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 ≤ 0arg3P ≤ 0arg4P ≤ 04 − arg1 ≤ 0arg3 ≤ 0arg4 ≤ 0x7 ≤ 0x32 ≤ 0x41 ≤ 0
5: 1 − arg2P ≤ 01 − arg2 ≤ 0
6: 4 − arg1P ≤ 03 − arg2P ≤ 0arg3P ≤ 0arg4P ≤ 0arg10P ≤ 04 − arg1 ≤ 03 − arg2 ≤ 0arg3 ≤ 0arg4 ≤ 0arg10 ≤ 0x7 ≤ 0x32 ≤ 0x41 ≤ 0
7: 4 − arg1P ≤ 0arg4P ≤ 04 − arg1 ≤ 0arg4 ≤ 0x145 ≤ 0x146 ≤ 0
8: 4 − arg1P ≤ 03 − arg3P ≤ 0arg4P ≤ 0arg8P ≤ 04 − arg1 ≤ 03 − arg3 ≤ 0arg4 ≤ 0arg8 ≤ 0x145 ≤ 0x146 ≤ 0
9: 4 − arg1P ≤ 01 − arg2P ≤ 01 − arg3P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 01 − arg3 ≤ 0x145 ≤ 0x146 ≤ 0
10: 4 − arg1P ≤ 01 − arg2P ≤ 0arg4P ≤ 01 − arg5P ≤ 01 − arg6P ≤ 04 − arg1 ≤ 01 − arg2 ≤ 0arg4 ≤ 01 − arg5 ≤ 01 − arg6 ≤ 0x145 ≤ 0x146 ≤ 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 29 3: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 36 4: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 43 7: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 50 9: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 57 10: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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, 7, 13, 14, 22, 23, 28 using the following ranking functions, which are bounded by −29.

11: 0
0: 0
1: 0
4: 0
6: 0
3: 0
7: 0
8: 0
5: 0
9: 0
10: 0
11: −9
0: −10
1: −11
4: −12
6: −12
4_var_snapshot: −12
4*: −12
3: −15
3_var_snapshot: −15
3*: −15
7: −18
8: −18
7_var_snapshot: −18
7*: −18
5: −21
9: −22
10: −22
9_var_snapshot: −22
9*: −22
10_var_snapshot: −22
10*: −22

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 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 30 3_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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* 39 4: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 37 4_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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* 46 7: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 44 7_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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.

9* 53 9: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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.

9 51 9_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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.

10* 60 10: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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.

10 58 10_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x42 + x42 ≤ 0x42x42 ≤ 0x41 + x41 ≤ 0x41x41 ≤ 0x338 + x338 ≤ 0x338x338 ≤ 0x326 + x326 ≤ 0x326x326 ≤ 0x32 + x32 ≤ 0x32x32 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0x29 + x29 ≤ 0x29x29 ≤ 0x196 + x196 ≤ 0x196x196 ≤ 0x146 + x146 ≤ 0x146x146 ≤ 0x145 + x145 ≤ 0x145x145 ≤ 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 { 4, 6, 4_var_snapshot, 4* }.

14.1.1 Transition Removal

We remove transitions 37, 39, 5, 6, 8, 9, 10, 11, 12 using the following ranking functions, which are bounded by −3.

4: −1 + 3⋅arg4
6: −3 + 3⋅arg2
4_var_snapshot: −2 + 3⋅arg4
4*: 3⋅arg4

14.1.2 Splitting Cut-Point Transitions

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

14.1.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 36.

14.1.2.1.1 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 { 9, 10, 9_var_snapshot, 9*, 10_var_snapshot, 10* }.

14.2.1 Transition Removal

We remove transition 24 using the following ranking functions, which are bounded by 8.

9: 2 − 8⋅arg4 + 8⋅arg8
10: 8⋅arg10 − 8⋅arg3
9_var_snapshot: 1 − 8⋅arg4 + 8⋅arg8
9*: 3 − 8⋅arg4 + 8⋅arg8
10_var_snapshot: 8⋅arg10 − 8⋅arg3
10*: 8⋅arg10 − 8⋅arg3

14.2.2 Transition Removal

We remove transitions 58, 60, 25, 27 using the following ranking functions, which are bounded by −1.

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

14.2.3 Transition Removal

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

9: −3⋅arg4 + 3⋅arg8
10: 0
9_var_snapshot: −1 − 3⋅arg4 + 3⋅arg8
9*: 1 − 3⋅arg4 + 3⋅arg8
10_var_snapshot: 0
10*: 0

14.2.4 Transition Removal

We remove transition 51 using the following ranking functions, which are bounded by −1.

9: 0
10: 0
9_var_snapshot: arg2P
9*: arg2
10_var_snapshot: 0
10*: 0

14.2.5 Transition Removal

We remove transition 53 using the following ranking functions, which are bounded by 0.

9: 0
10: 0
9_var_snapshot: 0
9*: arg3
10_var_snapshot: 0
10*: 0

14.2.6 Splitting Cut-Point Transitions

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

14.2.6.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 50.

14.2.6.1.1 Splitting Cut-Point Transitions

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

14.2.6.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 57.

14.2.6.2.1 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 { 7, 8, 7_var_snapshot, 7* }.

14.3.1 Transition Removal

We remove transitions 44, 46, 15, 16, 17, 18, 19, 20, 21 using the following ranking functions, which are bounded by −3.

7: −1 + 3⋅arg4
8: −3 + 3⋅arg3
7_var_snapshot: −2 + 3⋅arg4
7*: 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 43.

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 3 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 −1.

3: 0
3_var_snapshot: arg1
3*: arg1

14.4.3 Transition Removal

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

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 29.

14.4.4.1.1 Splitting Cut-Point Transitions

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

Tool configuration

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