LTS Termination Proof

Input

Integer Transition System

Initial Location: l5, l7, l11, l3, l13, l17, l2, l14, l9, l4, l6, l10, l8, l15, l16, l0, l12

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = ___const_12HAT0 ∧ x2 = ___const_5HAT0 ∧ x3 = _edgecountHAT0 ∧ x4 = _iHAT0 ∧ x5 = _jHAT0 ∧ x6 = _nodecountHAT0 ∧ x7 = _sourceHAT0 ∧ x8 = _xHAT0 ∧ x9 = _yHAT0 ∧ x1 = ___const_12HATpost ∧ x2 = ___const_5HATpost ∧ x3 = _edgecountHATpost ∧ x4 = _iHATpost ∧ x5 = _jHATpost ∧ x6 = _nodecountHATpost ∧ x7 = _sourceHATpost ∧ x8 = _xHATpost ∧ x9 = _yHATpost ∧ _yHAT0 = _yHATpost ∧ _xHAT0 = _xHATpost ∧ _sourceHAT0 = _sourceHATpost ∧ _nodecountHAT0 = _nodecountHATpost ∧ _jHAT0 = _jHATpost ∧ _iHAT0 = _iHATpost ∧ _edgecountHAT0 = _edgecountHATpost ∧ ___const_5HAT0 = ___const_5HATpost ∧ ___const_12HAT0 = ___const_12HATpost ∧ _nodecountHAT0 ≤ _iHAT0
l0	2	l2:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x6 = _x5 ∧ x7 = _x6 ∧ x8 = _x7 ∧ x9 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ x4 = _x12 ∧ x5 = _x13 ∧ x6 = _x14 ∧ x7 = _x15 ∧ x8 = _x16 ∧ x9 = _x17 ∧ _x8 = _x17 ∧ _x7 = _x16 ∧ _x6 = _x15 ∧ _x5 = _x14 ∧ _x4 = _x13 ∧ _x2 = _x11 ∧ _x1 = _x10 ∧ _x = _x9 ∧ _x12 = 1 + _x3 ∧ 1 + _x3 ≤ _x5
l3	3	l4:	x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x4 = _x21 ∧ x5 = _x22 ∧ x6 = _x23 ∧ x7 = _x24 ∧ x8 = _x25 ∧ x9 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ x4 = _x30 ∧ x5 = _x31 ∧ x6 = _x32 ∧ x7 = _x33 ∧ x8 = _x34 ∧ x9 = _x35 ∧ _x26 = _x35 ∧ _x25 = _x34 ∧ _x24 = _x33 ∧ _x23 = _x32 ∧ _x22 = _x31 ∧ _x20 = _x29 ∧ _x19 = _x28 ∧ _x18 = _x27 ∧ _x30 = 1 + _x21
l3	4	l1:	x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x4 = _x39 ∧ x5 = _x40 ∧ x6 = _x41 ∧ x7 = _x42 ∧ x8 = _x43 ∧ x9 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ x4 = _x48 ∧ x5 = _x49 ∧ x6 = _x50 ∧ x7 = _x51 ∧ x8 = _x52 ∧ x9 = _x53 ∧ _x44 = _x53 ∧ _x43 = _x52 ∧ _x42 = _x51 ∧ _x41 = _x50 ∧ _x40 = _x49 ∧ _x39 = _x48 ∧ _x38 = _x47 ∧ _x37 = _x46 ∧ _x36 = _x45
l5	5	l2:	x1 = _x54 ∧ x2 = _x55 ∧ x3 = _x56 ∧ x4 = _x57 ∧ x5 = _x58 ∧ x6 = _x59 ∧ x7 = _x60 ∧ x8 = _x61 ∧ x9 = _x62 ∧ x1 = _x63 ∧ x2 = _x64 ∧ x3 = _x65 ∧ x4 = _x66 ∧ x5 = _x67 ∧ x6 = _x68 ∧ x7 = _x69 ∧ x8 = _x70 ∧ x9 = _x71 ∧ _x62 = _x71 ∧ _x61 = _x70 ∧ _x60 = _x69 ∧ _x59 = _x68 ∧ _x58 = _x67 ∧ _x56 = _x65 ∧ _x55 = _x64 ∧ _x54 = _x63 ∧ _x66 = 0 ∧ _x56 ≤ _x57
l5	6	l3:	x1 = _x72 ∧ x2 = _x73 ∧ x3 = _x74 ∧ x4 = _x75 ∧ x5 = _x76 ∧ x6 = _x77 ∧ x7 = _x78 ∧ x8 = _x79 ∧ x9 = _x80 ∧ x1 = _x81 ∧ x2 = _x82 ∧ x3 = _x83 ∧ x4 = _x84 ∧ x5 = _x85 ∧ x6 = _x86 ∧ x7 = _x87 ∧ x8 = _x88 ∧ x9 = _x89 ∧ _x78 = _x87 ∧ _x77 = _x86 ∧ _x76 = _x85 ∧ _x75 = _x84 ∧ _x74 = _x83 ∧ _x73 = _x82 ∧ _x72 = _x81 ∧ _x89 = _x89 ∧ _x88 = _x88 ∧ 1 + _x75 ≤ _x74
l6	7	l7:	x1 = _x90 ∧ x2 = _x91 ∧ x3 = _x92 ∧ x4 = _x93 ∧ x5 = _x94 ∧ x6 = _x95 ∧ x7 = _x96 ∧ x8 = _x97 ∧ x9 = _x98 ∧ x1 = _x99 ∧ x2 = _x100 ∧ x3 = _x101 ∧ x4 = _x102 ∧ x5 = _x103 ∧ x6 = _x104 ∧ x7 = _x105 ∧ x8 = _x106 ∧ x9 = _x107 ∧ _x98 = _x107 ∧ _x97 = _x106 ∧ _x96 = _x105 ∧ _x95 = _x104 ∧ _x93 = _x102 ∧ _x92 = _x101 ∧ _x91 = _x100 ∧ _x90 = _x99 ∧ _x103 = 1 + _x94
l8	8	l9:	x1 = _x108 ∧ x2 = _x109 ∧ x3 = _x110 ∧ x4 = _x111 ∧ x5 = _x112 ∧ x6 = _x113 ∧ x7 = _x114 ∧ x8 = _x115 ∧ x9 = _x116 ∧ x1 = _x117 ∧ x2 = _x118 ∧ x3 = _x119 ∧ x4 = _x120 ∧ x5 = _x121 ∧ x6 = _x122 ∧ x7 = _x123 ∧ x8 = _x124 ∧ x9 = _x125 ∧ _x116 = _x125 ∧ _x115 = _x124 ∧ _x114 = _x123 ∧ _x113 = _x122 ∧ _x112 = _x121 ∧ _x111 = _x120 ∧ _x110 = _x119 ∧ _x109 = _x118 ∧ _x108 = _x117
l10	9	l11:	x1 = _x126 ∧ x2 = _x127 ∧ x3 = _x128 ∧ x4 = _x129 ∧ x5 = _x130 ∧ x6 = _x131 ∧ x7 = _x132 ∧ x8 = _x133 ∧ x9 = _x134 ∧ x1 = _x135 ∧ x2 = _x136 ∧ x3 = _x137 ∧ x4 = _x138 ∧ x5 = _x139 ∧ x6 = _x140 ∧ x7 = _x141 ∧ x8 = _x142 ∧ x9 = _x143 ∧ _x134 = _x143 ∧ _x133 = _x142 ∧ _x132 = _x141 ∧ _x131 = _x140 ∧ _x130 = _x139 ∧ _x128 = _x137 ∧ _x127 = _x136 ∧ _x126 = _x135 ∧ _x138 = 1 + _x129 ∧ _x128 ≤ _x130
l10	10	l6:	x1 = _x144 ∧ x2 = _x145 ∧ x3 = _x146 ∧ x4 = _x147 ∧ x5 = _x148 ∧ x6 = _x149 ∧ x7 = _x150 ∧ x8 = _x151 ∧ x9 = _x152 ∧ x1 = _x153 ∧ x2 = _x154 ∧ x3 = _x155 ∧ x4 = _x156 ∧ x5 = _x157 ∧ x6 = _x158 ∧ x7 = _x159 ∧ x8 = _x160 ∧ x9 = _x161 ∧ _x150 = _x159 ∧ _x149 = _x158 ∧ _x148 = _x157 ∧ _x147 = _x156 ∧ _x146 = _x155 ∧ _x145 = _x154 ∧ _x144 = _x153 ∧ _x161 = _x161 ∧ _x160 = _x160 ∧ 1 + _x148 ≤ _x146
l12	11	l4:	x1 = _x162 ∧ x2 = _x163 ∧ x3 = _x164 ∧ x4 = _x165 ∧ x5 = _x166 ∧ x6 = _x167 ∧ x7 = _x168 ∧ x8 = _x169 ∧ x9 = _x170 ∧ x1 = _x171 ∧ x2 = _x172 ∧ x3 = _x173 ∧ x4 = _x174 ∧ x5 = _x175 ∧ x6 = _x176 ∧ x7 = _x177 ∧ x8 = _x178 ∧ x9 = _x179 ∧ _x170 = _x179 ∧ _x169 = _x178 ∧ _x168 = _x177 ∧ _x167 = _x176 ∧ _x166 = _x175 ∧ _x164 = _x173 ∧ _x163 = _x172 ∧ _x162 = _x171 ∧ _x174 = 0 ∧ _x167 ≤ _x165
l12	12	l7:	x1 = _x180 ∧ x2 = _x181 ∧ x3 = _x182 ∧ x4 = _x183 ∧ x5 = _x184 ∧ x6 = _x185 ∧ x7 = _x186 ∧ x8 = _x187 ∧ x9 = _x188 ∧ x1 = _x189 ∧ x2 = _x190 ∧ x3 = _x191 ∧ x4 = _x192 ∧ x5 = _x193 ∧ x6 = _x194 ∧ x7 = _x195 ∧ x8 = _x196 ∧ x9 = _x197 ∧ _x188 = _x197 ∧ _x187 = _x196 ∧ _x186 = _x195 ∧ _x185 = _x194 ∧ _x183 = _x192 ∧ _x182 = _x191 ∧ _x181 = _x190 ∧ _x180 = _x189 ∧ _x193 = 0 ∧ 1 + _x183 ≤ _x185
l13	13	l14:	x1 = _x198 ∧ x2 = _x199 ∧ x3 = _x200 ∧ x4 = _x201 ∧ x5 = _x202 ∧ x6 = _x203 ∧ x7 = _x204 ∧ x8 = _x205 ∧ x9 = _x206 ∧ x1 = _x207 ∧ x2 = _x208 ∧ x3 = _x209 ∧ x4 = _x210 ∧ x5 = _x211 ∧ x6 = _x212 ∧ x7 = _x213 ∧ x8 = _x214 ∧ x9 = _x215 ∧ _x206 = _x215 ∧ _x205 = _x214 ∧ _x204 = _x213 ∧ _x203 = _x212 ∧ _x202 = _x211 ∧ _x201 = _x210 ∧ _x200 = _x209 ∧ _x199 = _x208 ∧ _x198 = _x207
l14	14	l8:	x1 = _x216 ∧ x2 = _x217 ∧ x3 = _x218 ∧ x4 = _x219 ∧ x5 = _x220 ∧ x6 = _x221 ∧ x7 = _x222 ∧ x8 = _x223 ∧ x9 = _x224 ∧ x1 = _x225 ∧ x2 = _x226 ∧ x3 = _x227 ∧ x4 = _x228 ∧ x5 = _x229 ∧ x6 = _x230 ∧ x7 = _x231 ∧ x8 = _x232 ∧ x9 = _x233 ∧ _x224 = _x233 ∧ _x223 = _x232 ∧ _x222 = _x231 ∧ _x221 = _x230 ∧ _x220 = _x229 ∧ _x218 = _x227 ∧ _x217 = _x226 ∧ _x216 = _x225 ∧ _x228 = 1 + _x219
l11	15	l12:	x1 = _x234 ∧ x2 = _x235 ∧ x3 = _x236 ∧ x4 = _x237 ∧ x5 = _x238 ∧ x6 = _x239 ∧ x7 = _x240 ∧ x8 = _x241 ∧ x9 = _x242 ∧ x1 = _x243 ∧ x2 = _x244 ∧ x3 = _x245 ∧ x4 = _x246 ∧ x5 = _x247 ∧ x6 = _x248 ∧ x7 = _x249 ∧ x8 = _x250 ∧ x9 = _x251 ∧ _x242 = _x251 ∧ _x241 = _x250 ∧ _x240 = _x249 ∧ _x239 = _x248 ∧ _x238 = _x247 ∧ _x237 = _x246 ∧ _x236 = _x245 ∧ _x235 = _x244 ∧ _x234 = _x243
l15	16	l13:	x1 = _x252 ∧ x2 = _x253 ∧ x3 = _x254 ∧ x4 = _x255 ∧ x5 = _x256 ∧ x6 = _x257 ∧ x7 = _x258 ∧ x8 = _x259 ∧ x9 = _x260 ∧ x1 = _x261 ∧ x2 = _x262 ∧ x3 = _x263 ∧ x4 = _x264 ∧ x5 = _x265 ∧ x6 = _x266 ∧ x7 = _x267 ∧ x8 = _x268 ∧ x9 = _x269 ∧ _x260 = _x269 ∧ _x259 = _x268 ∧ _x258 = _x267 ∧ _x257 = _x266 ∧ _x256 = _x265 ∧ _x255 = _x264 ∧ _x254 = _x263 ∧ _x253 = _x262 ∧ _x252 = _x261 ∧ 1 + _x258 ≤ _x255
l15	17	l13:	x1 = _x270 ∧ x2 = _x271 ∧ x3 = _x272 ∧ x4 = _x273 ∧ x5 = _x274 ∧ x6 = _x275 ∧ x7 = _x276 ∧ x8 = _x277 ∧ x9 = _x278 ∧ x1 = _x279 ∧ x2 = _x280 ∧ x3 = _x281 ∧ x4 = _x282 ∧ x5 = _x283 ∧ x6 = _x284 ∧ x7 = _x285 ∧ x8 = _x286 ∧ x9 = _x287 ∧ _x278 = _x287 ∧ _x277 = _x286 ∧ _x276 = _x285 ∧ _x275 = _x284 ∧ _x274 = _x283 ∧ _x273 = _x282 ∧ _x272 = _x281 ∧ _x271 = _x280 ∧ _x270 = _x279 ∧ 1 + _x273 ≤ _x276
l15	18	l14:	x1 = _x288 ∧ x2 = _x289 ∧ x3 = _x290 ∧ x4 = _x291 ∧ x5 = _x292 ∧ x6 = _x293 ∧ x7 = _x294 ∧ x8 = _x295 ∧ x9 = _x296 ∧ x1 = _x297 ∧ x2 = _x298 ∧ x3 = _x299 ∧ x4 = _x300 ∧ x5 = _x301 ∧ x6 = _x302 ∧ x7 = _x303 ∧ x8 = _x304 ∧ x9 = _x305 ∧ _x296 = _x305 ∧ _x295 = _x304 ∧ _x294 = _x303 ∧ _x293 = _x302 ∧ _x292 = _x301 ∧ _x291 = _x300 ∧ _x290 = _x299 ∧ _x289 = _x298 ∧ _x288 = _x297 ∧ _x294 ≤ _x291 ∧ _x291 ≤ _x294
l9	19	l11:	x1 = _x306 ∧ x2 = _x307 ∧ x3 = _x308 ∧ x4 = _x309 ∧ x5 = _x310 ∧ x6 = _x311 ∧ x7 = _x312 ∧ x8 = _x313 ∧ x9 = _x314 ∧ x1 = _x315 ∧ x2 = _x316 ∧ x3 = _x317 ∧ x4 = _x318 ∧ x5 = _x319 ∧ x6 = _x320 ∧ x7 = _x321 ∧ x8 = _x322 ∧ x9 = _x323 ∧ _x314 = _x323 ∧ _x313 = _x322 ∧ _x312 = _x321 ∧ _x311 = _x320 ∧ _x310 = _x319 ∧ _x308 = _x317 ∧ _x307 = _x316 ∧ _x306 = _x315 ∧ _x318 = 0 ∧ _x311 ≤ _x309
l9	20	l15:	x1 = _x324 ∧ x2 = _x325 ∧ x3 = _x326 ∧ x4 = _x327 ∧ x5 = _x328 ∧ x6 = _x329 ∧ x7 = _x330 ∧ x8 = _x331 ∧ x9 = _x332 ∧ x1 = _x333 ∧ x2 = _x334 ∧ x3 = _x335 ∧ x4 = _x336 ∧ x5 = _x337 ∧ x6 = _x338 ∧ x7 = _x339 ∧ x8 = _x340 ∧ x9 = _x341 ∧ _x332 = _x341 ∧ _x331 = _x340 ∧ _x330 = _x339 ∧ _x329 = _x338 ∧ _x328 = _x337 ∧ _x327 = _x336 ∧ _x326 = _x335 ∧ _x325 = _x334 ∧ _x324 = _x333 ∧ 1 + _x327 ≤ _x329
l7	21	l10:	x1 = _x342 ∧ x2 = _x343 ∧ x3 = _x344 ∧ x4 = _x345 ∧ x5 = _x346 ∧ x6 = _x347 ∧ x7 = _x348 ∧ x8 = _x349 ∧ x9 = _x350 ∧ x1 = _x351 ∧ x2 = _x352 ∧ x3 = _x353 ∧ x4 = _x354 ∧ x5 = _x355 ∧ x6 = _x356 ∧ x7 = _x357 ∧ x8 = _x358 ∧ x9 = _x359 ∧ _x350 = _x359 ∧ _x349 = _x358 ∧ _x348 = _x357 ∧ _x347 = _x356 ∧ _x346 = _x355 ∧ _x345 = _x354 ∧ _x344 = _x353 ∧ _x343 = _x352 ∧ _x342 = _x351
l4	22	l5:	x1 = _x360 ∧ x2 = _x361 ∧ x3 = _x362 ∧ x4 = _x363 ∧ x5 = _x364 ∧ x6 = _x365 ∧ x7 = _x366 ∧ x8 = _x367 ∧ x9 = _x368 ∧ x1 = _x369 ∧ x2 = _x370 ∧ x3 = _x371 ∧ x4 = _x372 ∧ x5 = _x373 ∧ x6 = _x374 ∧ x7 = _x375 ∧ x8 = _x376 ∧ x9 = _x377 ∧ _x368 = _x377 ∧ _x367 = _x376 ∧ _x366 = _x375 ∧ _x365 = _x374 ∧ _x364 = _x373 ∧ _x363 = _x372 ∧ _x362 = _x371 ∧ _x361 = _x370 ∧ _x360 = _x369
l2	23	l0:	x1 = _x378 ∧ x2 = _x379 ∧ x3 = _x380 ∧ x4 = _x381 ∧ x5 = _x382 ∧ x6 = _x383 ∧ x7 = _x384 ∧ x8 = _x385 ∧ x9 = _x386 ∧ x1 = _x387 ∧ x2 = _x388 ∧ x3 = _x389 ∧ x4 = _x390 ∧ x5 = _x391 ∧ x6 = _x392 ∧ x7 = _x393 ∧ x8 = _x394 ∧ x9 = _x395 ∧ _x386 = _x395 ∧ _x385 = _x394 ∧ _x384 = _x393 ∧ _x383 = _x392 ∧ _x382 = _x391 ∧ _x381 = _x390 ∧ _x380 = _x389 ∧ _x379 = _x388 ∧ _x378 = _x387
l16	24	l8:	x1 = _x396 ∧ x2 = _x397 ∧ x3 = _x398 ∧ x4 = _x399 ∧ x5 = _x400 ∧ x6 = _x401 ∧ x7 = _x402 ∧ x8 = _x403 ∧ x9 = _x404 ∧ x1 = _x405 ∧ x2 = _x406 ∧ x3 = _x407 ∧ x4 = _x408 ∧ x5 = _x409 ∧ x6 = _x410 ∧ x7 = _x411 ∧ x8 = _x412 ∧ x9 = _x413 ∧ _x404 = _x413 ∧ _x403 = _x412 ∧ _x400 = _x409 ∧ _x397 = _x406 ∧ _x396 = _x405 ∧ _x408 = 0 ∧ _x411 = 0 ∧ _x407 = _x396 ∧ _x410 = _x397
l17	25	l16:	x1 = _x414 ∧ x2 = _x415 ∧ x3 = _x416 ∧ x4 = _x417 ∧ x5 = _x418 ∧ x6 = _x419 ∧ x7 = _x420 ∧ x8 = _x421 ∧ x9 = _x422 ∧ x1 = _x423 ∧ x2 = _x424 ∧ x3 = _x425 ∧ x4 = _x426 ∧ x5 = _x427 ∧ x6 = _x428 ∧ x7 = _x429 ∧ x8 = _x430 ∧ x9 = _x431 ∧ _x422 = _x431 ∧ _x421 = _x430 ∧ _x420 = _x429 ∧ _x419 = _x428 ∧ _x418 = _x427 ∧ _x417 = _x426 ∧ _x416 = _x425 ∧ _x415 = _x424 ∧ _x414 = _x423

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
l7	l7	l7:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l11	l11	l11:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l3	l3	l3:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l13	l13	l13:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l17	l17	l17:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l2	l2	l2:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l14	l14	l14:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l9	l9	l9:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l4	l4	l4:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l6	l6	l6:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l10	l10	l10:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l8	l8	l8:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l15	l15	l15:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l16	l16	l16:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l0	l0	l0:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9
l12	l12	l12:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 ∧ x6 = x6 ∧ x7 = x7 ∧ x8 = x8 ∧ x9 = x9

and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 4 SCC(s) of the program graph.

2.1 SCC Subproblem 1/4

Here we consider the SCC { l8, l13, l15, l14, l9 }.

2.1.1 Transition Removal

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

l8:	−1 − x4 + x6
l9:	−1 − x4 + x6
l14:	−2 − x4 + x6
l15:	−2 − x4 + x6
l13:	−2 − x4 + x6

2.1.2 Transition Removal

We remove transitions 8, 14, 18, 13, 17, 16 using the following ranking functions, which are bounded by 0.

l8:	0
l9:	−1
l14:	1
l15:	3
l13:	2

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 2/4

Here we consider the SCC { l7, l6, l10, l11, l12 }.

2.2.1 Transition Removal

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

l6:	−2 − x4 + x6
l7:	−2 − x4 + x6
l10:	−2 − x4 + x6
l12:	−1 − x4 + x6
l11:	−1 − x4 + x6

2.2.2 Transition Removal

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

l6:	2
l7:	2
l10:	2
l11:	−1
l12:	−1

2.2.3 Transition Removal

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

l6:	−2 + x3 − x5
l7:	−1 + x3 − x5
l10:	−1 + x3 − x5
l11:	−1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9
l12:	−1 + 2⋅x1 + 3⋅x2 + 4⋅x3 + 5⋅x4 + 6⋅x6 + 7⋅x7 + 8⋅x8 + 9⋅x9

2.2.4 Transition Removal

We remove transitions 7, 21, 15 using the following ranking functions, which are bounded by 0.

l6:	2
l7:	1
l10:	0
l11:	1
l12:	0

2.2.5 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.3 SCC Subproblem 3/4

Here we consider the SCC { l5, l4, l3 }.

2.3.1 Transition Removal

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

l3:	−2 + x3 − x4
l4:	−1 + x3 − x4
l5:	−1 + x3 − x4

2.3.2 Transition Removal

We remove transitions 3, 22 using the following ranking functions, which are bounded by 0.

l3:	2
l4:	1
l5:	0

2.3.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.4 SCC Subproblem 4/4

Here we consider the SCC { l0, l2 }.

2.4.1 Transition Removal

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

l0:	−2⋅x4 + 2⋅x6
l2:	−2⋅x4 + 2⋅x6 + 1

2.4.2 Transition Removal

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

l2:	0
l0:	−1

2.4.3 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 % (18 real / 0 unknown / 0 assumptions / 18 total proof steps)