LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: 6 − arg1P ≤ 04 − arg2P ≤ 0arg3P ≤ 0arg3P ≤ 06 − arg1 ≤ 04 − arg2 ≤ 0arg3 ≤ 0arg3 ≤ 0x7 ≤ 0
3: 6 − arg1P ≤ 01 − arg2P ≤ 06 − arg1 ≤ 01 − arg2 ≤ 01 − arg4 ≤ 0x7 ≤ 0
4: 6 − arg1P ≤ 0arg2P ≤ 06 − arg1 ≤ 0arg2 ≤ 01 − arg4 ≤ 0x7 ≤ 0
5: 6 − arg1P ≤ 01 − arg2P ≤ 06 − arg1 ≤ 01 − arg2 ≤ 01 − arg4 ≤ 0x7 ≤ 0
6: 1 − arg1P ≤ 01 − arg1 ≤ 0
7: 4 − arg1P ≤ 0arg4P ≤ 04 − arg1 ≤ 0arg4 ≤ 0x111 ≤ 0x112 ≤ 0
8: 4 − arg1P ≤ 03 − arg3P ≤ 0arg4P ≤ 0arg8P ≤ 04 − arg1 ≤ 03 − arg3 ≤ 0arg4 ≤ 0arg8 ≤ 0x111 ≤ 0x112 ≤ 0
9: 4 − arg1P ≤ 01 − arg2P ≤ 01 − arg3P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 01 − arg3 ≤ 0x111 ≤ 0x112 ≤ 0
10: 4 − arg1P ≤ 01 − arg2P ≤ 0arg4P ≤ 01 − arg5P ≤ 01 − arg6P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 0arg4 ≤ 01 − arg5 ≤ 01 − arg6 ≤ 0x111 ≤ 0x112 ≤ 0
11: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
3 28 3: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
4 35 4: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
5 42 5: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
6 49 6: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
7 56 7: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
9 63 9: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
10 70 10: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 2, 4, 5, 11, 13, 21, 22, 27 using the following ranking functions, which are bounded by −33.

11: 0
0: 0
1: 0
3: 0
4: 0
5: 0
6: 0
7: 0
8: 0
9: 0
10: 0
11: −9
0: −10
1: −11
3: −12
3_var_snapshot: −12
3*: −12
4: −15
5: −15
4_var_snapshot: −15
4*: −15
5_var_snapshot: −15
5*: −15
6: −20
6_var_snapshot: −20
6*: −20
7: −23
8: −23
7_var_snapshot: −23
7*: −23
9: −26
10: −26
9_var_snapshot: −26
9*: −26
10_var_snapshot: −26
10*: −26

4 Location Addition

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

3* 31 3: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

5 Location Addition

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

3 29 3_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 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* 38 4: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 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 36 4_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

8 Location Addition

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

5* 45 5: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

9 Location Addition

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

5 43 5_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

10 Location Addition

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

6* 52 6: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

11 Location Addition

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

6 50 6_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

12 Location Addition

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

7* 59 7: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

13 Location Addition

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

7 57 7_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

14 Location Addition

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

9* 66 9: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

15 Location Addition

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

9 64 9_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

16 Location Addition

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

10* 73 10: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

17 Location Addition

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

10 71 10_var_snapshot: x99 + x99 ≤ 0x99x99 ≤ 0x98 + x98 ≤ 0x98x98 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x285 + x285 ≤ 0x285x285 ≤ 0x150 + x150 ≤ 0x150x150 ≤ 0x112 + x112 ≤ 0x112x112 ≤ 0x111 + x111 ≤ 0x111x111 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg13P + arg13P ≤ 0arg13Parg13P ≤ 0arg13 + arg13 ≤ 0arg13arg13 ≤ 0arg12P + arg12P ≤ 0arg12Parg12P ≤ 0arg12 + arg12 ≤ 0arg12arg12 ≤ 0arg11P + arg11P ≤ 0arg11Parg11P ≤ 0arg11 + arg11 ≤ 0arg11arg11 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

18 SCC Decomposition

We consider subproblems for each of the 5 SCC(s) of the program graph.

18.1 SCC Subproblem 1/5

Here we consider the SCC { 4, 5, 4_var_snapshot, 4*, 5_var_snapshot, 5* }.

18.1.1 Transition Removal

We remove transitions 9, 10 using the following ranking functions, which are bounded by 4.

4: −5⋅arg3 + 5⋅arg5
5: −5⋅arg3 + 5⋅arg6
4_var_snapshot: −5⋅arg3 + 5⋅arg5
4*: −5⋅arg3 + 5⋅arg5
5_var_snapshot: −5⋅arg3 + 5⋅arg6
5*: −5⋅arg3 + 5⋅arg6

18.1.2 Transition Removal

We remove transitions 36, 38, 43, 45, 6, 7, 8 using the following ranking functions, which are bounded by −1.

4: 1 + 3⋅arg2
5: 1 + 3⋅arg2
4_var_snapshot: 3⋅arg2
4*: 2 + 3⋅arg2
5_var_snapshot: 3⋅arg2
5*: 2 + 3⋅arg2

18.1.3 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

18.1.3.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 35.

18.1.3.1.1 Splitting Cut-Point Transitions

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

18.1.3.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 42.

18.1.3.2.1 Splitting Cut-Point Transitions

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

18.2 SCC Subproblem 2/5

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

18.2.1 Transition Removal

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

3: −4⋅arg3 + 4⋅arg6
3_var_snapshot: −4⋅arg3 + 4⋅arg6
3*: 1 − 4⋅arg3 + 4⋅arg6

18.2.2 Transition Removal

We remove transitions 29, 31 using the following ranking functions, which are bounded by −2.

3: −1
3_var_snapshot: −2⋅arg2P
3*: 0

18.2.3 Splitting Cut-Point Transitions

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

18.2.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 28.

18.2.3.1.1 Splitting Cut-Point Transitions

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

18.3 SCC Subproblem 3/5

Here we consider the SCC { 9, 10, 9_var_snapshot, 9*, 10_var_snapshot, 10* }.

18.3.1 Transition Removal

We remove transitions 23, 25 using the following ranking functions, which are bounded by 7.

9: 2 − 7⋅arg4 + 7⋅arg8
10: 7⋅arg10 − 7⋅arg3
9_var_snapshot: 1 − 7⋅arg4 + 7⋅arg8
9*: 3 − 7⋅arg4 + 7⋅arg8
10_var_snapshot: 7⋅arg10 − 7⋅arg3
10*: 7⋅arg10 − 7⋅arg3

18.3.2 Transition Removal

We remove transitions 64, 71, 73, 24, 26 using the following ranking functions, which are bounded by −3.

9: −2
10: 1 + 3⋅arg4
9_var_snapshot: −3⋅arg2P
9*: −1
10_var_snapshot: 3⋅arg4
10*: 2 + 3⋅arg4

18.3.3 Transition Removal

We remove transition 66 using the following ranking functions, which are bounded by 0.

9: 0
10: 0
9_var_snapshot: 0
9*: arg2P
10_var_snapshot: 0
10*: 0

18.3.4 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

18.3.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 63.

18.3.4.1.1 Splitting Cut-Point Transitions

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

18.3.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 70.

18.3.4.2.1 Splitting Cut-Point Transitions

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

18.4 SCC Subproblem 4/5

Here we consider the SCC { 7, 8, 7_var_snapshot, 7* }.

18.4.1 Transition Removal

We remove transitions 57, 59, 14, 15, 16, 17, 18, 19, 20 using the following ranking functions, which are bounded by −3.

7: −1 + 3⋅arg4
8: 1 + 3⋅arg8
7_var_snapshot: −2 + 3⋅arg4
7*: 3⋅arg4

18.4.2 Splitting Cut-Point Transitions

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

18.4.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 56.

18.4.2.1.1 Splitting Cut-Point Transitions

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

18.5 SCC Subproblem 5/5

Here we consider the SCC { 6, 6_var_snapshot, 6* }.

18.5.1 Transition Removal

We remove transition 12 using the following ranking functions, which are bounded by 2.

6: 1 + arg2 + arg3arg4
6_var_snapshot: arg2 + arg3arg4
6*: 2 + arg2 + arg3arg4

18.5.2 Transition Removal

We remove transition 52 using the following ranking functions, which are bounded by −1.

6: 0
6_var_snapshot: arg1
6*: arg1P

18.5.3 Transition Removal

We remove transition 50 using the following ranking functions, which are bounded by −1.

6: 0
6_var_snapshot: −1
6*: 0

18.5.4 Splitting Cut-Point Transitions

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

18.5.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 49.

18.5.4.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert