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: 4 − arg1P ≤ 04 − arg1 ≤ 0
5: 4 − arg1P ≤ 0arg4P ≤ 04 − arg1 ≤ 0arg4 ≤ 0
6: 4 − arg1P ≤ 03 − arg3P ≤ 0arg4P ≤ 0arg9P ≤ 04 − arg1 ≤ 03 − arg3 ≤ 0arg4 ≤ 02 − arg5 ≤ 0arg9 ≤ 0
7: 4 − arg1P ≤ 01 − arg2P ≤ 01 − arg3P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 01 − arg3 ≤ 0
8: 4 − arg1P ≤ 01 − arg2P ≤ 0arg4P ≤ 01 − arg5P ≤ 01 − arg6P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 0arg4 ≤ 01 − arg5 ≤ 01 − arg6 ≤ 0
9: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
3 21 3: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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 28 5: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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 35 7: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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 42 8: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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, 6, 14, 15, 20 using the following ranking functions, which are bounded by −25.

9: 0
0: 0
1: 0
3: 0
4: 0
5: 0
6: 0
7: 0
8: 0
9: −8
0: −9
1: −10
3: −11
3_var_snapshot: −11
3*: −11
4: −14
5: −15
6: −15
5_var_snapshot: −15
5*: −15
7: −18
8: −18
7_var_snapshot: −18
7*: −18
8_var_snapshot: −18
8*: −18

4 Location Addition

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

3* 24 3: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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 22 3_var_snapshot: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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.

5* 31 5: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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.

5 29 5_var_snapshot: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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.

7* 38 7: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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.

7 36 7_var_snapshot: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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.

8* 45 8: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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.

8 43 8_var_snapshot: x90 + x90 ≤ 0x90x90 ≤ 0x7 + x7 ≤ 0x7x7 ≤ 0x49 + x49 ≤ 0x49x49 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x38 + x38 ≤ 0x38x38 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x211 + x211 ≤ 0x211x211 ≤ 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 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

12.1 SCC Subproblem 1/3

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

12.1.1 Transition Removal

We remove transitions 16, 18 using the following ranking functions, which are bounded by 6.

7: 1 − 6⋅arg4 + 6⋅arg8
8: 6⋅arg10 − 6⋅arg3
7_var_snapshot: 1 − 6⋅arg4 + 6⋅arg8
7*: 2 − 6⋅arg4 + 6⋅arg8
8_var_snapshot: 6⋅arg10 − 6⋅arg3
8*: 6⋅arg10 − 6⋅arg3

12.1.2 Transition Removal

We remove transitions 38, 43, 45, 17, 19 using the following ranking functions, which are bounded by −3.

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

12.1.3 Transition Removal

We remove transition 36 using the following ranking functions, which are bounded by 0.

7: arg3
8: 0
7_var_snapshot: 0
7*: 0
8_var_snapshot: 0
8*: 0

12.1.4 Splitting Cut-Point Transitions

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

12.1.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 35.

12.1.4.1.1 Splitting Cut-Point Transitions

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

12.1.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 42.

12.1.4.2.1 Splitting Cut-Point Transitions

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

12.2 SCC Subproblem 2/3

Here we consider the SCC { 5, 6, 5_var_snapshot, 5* }.

12.2.1 Transition Removal

We remove transitions 29, 31, 7, 8, 9, 10, 11, 12, 13 using the following ranking functions, which are bounded by −3.

5: −1 + 3⋅arg4
6: −3 + 3⋅arg3
5_var_snapshot: −2 + 3⋅arg4
5*: 3⋅arg4

12.2.2 Splitting Cut-Point Transitions

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

12.2.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 28.

12.2.2.1.1 Splitting Cut-Point Transitions

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

12.3 SCC Subproblem 3/3

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

12.3.1 Transition Removal

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

3: 2 + 6⋅arg2
3_var_snapshot: 6⋅arg2
3*: 4 + 6⋅arg2

12.3.2 Transition Removal

We remove transitions 22, 24 using the following ranking functions, which are bounded by −2.

3: −1
3_var_snapshot: −2⋅arg1
3*: 0

12.3.3 Splitting Cut-Point Transitions

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

12.3.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 21.

12.3.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

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