = _x182 ∧ _x161 = _x181 ∧ _x160 = _x180 ∧ _x186 = 1 + _x166 ∧ _x177 ≤ _x160
l7	7	l6:	x1 = _x200 ∧ x2 = _x201 ∧ x3 = _x202 ∧ x4 = _x203 ∧ x5 = _x204 ∧ x6 = _x205 ∧ x7 = _x206 ∧ x8 = _x207 ∧ x9 = _x208 ∧ x10 = _x209 ∧ x11 = _x210 ∧ x12 = _x211 ∧ x13 = _x212 ∧ x14 = _x213 ∧ x15 = _x214 ∧ x16 = _x215 ∧ x17 = _x216 ∧ x18 = _x217 ∧ x19 = _x218 ∧ x20 = _x219 ∧ x1 = _x220 ∧ x2 = _x221 ∧ x3 = _x222 ∧ x4 = _x223 ∧ x5 = _x224 ∧ x6 = _x225 ∧ x7 = _x226 ∧ x8 = _x227 ∧ x9 = _x228 ∧ x10 = _x229 ∧ x11 = _x230 ∧ x12 = _x231 ∧ x13 = _x232 ∧ x14 = _x233 ∧ x15 = _x234 ∧ x16 = _x235 ∧ x17 = _x236 ∧ x18 = _x237 ∧ x19 = _x238 ∧ x20 = _x239 ∧ _x219 = _x239 ∧ _x218 = _x238 ∧ _x216 = _x236 ∧ _x217 = _x237 ∧ _x215 = _x235 ∧ _x214 = _x234 ∧ _x213 = _x233 ∧ _x212 = _x232 ∧ _x211 = _x231 ∧ _x210 = _x230 ∧ _x209 = _x229 ∧ _x208 = _x228 ∧ _x207 = _x227 ∧ _x206 = _x226 ∧ _x205 = _x225 ∧ _x204 = _x224 ∧ _x203 = _x223 ∧ _x202 = _x222 ∧ _x201 = _x221 ∧ _x200 = _x220 ∧ 1 + _x200 ≤ _x217
l9	8	l10:	x1 = _x240 ∧ x2 = _x241 ∧ x3 = _x242 ∧ x4 = _x243 ∧ x5 = _x244 ∧ x6 = _x245 ∧ x7 = _x246 ∧ x8 = _x247 ∧ x9 = _x248 ∧ x10 = _x249 ∧ x11 = _x250 ∧ x12 = _x251 ∧ x13 = _x252 ∧ x14 = _x253 ∧ x15 = _x254 ∧ x16 = _x255 ∧ x17 = _x256 ∧ x18 = _x257 ∧ x19 = _x258 ∧ x20 = _x259 ∧ x1 = _x260 ∧ x2 = _x261 ∧ x3 = _x262 ∧ x4 = _x263 ∧ x5 = _x264 ∧ x6 = _x265 ∧ x7 = _x266 ∧ x8 = _x267 ∧ x9 = _x268 ∧ x10 = _x269 ∧ x11 = _x270 ∧ x12 = _x271 ∧ x13 = _x272 ∧ x14 = _x273 ∧ x15 = _x274 ∧ x16 = _x275 ∧ x17 = _x276 ∧ x18 = _x277 ∧ x19 = _x278 ∧ x20 = _x279 ∧ _x259 = _x279 ∧ _x258 = _x278 ∧ _x256 = _x276 ∧ _x257 = _x277 ∧ _x253 = _x273 ∧ _x252 = _x272 ∧ _x251 = _x271 ∧ _x248 = _x268 ∧ _x247 = _x267 ∧ _x246 = _x266 ∧ _x245 = _x265 ∧ _x242 = _x262 ∧ _x241 = _x261 ∧ _x240 = _x260 ∧ _x275 = _x275 ∧ _x274 = _x258 ∧ _x263 = _x242 ∧ _x264 = _x245 ∧ _x269 = _x248 ∧ _x270 = _x251 ∧ _x257 ≤ _x246
l9	9	l3:	x1 = _x280 ∧ x2 = _x281 ∧ x3 = _x282 ∧ x4 = _x283 ∧ x5 = _x284 ∧ x6 = _x285 ∧ x7 = _x286 ∧ x8 = _x287 ∧ x9 = _x288 ∧ x10 = _x289 ∧ x11 = _x290 ∧ x12 = _x291 ∧ x13 = _x292 ∧ x14 = _x293 ∧ x15 = _x294 ∧ x16 = _x295 ∧ x17 = _x296 ∧ x18 = _x297 ∧ x19 = _x298 ∧ x20 = _x299 ∧ x1 = _x300 ∧ x2 = _x301 ∧ x3 = _x302 ∧ x4 = _x303 ∧ x5 = _x304 ∧ x6 = _x305 ∧ x7 = _x306 ∧ x8 = _x307 ∧ x9 = _x308 ∧ x10 = _x309 ∧ x11 = _x310 ∧ x12 = _x311 ∧ x13 = _x312 ∧ x14 = _x313 ∧ x15 = _x314 ∧ x16 = _x315 ∧ x17 = _x316 ∧ x18 = _x317 ∧ x19 = _x318 ∧ x20 = _x319 ∧ _x299 = _x319 ∧ _x298 = _x318 ∧ _x296 = _x316 ∧ _x297 = _x317 ∧ _x295 = _x315 ∧ _x294 = _x314 ∧ _x293 = _x313 ∧ _x292 = _x312 ∧ _x291 = _x311 ∧ _x290 = _x310 ∧ _x289 = _x309 ∧ _x288 = _x308 ∧ _x287 = _x307 ∧ _x286 = _x306 ∧ _x285 = _x305 ∧ _x284 = _x304 ∧ _x283 = _x303 ∧ _x282 = _x302 ∧ _x281 = _x301 ∧ _x300 = 0 ∧ 1 + _x286 ≤ _x297
l8	10	l9:	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 ∧ 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 ∧ x18 = _x357 ∧ x19 = _x358 ∧ x20 = _x359 ∧ _x339 = _x359 ∧ _x338 = _x358 ∧ _x336 = _x356 ∧ _x337 = _x357 ∧ _x335 = _x355 ∧ _x334 = _x354 ∧ _x333 = _x353 ∧ _x332 = _x352 ∧ _x331 = _x351 ∧ _x330 = _x350 ∧ _x329 = _x349 ∧ _x328 = _x348 ∧ _x327 = _x347 ∧ _x326 = _x346 ∧ _x325 = _x345 ∧ _x324 = _x344 ∧ _x323 = _x343 ∧ _x322 = _x342 ∧ _x321 = _x341 ∧ _x320 = _x340
l3	11	l7:	x1 = _x360 ∧ x2 = _x361 ∧ x3 = _x362 ∧ x4 = _x363 ∧ x5 = _x364 ∧ x6 = _x365 ∧ x7 = _x366 ∧ x8 = _x367 ∧ x9 = _x368 ∧ x10 = _x369 ∧ x11 = _x370 ∧ x12 = _x371 ∧ x13 = _x372 ∧ x14 = _x373 ∧ x15 = _x374 ∧ x16 = _x375 ∧ x17 = _x376 ∧ x18 = _x377 ∧ x19 = _x378 ∧ x20 = _x379 ∧ x1 = _x380 ∧ x2 = _x381 ∧ x3 = _x382 ∧ x4 = _x383 ∧ x5 = _x384 ∧ x6 = _x385 ∧ x7 = _x386 ∧ x8 = _x387 ∧ x9 = _x388 ∧ x10 = _x389 ∧ x11 = _x390 ∧ x12 = _x391 ∧ x13 = _x392 ∧ x14 = _x393 ∧ x15 = _x394 ∧ x16 = _x395 ∧ x17 = _x396 ∧ x18 = _x397 ∧ x19 = _x398 ∧ x20 = _x399 ∧ _x379 = _x399 ∧ _x378 = _x398 ∧ _x376 = _x396 ∧ _x377 = _x397 ∧ _x375 = _x395 ∧ _x374 = _x394 ∧ _x373 = _x393 ∧ _x372 = _x392 ∧ _x371 = _x391 ∧ _x370 = _x390 ∧ _x369 = _x389 ∧ _x368 = _x388 ∧ _x367 = _x387 ∧ _x366 = _x386 ∧ _x365 = _x385 ∧ _x364 = _x384 ∧ _x363 = _x383 ∧ _x362 = _x382 ∧ _x361 = _x381 ∧ _x360 = _x380
l5	12	l0:	x1 = _x400 ∧ x2 = _x401 ∧ x3 = _x402 ∧ x4 = _x403 ∧ x5 = _x404 ∧ x6 = _x405 ∧ x7 = _x406 ∧ x8 = _x407 ∧ x9 = _x408 ∧ x10 = _x409 ∧ x11 = _x410 ∧ x12 = _x411 ∧ x13 = _x412 ∧ x14 = _x413 ∧ x15 = _x414 ∧ x16 = _x415 ∧ x17 = _x416 ∧ x18 = _x417 ∧ x19 = _x418 ∧ x20 = _x419 ∧ x1 = _x420 ∧ x2 = _x421 ∧ x3 = _x422 ∧ x4 = _x423 ∧ x5 = _x424 ∧ x6 = _x425 ∧ x7 = _x426 ∧ x8 = _x427 ∧ x9 = _x428 ∧ x10 = _x429 ∧ x11 = _x430 ∧ x12 = _x431 ∧ x13 = _x432 ∧ x14 = _x433 ∧ x15 = _x434 ∧ x16 = _x435 ∧ x17 = _x436 ∧ x18 = _x437 ∧ x19 = _x438 ∧ x20 = _x439 ∧ _x419 = _x439 ∧ _x418 = _x438 ∧ _x416 = _x436 ∧ _x417 = _x437 ∧ _x415 = _x435 ∧ _x414 = _x434 ∧ _x413 = _x433 ∧ _x412 = _x432 ∧ _x411 = _x431 ∧ _x410 = _x430 ∧ _x409 = _x429 ∧ _x408 = _x428 ∧ _x406 = _x426 ∧ _x405 = _x425 ∧ _x404 = _x424 ∧ _x403 = _x423 ∧ _x402 = _x422 ∧ _x401 = _x421 ∧ _x400 = _x420 ∧ _x427 = 1 + _x407 ∧ _x417 ≤ _x401
l5	13	l4:	x1 = _x440 ∧ x2 = _x441 ∧ x3 = _x442 ∧ x4 = _x443 ∧ x5 = _x444 ∧ x6 = _x445 ∧ x7 = _x446 ∧ x8 = _x447 ∧ x9 = _x448 ∧ x10 = _x449 ∧ x11 = _x450 ∧ x12 = _x451 ∧ x13 = _x452 ∧ x14 = _x453 ∧ x15 = _x454 ∧ x16 = _x455 ∧ x17 = _x456 ∧ x18 = _x457 ∧ x19 = _x458 ∧ x20 = _x459 ∧ x1 = _x460 ∧ x2 = _x461 ∧ x3 = _x462 ∧ x4 = _x463 ∧ x5 = _x464 ∧ x6 = _x465 ∧ x7 = _x466 ∧ x8 = _x467 ∧ x9 = _x468 ∧ x10 = _x469 ∧ x11 = _x470 ∧ x12 = _x471 ∧ x13 = _x472 ∧ x14 = _x473 ∧ x15 = _x474 ∧ x16 = _x475 ∧ x17 = _x476 ∧ x18 = _x477 ∧ x19 = _x478 ∧ x20 = _x479 ∧ _x458 = _x478 ∧ _x456 = _x476 ∧ _x457 = _x477 ∧ _x455 = _x475 ∧ _x454 = _x474 ∧ _x453 = _x473 ∧ _x451 = _x471 ∧ _x450 = _x470 ∧ _x449 = _x469 ∧ _x448 = _x468 ∧ _x447 = _x467 ∧ _x446 = _x466 ∧ _x445 = _x465 ∧ _x444 = _x464 ∧ _x443 = _x463 ∧ _x442 = _x462 ∧ _x440 = _x460 ∧ _x461 = 1 + _x441 ∧ _x479 = _x472 ∧ _x472 = _x472 ∧ 1 + _x441 ≤ _x457
l1	14	l8:	x1 = _x480 ∧ x2 = _x481 ∧ x3 = _x482 ∧ x4 = _x483 ∧ x5 = _x484 ∧ x6 = _x485 ∧ x7 = _x486 ∧ x8 = _x487 ∧ x9 = _x488 ∧ x10 = _x489 ∧ x11 = _x490 ∧ x12 = _x491 ∧ x13 = _x492 ∧ x14 = _x493 ∧ x15 = _x494 ∧ x16 = _x495 ∧ x17 = _x496 ∧ x18 = _x497 ∧ x19 = _x498 ∧ x20 = _x499 ∧ x1 = _x500 ∧ x2 = _x501 ∧ x3 = _x502 ∧ x4 = _x503 ∧ x5 = _x504 ∧ x6 = _x505 ∧ x7 = _x506 ∧ x8 = _x507 ∧ x9 = _x508 ∧ x10 = _x509 ∧ x11 = _x510 ∧ x12 = _x511 ∧ x13 = _x512 ∧ x14 = _x513 ∧ x15 = _x514 ∧ x16 = _x515 ∧ x17 = _x516 ∧ x18 = _x517 ∧ x19 = _x518 ∧ x20 = _x519 ∧ _x499 = _x519 ∧ _x498 = _x518 ∧ _x496 = _x516 ∧ _x497 = _x517 ∧ _x495 = _x515 ∧ _x494 = _x514 ∧ _x492 = _x512 ∧ _x490 = _x510 ∧ _x489 = _x509 ∧ _x487 = _x507 ∧ _x484 = _x504 ∧ _x483 = _x503 ∧ _x481 = _x501 ∧ _x480 = _x500 ∧ _x506 = 0 ∧ _x502 = 0 ∧ _x508 = 0 ∧ _x505 = 0 ∧ _x511 = 0 ∧ _x513 = _x496 ∧ _x497 ≤ _x487
l1	15	l4:	x1 = _x520 ∧ x2 = _x521 ∧ x3 = _x522 ∧ x4 = _x523 ∧ x5 = _x524 ∧ x6 = _x525 ∧ x7 = _x526 ∧ x8 = _x527 ∧ x9 = _x528 ∧ x10 = _x529 ∧ x11 = _x530 ∧ x12 = _x531 ∧ x13 = _x532 ∧ x14 = _x533 ∧ x15 = _x534 ∧ x16 = _x535 ∧ x17 = _x536 ∧ x18 = _x537 ∧ x19 = _x538 ∧ x20 = _x539 ∧ x1 = _x540 ∧ x2 = _x541 ∧ x3 = _x542 ∧ x4 = _x543 ∧ x5 = _x544 ∧ x6 = _x545 ∧ x7 = _x546 ∧ x8 = _x547 ∧ x9 = _x548 ∧ x10 = _x549 ∧ x11 = _x550 ∧ x12 = _x551 ∧ x13 = _x552 ∧ x14 = _x553 ∧ x15 = _x554 ∧ x16 = _x555 ∧ x17 = _x556 ∧ x18 = _x557 ∧ x19 = _x558 ∧ x20 = _x559 ∧ _x539 = _x559 ∧ _x538 = _x558 ∧ _x536 = _x556 ∧ _x537 = _x557 ∧ _x535 = _x555 ∧ _x534 = _x554 ∧ _x533 = _x553 ∧ _x532 = _x552 ∧ _x531 = _x551 ∧ _x530 = _x550 ∧ _x529 = _x549 ∧ _x528 = _x548 ∧ _x527 = _x547 ∧ _x526 = _x546 ∧ _x525 = _x545 ∧ _x524 = _x544 ∧ _x523 = _x543 ∧ _x522 = _x542 ∧ _x520 = _x540 ∧ _x541 = 0 ∧ 1 + _x527 ≤ _x537
l11	16	l0:	x1 = _x560 ∧ x2 = _x561 ∧ x3 = _x562 ∧ x4 = _x563 ∧ x5 = _x564 ∧ x6 = _x565 ∧ x7 = _x566 ∧ x8 = _x567 ∧ x9 = _x568 ∧ x10 = _x569 ∧ x11 = _x570 ∧ x12 = _x571 ∧ x13 = _x572 ∧ x14 = _x573 ∧ x15 = _x574 ∧ x16 = _x575 ∧ x17 = _x576 ∧ x18 = _x577 ∧ x19 = _x578 ∧ x20 = _x579 ∧ x1 = _x580 ∧ x2 = _x581 ∧ x3 = _x582 ∧ x4 = _x583 ∧ x5 = _x584 ∧ x6 = _x585 ∧ x7 = _x586 ∧ x8 = _x587 ∧ x9 = _x588 ∧ x10 = _x589 ∧ x11 = _x590 ∧ x12 = _x591 ∧ x13 = _x592 ∧ x14 = _x593 ∧ x15 = _x594 ∧ x16 = _x595 ∧ x17 = _x596 ∧ x18 = _x597 ∧ x19 = _x598 ∧ x20 = _x599 ∧ _x579 = _x599 ∧ _x578 = _x598 ∧ _x576 = _x596 ∧ _x577 = _x597 ∧ _x575 = _x595 ∧ _x574 = _x594 ∧ _x573 = _x593 ∧ _x571 = _x591 ∧ _x570 = _x590 ∧ _x569 = _x589 ∧ _x568 = _x588 ∧ _x566 = _x586 ∧ _x565 = _x585 ∧ _x564 = _x584 ∧ _x563 = _x583 ∧ _x562 = _x582 ∧ _x561 = _x581 ∧ _x560 = _x580 ∧ _x587 = 0 ∧ _x592 = 0
l12	17	l11:	x1 = _x600 ∧ x2 = _x601 ∧ x3 = _x602 ∧ x4 = _x603 ∧ x5 = _x604 ∧ x6 = _x605 ∧ x7 = _x606 ∧ x8 = _x607 ∧ x9 = _x608 ∧ x10 = _x609 ∧ x11 = _x610 ∧ x12 = _x611 ∧ x13 = _x612 ∧ x14 = _x613 ∧ x15 = _x614 ∧ x16 = _x615 ∧ x17 = _x616 ∧ x18 = _x617 ∧ x19 = _x618 ∧ x20 = _x619 ∧ x1 = _x620 ∧ x2 = _x621 ∧ x3 = _x622 ∧ x4 = _x623 ∧ x5 = _x624 ∧ x6 = _x625 ∧ x7 = _x626 ∧ x8 = _x627 ∧ x9 = _x628 ∧ x10 = _x629 ∧ x11 = _x630 ∧ x12 = _x631 ∧ x13 = _x632 ∧ x14 = _x633 ∧ x15 = _x634 ∧ x16 = _x635 ∧ x17 = _x636 ∧ x18 = _x637 ∧ x19 = _x638 ∧ x20 = _x639 ∧ _x619 = _x639 ∧ _x618 = _x638 ∧ _x616 = _x636 ∧ _x617 = _x637 ∧ _x615 = _x635 ∧ _x614 = _x634 ∧ _x613 = _x633 ∧ _x612 = _x632 ∧ _x611 = _x631 ∧ _x610 = _x630 ∧ _x609 = _x629 ∧ _x608 = _x628 ∧ _x607 = _x627 ∧ _x606 = _x626 ∧ _x605 = _x625 ∧ _x604 = _x624 ∧ _x603 = _x623 ∧ _x602 = _x622 ∧ _x601 = _x621 ∧ _x600 = _x620

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 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20
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
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
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 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20
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 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20
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 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20
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
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
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
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 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20
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
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 ∧ x18 = x18 ∧ x19 = x19 ∧ x20 = x20

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:	−1 − x8 + x18
l1:	−1 − x8 + x18
l5:	−2 − x8 + x18
l4:	−2 − x8 + x18

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:	−1 − x2 + x18
l5:	−1 − x2 + x18

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:	−1 − x7 + x18
l9:	−1 − x7 + x18
l7:	−2 − x7 + x18
l3:	−2 − x7 + x18
l2:	−2 − x7 + x18
l6:	−2 − x7 + x18

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:	−1 − x1 + x18
l7:	−1 − x1 + x18
l2:	−2 − x1 + x18
l6:	−2 − x1 + x18

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)