LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: 4 − arg1P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 0x7 ≤ 0
3: 1 − arg1P ≤ 01 − arg1 ≤ 0
4: 1 − arg1P ≤ 01 − arg1 ≤ 0x7 ≤ 0x32 ≤ 0x38 ≤ 0
5: 1 − arg1P ≤ 0arg3P ≤ 01 − arg1 ≤ 0arg3 ≤ 0x7 ≤ 0x32 ≤ 0x38 ≤ 0
6: 1 − arg2P ≤ 01 − arg2 ≤ 0
7: 1 − arg1P ≤ 03 − arg3P ≤ 0arg4P ≤ 0arg8P ≤ 01 − arg1 ≤ 03 − arg3 ≤ 0arg4 ≤ 0arg8 ≤ 0x7 ≤ 0x32 ≤ 0x38 ≤ 0
8: 4 − arg1P ≤ 0arg4P ≤ 04 − arg1 ≤ 0arg4 ≤ 0x118 ≤ 0x119 ≤ 0
9: 4 − arg1P ≤ 03 − arg3P ≤ 0arg4P ≤ 0arg10P ≤ 04 − arg1 ≤ 03 − arg3 ≤ 0arg4 ≤ 02 − arg5 ≤ 02 − arg6 ≤ 0arg10 ≤ 0x118 ≤ 0x119 ≤ 0
10: 4 − arg1P ≤ 01 − arg2P ≤ 01 − arg3P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 01 − arg3 ≤ 0x118 ≤ 0x119 ≤ 0
11: 4 − arg1P ≤ 01 − arg2P ≤ 0arg4P ≤ 01 − arg5P ≤ 01 − arg6P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 0arg4 ≤ 01 − arg5 ≤ 01 − arg6 ≤ 0x118 ≤ 0x119 ≤ 0
12: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
3 29 3: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 36 4: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 43 5: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 50 8: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 57 10: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 64 11: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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, 7, 13, 14, 22, 23, 28 using the following ranking functions, which are bounded by −31.

12: 0
0: 0
1: 0
4: 0
5: 0
7: 0
3: 0
8: 0
9: 0
6: 0
10: 0
11: 0
12: −9
0: −10
1: −11
4: −12
5: −12
7: −12
4_var_snapshot: −12
4*: −12
5_var_snapshot: −12
5*: −12
3: −17
3_var_snapshot: −17
3*: −17
8: −20
9: −20
8_var_snapshot: −20
8*: −20
6: −23
10: −24
11: −24
10_var_snapshot: −24
10*: −24
11_var_snapshot: −24
11*: −24

4 Location Addition

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

3* 32 3: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 30 3_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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* 39 4: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 37 4_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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* 46 5: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 44 5_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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.

8* 53 8: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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.

8 51 8_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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.

10* 60 10: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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.

10 58 10_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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.

11* 67 11: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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.

11 65 11_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x299 + x299 ≤ 0x299x299 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x168 + x168 ≤ 0x168x168 ≤ 0x119 + x119 ≤ 0x119x119 ≤ 0x118 + x118 ≤ 0x118x118 ≤ 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 ≤ 0arg14P + arg14P ≤ 0arg14Parg14P ≤ 0arg14 + arg14 ≤ 0arg14arg14 ≤ 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 SCC Decomposition

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

16.1 SCC Subproblem 1/4

Here we consider the SCC { 4, 5, 7, 4_var_snapshot, 4*, 5_var_snapshot, 5* }.

16.1.1 Transition Removal

We remove transitions 5, 9 using the following ranking functions, which are bounded by 3.

4: 2 − 4⋅arg2 + 4⋅arg3
5: −4⋅arg2 + 4⋅arg5
7: −4⋅arg2arg4 + 4⋅arg6
4_var_snapshot: 1 − 4⋅arg2 + 4⋅arg3
4*: 3 − 4⋅arg2 + 4⋅arg3
5_var_snapshot: −4⋅arg2 + 4⋅arg5
5*: −4⋅arg2 + 4⋅arg5

16.1.2 Transition Removal

We remove transitions 37, 39, 44, 46, 6, 8, 10, 11, 12 using the following ranking functions, which are bounded by −3.

4: −2
5: 1 + 2⋅arg3
7: −1 + 2⋅arg3
4_var_snapshot: −3
4*: −1
5_var_snapshot: 2⋅arg3
5*: 2 + 2⋅arg3

16.1.3 Splitting Cut-Point Transitions

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

16.1.3.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 36.

16.1.3.1.1 Splitting Cut-Point Transitions

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

16.1.3.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 43.

16.1.3.2.1 Splitting Cut-Point Transitions

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

16.2 SCC Subproblem 2/4

Here we consider the SCC { 10, 11, 10_var_snapshot, 10*, 11_var_snapshot, 11* }.

16.2.1 Transition Removal

We remove transition 26 using the following ranking functions, which are bounded by 6.

10: 1 − 7⋅arg4 + 7⋅arg8
11: 7⋅arg10 − 7⋅arg3
10_var_snapshot: −7⋅arg4 + 7⋅arg8
10*: 2 − 7⋅arg4 + 7⋅arg8
11_var_snapshot: 7⋅arg10 − 7⋅arg3
11*: 7⋅arg10 − 7⋅arg3

16.2.2 Transition Removal

We remove transition 24 using the following ranking functions, which are bounded by 6.

10: 2 − 6⋅arg4 + 6⋅arg8
11: 6⋅arg10 − 6⋅arg3
10_var_snapshot: 1 − 6⋅arg4 + 6⋅arg8
10*: 3 − 6⋅arg4 + 6⋅arg8
11_var_snapshot: 6⋅arg10 − 6⋅arg3
11*: 6⋅arg10 − 6⋅arg3

16.2.3 Transition Removal

We remove transitions 60, 65, 67, 25, 27 using the following ranking functions, which are bounded by 1.

10: 2⋅arg2P
11: 2 + 2⋅arg5
10_var_snapshot: 2⋅arg2Parg3P
10*: 1 + 2⋅arg2P
11_var_snapshot: 2⋅arg5
11*: 3 + 2⋅arg5

16.2.4 Transition Removal

We remove transition 58 using the following ranking functions, which are bounded by −1.

10: 0
11: 0
10_var_snapshot: −1
10*: 0
11_var_snapshot: 0
11*: 0

16.2.5 Splitting Cut-Point Transitions

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

16.2.5.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 57.

16.2.5.1.1 Splitting Cut-Point Transitions

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

16.2.5.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 64.

16.2.5.2.1 Splitting Cut-Point Transitions

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

16.3 SCC Subproblem 3/4

Here we consider the SCC { 8, 9, 8_var_snapshot, 8* }.

16.3.1 Transition Removal

We remove transitions 51, 53, 15, 16, 17, 18, 19, 20, 21 using the following ranking functions, which are bounded by −3.

8: −1 + 3⋅arg4
9: −3 + 3⋅arg3
8_var_snapshot: −2 + 3⋅arg4
8*: 3⋅arg4

16.3.2 Splitting Cut-Point Transitions

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

16.3.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 50.

16.3.2.1.1 Splitting Cut-Point Transitions

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

16.4 SCC Subproblem 4/4

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

16.4.1 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 2.

3: 1 + arg2 + arg3arg4
3_var_snapshot: arg2 + arg3arg4
3*: 2 + arg2 + arg3arg4

16.4.2 Transition Removal

We remove transitions 30, 32 using the following ranking functions, which are bounded by −1.

3: 0
3_var_snapshot: −1
3*: arg1P

16.4.3 Splitting Cut-Point Transitions

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

16.4.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 29.

16.4.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

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