LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: arg1P ≤ 0arg1 ≤ 0
2: TRUE
3: TRUE
4: x96 ≤ 0x95 ≤ 0
5: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
2 18 2: x99 + x99 ≤ 0x99x99 ≤ 0x96 + x96 ≤ 0x96x96 ≤ 0x95 + x95 ≤ 0x95x95 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0x4 + x4 ≤ 0x4x4 ≤ 0x269 + x269 ≤ 0x269x269 ≤ 0x268 + x268 ≤ 0x268x268 ≤ 0x267 + x267 ≤ 0x267x267 ≤ 0x266 + x266 ≤ 0x266x266 ≤ 0x251 + x251 ≤ 0x251x251 ≤ 0x250 + x250 ≤ 0x250x250 ≤ 0x249 + x249 ≤ 0x249x249 ≤ 0x248 + x248 ≤ 0x248x248 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x246 + x246 ≤ 0x246x246 ≤ 0x245 + x245 ≤ 0x245x245 ≤ 0x237 + x237 ≤ 0x237x237 ≤ 0x236 + x236 ≤ 0x236x236 ≤ 0x235 + x235 ≤ 0x235x235 ≤ 0x221 + x221 ≤ 0x221x221 ≤ 0x220 + x220 ≤ 0x220x220 ≤ 0x219 + x219 ≤ 0x219x219 ≤ 0x218 + x218 ≤ 0x218x218 ≤ 0x217 + x217 ≤ 0x217x217 ≤ 0x216 + x216 ≤ 0x216x216 ≤ 0x215 + x215 ≤ 0x215x215 ≤ 0x214 + x214 ≤ 0x214x214 ≤ 0x206 + x206 ≤ 0x206x206 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x203 + x203 ≤ 0x203x203 ≤ 0x202 + x202 ≤ 0x202x202 ≤ 0x189 + x189 ≤ 0x189x189 ≤ 0x188 + x188 ≤ 0x188x188 ≤ 0x187 + x187 ≤ 0x187x187 ≤ 0x186 + x186 ≤ 0x186x186 ≤ 0x185 + x185 ≤ 0x185x185 ≤ 0x184 + x184 ≤ 0x184x184 ≤ 0x183 + x183 ≤ 0x183x183 ≤ 0x182 + x182 ≤ 0x182x182 ≤ 0x181 + x181 ≤ 0x181x181 ≤ 0x173 + x173 ≤ 0x173x173 ≤ 0x172 + x172 ≤ 0x172x172 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0x160 + x160 ≤ 0x160x160 ≤ 0x159 + x159 ≤ 0x159x159 ≤ 0x158 + x158 ≤ 0x158x158 ≤ 0x157 + x157 ≤ 0x157x157 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 0x133 + x133 ≤ 0x133x133 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x129 + x129 ≤ 0x129x129 ≤ 0x128 + x128 ≤ 0x128x128 ≤ 0x120 + x120 ≤ 0x120x120 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 0x117 + x117 ≤ 0x117x117 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0x104 + x104 ≤ 0x104x104 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0x102 + x102 ≤ 0x102x102 ≤ 0x101 + x101 ≤ 0x101x101 ≤ 0x100 + x100 ≤ 0x100x100 ≤ 0x10 + x10 ≤ 0x10x10 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
4 25 4: x99 + x99 ≤ 0x99x99 ≤ 0x96 + x96 ≤ 0x96x96 ≤ 0x95 + x95 ≤ 0x95x95 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0x4 + x4 ≤ 0x4x4 ≤ 0x269 + x269 ≤ 0x269x269 ≤ 0x268 + x268 ≤ 0x268x268 ≤ 0x267 + x267 ≤ 0x267x267 ≤ 0x266 + x266 ≤ 0x266x266 ≤ 0x251 + x251 ≤ 0x251x251 ≤ 0x250 + x250 ≤ 0x250x250 ≤ 0x249 + x249 ≤ 0x249x249 ≤ 0x248 + x248 ≤ 0x248x248 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x246 + x246 ≤ 0x246x246 ≤ 0x245 + x245 ≤ 0x245x245 ≤ 0x237 + x237 ≤ 0x237x237 ≤ 0x236 + x236 ≤ 0x236x236 ≤ 0x235 + x235 ≤ 0x235x235 ≤ 0x221 + x221 ≤ 0x221x221 ≤ 0x220 + x220 ≤ 0x220x220 ≤ 0x219 + x219 ≤ 0x219x219 ≤ 0x218 + x218 ≤ 0x218x218 ≤ 0x217 + x217 ≤ 0x217x217 ≤ 0x216 + x216 ≤ 0x216x216 ≤ 0x215 + x215 ≤ 0x215x215 ≤ 0x214 + x214 ≤ 0x214x214 ≤ 0x206 + x206 ≤ 0x206x206 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x203 + x203 ≤ 0x203x203 ≤ 0x202 + x202 ≤ 0x202x202 ≤ 0x189 + x189 ≤ 0x189x189 ≤ 0x188 + x188 ≤ 0x188x188 ≤ 0x187 + x187 ≤ 0x187x187 ≤ 0x186 + x186 ≤ 0x186x186 ≤ 0x185 + x185 ≤ 0x185x185 ≤ 0x184 + x184 ≤ 0x184x184 ≤ 0x183 + x183 ≤ 0x183x183 ≤ 0x182 + x182 ≤ 0x182x182 ≤ 0x181 + x181 ≤ 0x181x181 ≤ 0x173 + x173 ≤ 0x173x173 ≤ 0x172 + x172 ≤ 0x172x172 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0x160 + x160 ≤ 0x160x160 ≤ 0x159 + x159 ≤ 0x159x159 ≤ 0x158 + x158 ≤ 0x158x158 ≤ 0x157 + x157 ≤ 0x157x157 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 0x133 + x133 ≤ 0x133x133 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x129 + x129 ≤ 0x129x129 ≤ 0x128 + x128 ≤ 0x128x128 ≤ 0x120 + x120 ≤ 0x120x120 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 0x117 + x117 ≤ 0x117x117 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0x104 + x104 ≤ 0x104x104 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0x102 + x102 ≤ 0x102x102 ≤ 0x101 + x101 ≤ 0x101x101 ≤ 0x100 + x100 ≤ 0x100x100 ≤ 0x10 + x10 ≤ 0x10x10 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 1, 2, 15, 17 using the following ranking functions, which are bounded by −17.

5: 0
0: 0
1: 0
2: 0
3: 0
4: 0
5: −6
0: −7
1: −8
2: −9
3: −9
2_var_snapshot: −9
2*: −9
4: −12
4_var_snapshot: −12
4*: −12

4 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

2* 21 2: x99 + x99 ≤ 0x99x99 ≤ 0x96 + x96 ≤ 0x96x96 ≤ 0x95 + x95 ≤ 0x95x95 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0x4 + x4 ≤ 0x4x4 ≤ 0x269 + x269 ≤ 0x269x269 ≤ 0x268 + x268 ≤ 0x268x268 ≤ 0x267 + x267 ≤ 0x267x267 ≤ 0x266 + x266 ≤ 0x266x266 ≤ 0x251 + x251 ≤ 0x251x251 ≤ 0x250 + x250 ≤ 0x250x250 ≤ 0x249 + x249 ≤ 0x249x249 ≤ 0x248 + x248 ≤ 0x248x248 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x246 + x246 ≤ 0x246x246 ≤ 0x245 + x245 ≤ 0x245x245 ≤ 0x237 + x237 ≤ 0x237x237 ≤ 0x236 + x236 ≤ 0x236x236 ≤ 0x235 + x235 ≤ 0x235x235 ≤ 0x221 + x221 ≤ 0x221x221 ≤ 0x220 + x220 ≤ 0x220x220 ≤ 0x219 + x219 ≤ 0x219x219 ≤ 0x218 + x218 ≤ 0x218x218 ≤ 0x217 + x217 ≤ 0x217x217 ≤ 0x216 + x216 ≤ 0x216x216 ≤ 0x215 + x215 ≤ 0x215x215 ≤ 0x214 + x214 ≤ 0x214x214 ≤ 0x206 + x206 ≤ 0x206x206 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x203 + x203 ≤ 0x203x203 ≤ 0x202 + x202 ≤ 0x202x202 ≤ 0x189 + x189 ≤ 0x189x189 ≤ 0x188 + x188 ≤ 0x188x188 ≤ 0x187 + x187 ≤ 0x187x187 ≤ 0x186 + x186 ≤ 0x186x186 ≤ 0x185 + x185 ≤ 0x185x185 ≤ 0x184 + x184 ≤ 0x184x184 ≤ 0x183 + x183 ≤ 0x183x183 ≤ 0x182 + x182 ≤ 0x182x182 ≤ 0x181 + x181 ≤ 0x181x181 ≤ 0x173 + x173 ≤ 0x173x173 ≤ 0x172 + x172 ≤ 0x172x172 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0x160 + x160 ≤ 0x160x160 ≤ 0x159 + x159 ≤ 0x159x159 ≤ 0x158 + x158 ≤ 0x158x158 ≤ 0x157 + x157 ≤ 0x157x157 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 0x133 + x133 ≤ 0x133x133 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x129 + x129 ≤ 0x129x129 ≤ 0x128 + x128 ≤ 0x128x128 ≤ 0x120 + x120 ≤ 0x120x120 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 0x117 + x117 ≤ 0x117x117 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0x104 + x104 ≤ 0x104x104 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0x102 + x102 ≤ 0x102x102 ≤ 0x101 + x101 ≤ 0x101x101 ≤ 0x100 + x100 ≤ 0x100x100 ≤ 0x10 + x10 ≤ 0x10x10 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

5 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

2 19 2_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x96 + x96 ≤ 0x96x96 ≤ 0x95 + x95 ≤ 0x95x95 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0x4 + x4 ≤ 0x4x4 ≤ 0x269 + x269 ≤ 0x269x269 ≤ 0x268 + x268 ≤ 0x268x268 ≤ 0x267 + x267 ≤ 0x267x267 ≤ 0x266 + x266 ≤ 0x266x266 ≤ 0x251 + x251 ≤ 0x251x251 ≤ 0x250 + x250 ≤ 0x250x250 ≤ 0x249 + x249 ≤ 0x249x249 ≤ 0x248 + x248 ≤ 0x248x248 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x246 + x246 ≤ 0x246x246 ≤ 0x245 + x245 ≤ 0x245x245 ≤ 0x237 + x237 ≤ 0x237x237 ≤ 0x236 + x236 ≤ 0x236x236 ≤ 0x235 + x235 ≤ 0x235x235 ≤ 0x221 + x221 ≤ 0x221x221 ≤ 0x220 + x220 ≤ 0x220x220 ≤ 0x219 + x219 ≤ 0x219x219 ≤ 0x218 + x218 ≤ 0x218x218 ≤ 0x217 + x217 ≤ 0x217x217 ≤ 0x216 + x216 ≤ 0x216x216 ≤ 0x215 + x215 ≤ 0x215x215 ≤ 0x214 + x214 ≤ 0x214x214 ≤ 0x206 + x206 ≤ 0x206x206 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x203 + x203 ≤ 0x203x203 ≤ 0x202 + x202 ≤ 0x202x202 ≤ 0x189 + x189 ≤ 0x189x189 ≤ 0x188 + x188 ≤ 0x188x188 ≤ 0x187 + x187 ≤ 0x187x187 ≤ 0x186 + x186 ≤ 0x186x186 ≤ 0x185 + x185 ≤ 0x185x185 ≤ 0x184 + x184 ≤ 0x184x184 ≤ 0x183 + x183 ≤ 0x183x183 ≤ 0x182 + x182 ≤ 0x182x182 ≤ 0x181 + x181 ≤ 0x181x181 ≤ 0x173 + x173 ≤ 0x173x173 ≤ 0x172 + x172 ≤ 0x172x172 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0x160 + x160 ≤ 0x160x160 ≤ 0x159 + x159 ≤ 0x159x159 ≤ 0x158 + x158 ≤ 0x158x158 ≤ 0x157 + x157 ≤ 0x157x157 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 0x133 + x133 ≤ 0x133x133 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x129 + x129 ≤ 0x129x129 ≤ 0x128 + x128 ≤ 0x128x128 ≤ 0x120 + x120 ≤ 0x120x120 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 0x117 + x117 ≤ 0x117x117 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0x104 + x104 ≤ 0x104x104 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0x102 + x102 ≤ 0x102x102 ≤ 0x101 + x101 ≤ 0x101x101 ≤ 0x100 + x100 ≤ 0x100x100 ≤ 0x10 + x10 ≤ 0x10x10 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

6 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

4* 28 4: x99 + x99 ≤ 0x99x99 ≤ 0x96 + x96 ≤ 0x96x96 ≤ 0x95 + x95 ≤ 0x95x95 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0x4 + x4 ≤ 0x4x4 ≤ 0x269 + x269 ≤ 0x269x269 ≤ 0x268 + x268 ≤ 0x268x268 ≤ 0x267 + x267 ≤ 0x267x267 ≤ 0x266 + x266 ≤ 0x266x266 ≤ 0x251 + x251 ≤ 0x251x251 ≤ 0x250 + x250 ≤ 0x250x250 ≤ 0x249 + x249 ≤ 0x249x249 ≤ 0x248 + x248 ≤ 0x248x248 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x246 + x246 ≤ 0x246x246 ≤ 0x245 + x245 ≤ 0x245x245 ≤ 0x237 + x237 ≤ 0x237x237 ≤ 0x236 + x236 ≤ 0x236x236 ≤ 0x235 + x235 ≤ 0x235x235 ≤ 0x221 + x221 ≤ 0x221x221 ≤ 0x220 + x220 ≤ 0x220x220 ≤ 0x219 + x219 ≤ 0x219x219 ≤ 0x218 + x218 ≤ 0x218x218 ≤ 0x217 + x217 ≤ 0x217x217 ≤ 0x216 + x216 ≤ 0x216x216 ≤ 0x215 + x215 ≤ 0x215x215 ≤ 0x214 + x214 ≤ 0x214x214 ≤ 0x206 + x206 ≤ 0x206x206 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x203 + x203 ≤ 0x203x203 ≤ 0x202 + x202 ≤ 0x202x202 ≤ 0x189 + x189 ≤ 0x189x189 ≤ 0x188 + x188 ≤ 0x188x188 ≤ 0x187 + x187 ≤ 0x187x187 ≤ 0x186 + x186 ≤ 0x186x186 ≤ 0x185 + x185 ≤ 0x185x185 ≤ 0x184 + x184 ≤ 0x184x184 ≤ 0x183 + x183 ≤ 0x183x183 ≤ 0x182 + x182 ≤ 0x182x182 ≤ 0x181 + x181 ≤ 0x181x181 ≤ 0x173 + x173 ≤ 0x173x173 ≤ 0x172 + x172 ≤ 0x172x172 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0x160 + x160 ≤ 0x160x160 ≤ 0x159 + x159 ≤ 0x159x159 ≤ 0x158 + x158 ≤ 0x158x158 ≤ 0x157 + x157 ≤ 0x157x157 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 0x133 + x133 ≤ 0x133x133 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x129 + x129 ≤ 0x129x129 ≤ 0x128 + x128 ≤ 0x128x128 ≤ 0x120 + x120 ≤ 0x120x120 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 0x117 + x117 ≤ 0x117x117 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0x104 + x104 ≤ 0x104x104 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0x102 + x102 ≤ 0x102x102 ≤ 0x101 + x101 ≤ 0x101x101 ≤ 0x100 + x100 ≤ 0x100x100 ≤ 0x10 + x10 ≤ 0x10x10 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

7 Location Addition

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

4 26 4_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x96 + x96 ≤ 0x96x96 ≤ 0x95 + x95 ≤ 0x95x95 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0x4 + x4 ≤ 0x4x4 ≤ 0x269 + x269 ≤ 0x269x269 ≤ 0x268 + x268 ≤ 0x268x268 ≤ 0x267 + x267 ≤ 0x267x267 ≤ 0x266 + x266 ≤ 0x266x266 ≤ 0x251 + x251 ≤ 0x251x251 ≤ 0x250 + x250 ≤ 0x250x250 ≤ 0x249 + x249 ≤ 0x249x249 ≤ 0x248 + x248 ≤ 0x248x248 ≤ 0x247 + x247 ≤ 0x247x247 ≤ 0x246 + x246 ≤ 0x246x246 ≤ 0x245 + x245 ≤ 0x245x245 ≤ 0x237 + x237 ≤ 0x237x237 ≤ 0x236 + x236 ≤ 0x236x236 ≤ 0x235 + x235 ≤ 0x235x235 ≤ 0x221 + x221 ≤ 0x221x221 ≤ 0x220 + x220 ≤ 0x220x220 ≤ 0x219 + x219 ≤ 0x219x219 ≤ 0x218 + x218 ≤ 0x218x218 ≤ 0x217 + x217 ≤ 0x217x217 ≤ 0x216 + x216 ≤ 0x216x216 ≤ 0x215 + x215 ≤ 0x215x215 ≤ 0x214 + x214 ≤ 0x214x214 ≤ 0x206 + x206 ≤ 0x206x206 ≤ 0x205 + x205 ≤ 0x205x205 ≤ 0x204 + x204 ≤ 0x204x204 ≤ 0x203 + x203 ≤ 0x203x203 ≤ 0x202 + x202 ≤ 0x202x202 ≤ 0x189 + x189 ≤ 0x189x189 ≤ 0x188 + x188 ≤ 0x188x188 ≤ 0x187 + x187 ≤ 0x187x187 ≤ 0x186 + x186 ≤ 0x186x186 ≤ 0x185 + x185 ≤ 0x185x185 ≤ 0x184 + x184 ≤ 0x184x184 ≤ 0x183 + x183 ≤ 0x183x183 ≤ 0x182 + x182 ≤ 0x182x182 ≤ 0x181 + x181 ≤ 0x181x181 ≤ 0x173 + x173 ≤ 0x173x173 ≤ 0x172 + x172 ≤ 0x172x172 ≤ 0x170 + x170 ≤ 0x170x170 ≤ 0x160 + x160 ≤ 0x160x160 ≤ 0x159 + x159 ≤ 0x159x159 ≤ 0x158 + x158 ≤ 0x158x158 ≤ 0x157 + x157 ≤ 0x157x157 ≤ 0x156 + x156 ≤ 0x156x156 ≤ 0x147 + x147 ≤ 0x147x147 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 0x133 + x133 ≤ 0x133x133 ≤ 0x132 + x132 ≤ 0x132x132 ≤ 0x131 + x131 ≤ 0x131x131 ≤ 0x130 + x130 ≤ 0x130x130 ≤ 0x129 + x129 ≤ 0x129x129 ≤ 0x128 + x128 ≤ 0x128x128 ≤ 0x120 + x120 ≤ 0x120x120 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 0x117 + x117 ≤ 0x117x117 ≤ 0x105 + x105 ≤ 0x105x105 ≤ 0x104 + x104 ≤ 0x104x104 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0x102 + x102 ≤ 0x102x102 ≤ 0x101 + x101 ≤ 0x101x101 ≤ 0x100 + x100 ≤ 0x100x100 ≤ 0x10 + x10 ≤ 0x10x10 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

8 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

8.1 SCC Subproblem 1/2

Here we consider the SCC { 2, 3, 2_var_snapshot, 2* }.

8.1.1 Transition Removal

We remove transitions 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 using the following ranking functions, which are bounded by 3.

2: 2 + 4⋅arg4
3: 4⋅arg4
2_var_snapshot: 1 + 4⋅arg4
2*: 3 + 4⋅arg4

8.1.2 Transition Removal

We remove transition 19 using the following ranking functions, which are bounded by −1.

2: 0
3: 0
2_var_snapshot: −1
2*: 1

8.1.3 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by −1.

2: −1
3: 0
2_var_snapshot: 0
2*: 0

8.1.4 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

8.1.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 18.

8.1.4.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

8.2 SCC Subproblem 2/2

Here we consider the SCC { 4, 4_var_snapshot, 4* }.

8.2.1 Transition Removal

We remove transition 16 using the following ranking functions, which are bounded by 2.

4: 1 + 3⋅arg1
4_var_snapshot: 3⋅arg1
4*: 2 + 3⋅arg1

8.2.2 Transition Removal

We remove transition 26 using the following ranking functions, which are bounded by −1.

4: 0
4_var_snapshot: −1
4*: 1

8.2.3 Transition Removal

We remove transition 28 using the following ranking functions, which are bounded by 0.

4: 0
4_var_snapshot: 0
4*: 1

8.2.4 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

8.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 25.

8.2.4.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

Tool configuration

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