LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: 4 − arg1P ≤ 01 − arg2P ≤ 0arg6P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 0arg6 ≤ 0x7 ≤ 0
3: 1 − arg1P ≤ 01 − arg1 ≤ 0
4: 4 − arg1P ≤ 0arg4P ≤ 04 − arg1 ≤ 0arg4 ≤ 0x48 ≤ 0x49 ≤ 0
5: 4 − arg1P ≤ 03 − arg3P ≤ 0arg4P ≤ 0arg9P ≤ 04 − arg1 ≤ 03 − arg3 ≤ 0arg4 ≤ 0arg9 ≤ 0x48 ≤ 0x49 ≤ 0
6: 4 − arg1P ≤ 01 − arg2P ≤ 01 − arg3P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 01 − arg3 ≤ 0x48 ≤ 0x49 ≤ 0
7: 4 − arg1P ≤ 01 − arg2P ≤ 0arg4P ≤ 01 − arg5P ≤ 01 − arg6P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 0arg4 ≤ 01 − arg5 ≤ 01 − arg6 ≤ 0x48 ≤ 0x49 ≤ 0
8: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
1 20 1: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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
3 27 3: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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 34 4: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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 41 6: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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 48 7: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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, 3, 5, 13, 14, 19 using the following ranking functions, which are bounded by −25.

8: 0
0: 0
1: 0
3: 0
4: 0
5: 0
6: 0
7: 0
8: −7
0: −8
1: −9
1_var_snapshot: −9
1*: −9
3: −12
3_var_snapshot: −12
3*: −12
4: −15
5: −15
4_var_snapshot: −15
4*: −15
6: −18
7: −18
6_var_snapshot: −18
6*: −18
7_var_snapshot: −18
7*: −18

4 Location Addition

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

1* 23 1: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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.

1 21 1_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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.

3* 30 3: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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.

3 28 3_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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.

4* 37 4: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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.

4 35 4_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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* 44 6: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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 42 6_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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* 51 7: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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 49 7_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x35 + x35 ≤ 0x35x35 ≤ 0x222 + x222 ≤ 0x222x222 ≤ 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 SCC Decomposition

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

14.1 SCC Subproblem 1/4

Here we consider the SCC { 1, 1_var_snapshot, 1* }.

14.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 1.

1: −2⋅arg3 + 2⋅arg6
1_var_snapshot: −2⋅arg3 + 2⋅arg6
1*: 1 − 2⋅arg3 + 2⋅arg6

14.1.2 Transition Removal

We remove transitions 21, 23 using the following ranking functions, which are bounded by −1.

1: 0
1_var_snapshot: arg2P
1*: arg2

14.1.3 Splitting Cut-Point Transitions

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

14.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 20.

14.1.3.1.1 Splitting Cut-Point Transitions

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

14.2 SCC Subproblem 2/4

Here we consider the SCC { 6, 7, 6_var_snapshot, 6*, 7_var_snapshot, 7* }.

14.2.1 Transition Removal

We remove transitions 15, 17 using the following ranking functions, which are bounded by 7.

6: 2 − 7⋅arg4 + 7⋅arg8
7: 7⋅arg10 − 7⋅arg3
6_var_snapshot: 1 − 7⋅arg4 + 7⋅arg8
6*: 3 − 7⋅arg4 + 7⋅arg8
7_var_snapshot: 7⋅arg10 − 7⋅arg3
7*: 7⋅arg10 − 7⋅arg3

14.2.2 Transition Removal

We remove transitions 42, 49, 51, 16, 18 using the following ranking functions, which are bounded by −9.

6: −8
7: 1 + 3⋅arg4
6_var_snapshot: −3⋅arg1P
6*: −4
7_var_snapshot: 3⋅arg4
7*: 2 + 3⋅arg4

14.2.3 Transition Removal

We remove transition 44 using the following ranking functions, which are bounded by 3.

6: 0
7: 0
6_var_snapshot: 0
6*: arg1
7_var_snapshot: 0
7*: 0

14.2.4 Splitting Cut-Point Transitions

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

14.2.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 41.

14.2.4.1.1 Splitting Cut-Point Transitions

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

14.2.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 48.

14.2.4.2.1 Splitting Cut-Point Transitions

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

14.3 SCC Subproblem 3/4

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

14.3.1 Transition Removal

We remove transitions 35, 37, 6, 7, 8, 9, 10, 11, 12 using the following ranking functions, which are bounded by −3.

4: −1 + 3⋅arg4
5: −3 + 3⋅arg3
4_var_snapshot: −2 + 3⋅arg4
4*: 3⋅arg4

14.3.2 Splitting Cut-Point Transitions

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

14.3.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 34.

14.3.2.1.1 Splitting Cut-Point Transitions

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

14.4 SCC Subproblem 4/4

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

14.4.1 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by 2.

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

14.4.2 Transition Removal

We remove transition 30 using the following ranking functions, which are bounded by −2.

3: −1
3_var_snapshot: −2⋅arg1P
3*: 0

14.4.3 Transition Removal

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

3: 1
3_var_snapshot: 0
3*: 0

14.4.4 Splitting Cut-Point Transitions

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

14.4.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 27.

14.4.4.1.1 Splitting Cut-Point Transitions

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

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